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+
@@ -131,10 +131,10 @@

Lista prezentacija

- tinytable_u8ozg9qstljyujg4n9q9 + tinytable_i9539dfmhdsrv6qta809 @@ -152,7 +152,7 @@

Lista prezentacija

- +
@@ -188,19 +188,27 @@

Lista prezentacija

- + + + + + + + + +
7Korelacija i regresijaTestiranje hipoteza o učestalostima
8Korelacija
9Regresija
@@ -293,7 +305,18 @@

Lista prezentacija

} return false; } - const onCopySuccess = function(e) { + const clipboard = new window.ClipboardJS('.code-copy-button', { + text: function(trigger) { + const codeEl = trigger.previousElementSibling.cloneNode(true); + for (const childEl of codeEl.children) { + if (isCodeAnnotation(childEl)) { + childEl.remove(); + } + } + return codeEl.innerText; + } + }); + clipboard.on('success', function(e) { // button target const button = e.trigger; // don't keep focus @@ -325,29 +348,7 @@

Lista prezentacija

}, 1000); // clear code selection e.clearSelection(); - } - const getTextToCopy = function(trigger) { - const codeEl = trigger.previousElementSibling.cloneNode(true); - for (const childEl of codeEl.children) { - if (isCodeAnnotation(childEl)) { - childEl.remove(); - } - } - return codeEl.innerText; - } - const clipboard = new window.ClipboardJS('.code-copy-button:not([data-in-quarto-modal])', { - text: getTextToCopy }); - clipboard.on('success', onCopySuccess); - if (window.document.getElementById('quarto-embedded-source-code-modal')) { - // For code content inside modals, clipBoardJS needs to be initialized with a container option - // TODO: Check when it could be a function (https://github.com/zenorocha/clipboard.js/issues/860) - const clipboardModal = new window.ClipboardJS('.code-copy-button[data-in-quarto-modal]', { - text: getTextToCopy, - container: window.document.getElementById('quarto-embedded-source-code-modal') - }); - clipboardModal.on('success', onCopySuccess); - } var localhostRegex = new RegExp(/^(?:http|https):\/\/localhost\:?[0-9]*\//); var mailtoRegex = new RegExp(/^mailto:/); var filterRegex = new RegExp('/' + window.location.host + '/'); @@ -355,7 +356,7 @@

Lista prezentacija

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1rem;--bs-nav-link-padding-y: 0.5rem;--bs-nav-link-font-weight: ;--bs-nav-link-color: #0d6efd;--bs-nav-link-hover-color: #0a58ca;--bs-nav-link-disabled-color: rgba(33, 37, 41, 0.75);display:flex;display:-webkit-flex;flex-wrap:wrap;-webkit-flex-wrap:wrap;padding-left:0;margin-bottom:0;list-style:none}.nav-link{display:block;padding:var(--bs-nav-link-padding-y) var(--bs-nav-link-padding-x);font-size:var(--bs-nav-link-font-size);font-weight:var(--bs-nav-link-font-weight);color:var(--bs-nav-link-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background:none;border:0;transition:color .15s ease-in-out,background-color .15s ease-in-out,border-color .15s ease-in-out}@media(prefers-reduced-motion: reduce){.nav-link{transition:none}}.nav-link:hover,.nav-link:focus{color:var(--bs-nav-link-hover-color)}.nav-link:focus-visible{outline:0;box-shadow:0 0 0 .25rem 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var(--bs-accordion-border-color)}.accordion-item:first-of-type{border-top-left-radius:var(--bs-accordion-border-radius);border-top-right-radius:var(--bs-accordion-border-radius)}.accordion-item:first-of-type .accordion-button{border-top-left-radius:var(--bs-accordion-inner-border-radius);border-top-right-radius:var(--bs-accordion-inner-border-radius)}.accordion-item:not(:first-of-type){border-top:0}.accordion-item:last-of-type{border-bottom-right-radius:var(--bs-accordion-border-radius);border-bottom-left-radius:var(--bs-accordion-border-radius)}.accordion-item:last-of-type .accordion-button.collapsed{border-bottom-right-radius:var(--bs-accordion-inner-border-radius);border-bottom-left-radius:var(--bs-accordion-inner-border-radius)}.accordion-item:last-of-type .accordion-collapse{border-bottom-right-radius:var(--bs-accordion-border-radius);border-bottom-left-radius:var(--bs-accordion-border-radius)}.accordion-body{padding:var(--bs-accordion-body-padding-y) var(--bs-accordion-body-padding-x)}.accordion-flush .accordion-collapse{border-width:0}.accordion-flush .accordion-item{border-right:0;border-left:0;border-radius:0}.accordion-flush .accordion-item:first-child{border-top:0}.accordion-flush .accordion-item:last-child{border-bottom:0}.accordion-flush .accordion-item .accordion-button,.accordion-flush .accordion-item .accordion-button.collapsed{border-radius:0}[data-bs-theme=dark] .accordion-button::after{--bs-accordion-btn-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%236ea8fe'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e");--bs-accordion-btn-active-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%236ea8fe'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e")}.breadcrumb{--bs-breadcrumb-padding-x: 0;--bs-breadcrumb-padding-y: 0;--bs-breadcrumb-margin-bottom: 1rem;--bs-breadcrumb-bg: ;--bs-breadcrumb-border-radius: ;--bs-breadcrumb-divider-color: rgba(33, 37, 41, 0.75);--bs-breadcrumb-item-padding-x: 0.5rem;--bs-breadcrumb-item-active-color: rgba(33, 37, 41, 0.75);display:flex;display:-webkit-flex;flex-wrap:wrap;-webkit-flex-wrap:wrap;padding:var(--bs-breadcrumb-padding-y) var(--bs-breadcrumb-padding-x);margin-bottom:var(--bs-breadcrumb-margin-bottom);font-size:var(--bs-breadcrumb-font-size);list-style:none;background-color:var(--bs-breadcrumb-bg);border-radius:var(--bs-breadcrumb-border-radius)}.breadcrumb-item+.breadcrumb-item{padding-left:var(--bs-breadcrumb-item-padding-x)}.breadcrumb-item+.breadcrumb-item::before{float:left;padding-right:var(--bs-breadcrumb-item-padding-x);color:var(--bs-breadcrumb-divider-color);content:var(--bs-breadcrumb-divider, ">") /* rtl: var(--bs-breadcrumb-divider, ">") */}.breadcrumb-item.active{color:var(--bs-breadcrumb-item-active-color)}.pagination{--bs-pagination-padding-x: 0.75rem;--bs-pagination-padding-y: 0.375rem;--bs-pagination-font-size:1rem;--bs-pagination-color: #0d6efd;--bs-pagination-bg: #ffffff;--bs-pagination-border-width: 1px;--bs-pagination-border-color: #dee2e6;--bs-pagination-border-radius: 0.25rem;--bs-pagination-hover-color: #0a58ca;--bs-pagination-hover-bg: #f8f9fa;--bs-pagination-hover-border-color: #dee2e6;--bs-pagination-focus-color: #0a58ca;--bs-pagination-focus-bg: #e9ecef;--bs-pagination-focus-box-shadow: 0 0 0 0.25rem rgba(13, 110, 253, 0.25);--bs-pagination-active-color: #ffffff;--bs-pagination-active-bg: #0d6efd;--bs-pagination-active-border-color: #0d6efd;--bs-pagination-disabled-color: rgba(33, 37, 41, 0.75);--bs-pagination-disabled-bg: #e9ecef;--bs-pagination-disabled-border-color: #dee2e6;display:flex;display:-webkit-flex;padding-left:0;list-style:none}.page-link{position:relative;display:block;padding:var(--bs-pagination-padding-y) var(--bs-pagination-padding-x);font-size:var(--bs-pagination-font-size);color:var(--bs-pagination-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background-color:var(--bs-pagination-bg);border:var(--bs-pagination-border-width) solid var(--bs-pagination-border-color);transition:color .15s ease-in-out,background-color .15s ease-in-out,border-color .15s ease-in-out,box-shadow .15s ease-in-out}@media(prefers-reduced-motion: reduce){.page-link{transition:none}}.page-link:hover{z-index:2;color:var(--bs-pagination-hover-color);background-color:var(--bs-pagination-hover-bg);border-color:var(--bs-pagination-hover-border-color)}.page-link:focus{z-index:3;color:var(--bs-pagination-focus-color);background-color:var(--bs-pagination-focus-bg);outline:0;box-shadow:var(--bs-pagination-focus-box-shadow)}.page-link.active,.active>.page-link{z-index:3;color:var(--bs-pagination-active-color);background-color:var(--bs-pagination-active-bg);border-color:var(--bs-pagination-active-border-color)}.page-link.disabled,.disabled>.page-link{color:var(--bs-pagination-disabled-color);pointer-events:none;background-color:var(--bs-pagination-disabled-bg);border-color:var(--bs-pagination-disabled-border-color)}.page-item:not(:first-child) .page-link{margin-left:calc(1px*-1)}.page-item:first-child .page-link{border-top-left-radius:var(--bs-pagination-border-radius);border-bottom-left-radius:var(--bs-pagination-border-radius)}.page-item:last-child .page-link{border-top-right-radius:var(--bs-pagination-border-radius);border-bottom-right-radius:var(--bs-pagination-border-radius)}.pagination-lg{--bs-pagination-padding-x: 1.5rem;--bs-pagination-padding-y: 0.75rem;--bs-pagination-font-size:1.25rem;--bs-pagination-border-radius: 0.5rem}.pagination-sm{--bs-pagination-padding-x: 0.5rem;--bs-pagination-padding-y: 0.25rem;--bs-pagination-font-size:0.875rem;--bs-pagination-border-radius: 0.2em}.badge{--bs-badge-padding-x: 0.65em;--bs-badge-padding-y: 0.35em;--bs-badge-font-size:0.75em;--bs-badge-font-weight: 700;--bs-badge-color: #ffffff;--bs-badge-border-radius: 0.25rem;display:inline-block;padding:var(--bs-badge-padding-y) var(--bs-badge-padding-x);font-size:var(--bs-badge-font-size);font-weight:var(--bs-badge-font-weight);line-height:1;color:var(--bs-badge-color);text-align:center;white-space:nowrap;vertical-align:baseline;border-radius:var(--bs-badge-border-radius)}.badge:empty{display:none}.btn .badge{position:relative;top:-1px}.alert{--bs-alert-bg: transparent;--bs-alert-padding-x: 1rem;--bs-alert-padding-y: 1rem;--bs-alert-margin-bottom: 1rem;--bs-alert-color: inherit;--bs-alert-border-color: transparent;--bs-alert-border: 1px solid var(--bs-alert-border-color);--bs-alert-border-radius: 0.25rem;--bs-alert-link-color: inherit;position:relative;padding:var(--bs-alert-padding-y) var(--bs-alert-padding-x);margin-bottom:var(--bs-alert-margin-bottom);color:var(--bs-alert-color);background-color:var(--bs-alert-bg);border:var(--bs-alert-border);border-radius:var(--bs-alert-border-radius)}.alert-heading{color:inherit}.alert-link{font-weight:700;color:var(--bs-alert-link-color)}.alert-dismissible{padding-right:3rem}.alert-dismissible .btn-close{position:absolute;top:0;right:0;z-index:2;padding:1.25rem 1rem}.alert-default{--bs-alert-color: var(--bs-default-text-emphasis);--bs-alert-bg: var(--bs-default-bg-subtle);--bs-alert-border-color: var(--bs-default-border-subtle);--bs-alert-link-color: var(--bs-default-text-emphasis)}.alert-primary{--bs-alert-color: var(--bs-primary-text-emphasis);--bs-alert-bg: var(--bs-primary-bg-subtle);--bs-alert-border-color: var(--bs-primary-border-subtle);--bs-alert-link-color: var(--bs-primary-text-emphasis)}.alert-secondary{--bs-alert-color: var(--bs-secondary-text-emphasis);--bs-alert-bg: var(--bs-secondary-bg-subtle);--bs-alert-border-color: var(--bs-secondary-border-subtle);--bs-alert-link-color: var(--bs-secondary-text-emphasis)}.alert-success{--bs-alert-color: var(--bs-success-text-emphasis);--bs-alert-bg: var(--bs-success-bg-subtle);--bs-alert-border-color: var(--bs-success-border-subtle);--bs-alert-link-color: var(--bs-success-text-emphasis)}.alert-info{--bs-alert-color: var(--bs-info-text-emphasis);--bs-alert-bg: var(--bs-info-bg-subtle);--bs-alert-border-color: var(--bs-info-border-subtle);--bs-alert-link-color: var(--bs-info-text-emphasis)}.alert-warning{--bs-alert-color: var(--bs-warning-text-emphasis);--bs-alert-bg: var(--bs-warning-bg-subtle);--bs-alert-border-color: var(--bs-warning-border-subtle);--bs-alert-link-color: var(--bs-warning-text-emphasis)}.alert-danger{--bs-alert-color: var(--bs-danger-text-emphasis);--bs-alert-bg: var(--bs-danger-bg-subtle);--bs-alert-border-color: var(--bs-danger-border-subtle);--bs-alert-link-color: var(--bs-danger-text-emphasis)}.alert-light{--bs-alert-color: var(--bs-light-text-emphasis);--bs-alert-bg: var(--bs-light-bg-subtle);--bs-alert-border-color: var(--bs-light-border-subtle);--bs-alert-link-color: var(--bs-light-text-emphasis)}.alert-dark{--bs-alert-color: var(--bs-dark-text-emphasis);--bs-alert-bg: var(--bs-dark-bg-subtle);--bs-alert-border-color: var(--bs-dark-border-subtle);--bs-alert-link-color: var(--bs-dark-text-emphasis)}@keyframes progress-bar-stripes{0%{background-position-x:1rem}}.progress,.progress-stacked{--bs-progress-height: 1rem;--bs-progress-font-size:0.75rem;--bs-progress-bg: #e9ecef;--bs-progress-border-radius: 0.25rem;--bs-progress-box-shadow: inset 0 1px 2px rgba(0, 0, 0, 0.075);--bs-progress-bar-color: #ffffff;--bs-progress-bar-bg: #0d6efd;--bs-progress-bar-transition: width 0.6s ease;display:flex;display:-webkit-flex;height:var(--bs-progress-height);overflow:hidden;font-size:var(--bs-progress-font-size);background-color:var(--bs-progress-bg);border-radius:var(--bs-progress-border-radius)}.progress-bar{display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;justify-content:center;-webkit-justify-content:center;overflow:hidden;color:var(--bs-progress-bar-color);text-align:center;white-space:nowrap;background-color:var(--bs-progress-bar-bg);transition:var(--bs-progress-bar-transition)}@media(prefers-reduced-motion: reduce){.progress-bar{transition:none}}.progress-bar-striped{background-image:linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);background-size:var(--bs-progress-height) var(--bs-progress-height)}.progress-stacked>.progress{overflow:visible}.progress-stacked>.progress>.progress-bar{width:100%}.progress-bar-animated{animation:1s linear infinite progress-bar-stripes}@media(prefers-reduced-motion: reduce){.progress-bar-animated{animation:none}}.list-group{--bs-list-group-color: #212529;--bs-list-group-bg: #ffffff;--bs-list-group-border-color: #dee2e6;--bs-list-group-border-width: 1px;--bs-list-group-border-radius: 0.25rem;--bs-list-group-item-padding-x: 1rem;--bs-list-group-item-padding-y: 0.5rem;--bs-list-group-action-color: rgba(33, 37, 41, 0.75);--bs-list-group-action-hover-color: #000;--bs-list-group-action-hover-bg: #f8f9fa;--bs-list-group-action-active-color: #212529;--bs-list-group-action-active-bg: #e9ecef;--bs-list-group-disabled-color: rgba(33, 37, 41, 0.75);--bs-list-group-disabled-bg: #ffffff;--bs-list-group-active-color: #ffffff;--bs-list-group-active-bg: #0d6efd;--bs-list-group-active-border-color: #0d6efd;display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;padding-left:0;margin-bottom:0;border-radius:var(--bs-list-group-border-radius)}.list-group-numbered{list-style-type:none;counter-reset:section}.list-group-numbered>.list-group-item::before{content:counters(section, ".") ". ";counter-increment:section}.list-group-item-action{width:100%;color:var(--bs-list-group-action-color);text-align:inherit}.list-group-item-action:hover,.list-group-item-action:focus{z-index:1;color:var(--bs-list-group-action-hover-color);text-decoration:none;background-color:var(--bs-list-group-action-hover-bg)}.list-group-item-action:active{color:var(--bs-list-group-action-active-color);background-color:var(--bs-list-group-action-active-bg)}.list-group-item{position:relative;display:block;padding:var(--bs-list-group-item-padding-y) var(--bs-list-group-item-padding-x);color:var(--bs-list-group-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background-color:var(--bs-list-group-bg);border:var(--bs-list-group-border-width) solid var(--bs-list-group-border-color)}.list-group-item:first-child{border-top-left-radius:inherit;border-top-right-radius:inherit}.list-group-item:last-child{border-bottom-right-radius:inherit;border-bottom-left-radius:inherit}.list-group-item.disabled,.list-group-item:disabled{color:var(--bs-list-group-disabled-color);pointer-events:none;background-color:var(--bs-list-group-disabled-bg)}.list-group-item.active{z-index:2;color:var(--bs-list-group-active-color);background-color:var(--bs-list-group-active-bg);border-color:var(--bs-list-group-active-border-color)}.list-group-item+.list-group-item{border-top-width:0}.list-group-item+.list-group-item.active{margin-top:calc(-1*var(--bs-list-group-border-width));border-top-width:var(--bs-list-group-border-width)}.list-group-horizontal{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal>.list-group-item.active{margin-top:0}.list-group-horizontal>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}@media(min-width: 576px){.list-group-horizontal-sm{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-sm>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-sm>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-sm>.list-group-item.active{margin-top:0}.list-group-horizontal-sm>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-sm>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 768px){.list-group-horizontal-md{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-md>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-md>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-md>.list-group-item.active{margin-top:0}.list-group-horizontal-md>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-md>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 992px){.list-group-horizontal-lg{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-lg>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-lg>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-lg>.list-group-item.active{margin-top:0}.list-group-horizontal-lg>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-lg>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 1200px){.list-group-horizontal-xl{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-xl>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-xl>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-xl>.list-group-item.active{margin-top:0}.list-group-horizontal-xl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xl>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 1400px){.list-group-horizontal-xxl{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-xxl>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-xxl>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-xxl>.list-group-item.active{margin-top:0}.list-group-horizontal-xxl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xxl>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}.list-group-flush{border-radius:0}.list-group-flush>.list-group-item{border-width:0 0 var(--bs-list-group-border-width)}.list-group-flush>.list-group-item:last-child{border-bottom-width:0}.list-group-item-default{--bs-list-group-color: var(--bs-default-text-emphasis);--bs-list-group-bg: var(--bs-default-bg-subtle);--bs-list-group-border-color: var(--bs-default-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-default-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-default-border-subtle);--bs-list-group-active-color: var(--bs-default-bg-subtle);--bs-list-group-active-bg: var(--bs-default-text-emphasis);--bs-list-group-active-border-color: var(--bs-default-text-emphasis)}.list-group-item-primary{--bs-list-group-color: var(--bs-primary-text-emphasis);--bs-list-group-bg: var(--bs-primary-bg-subtle);--bs-list-group-border-color: var(--bs-primary-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-primary-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-primary-border-subtle);--bs-list-group-active-color: var(--bs-primary-bg-subtle);--bs-list-group-active-bg: var(--bs-primary-text-emphasis);--bs-list-group-active-border-color: var(--bs-primary-text-emphasis)}.list-group-item-secondary{--bs-list-group-color: var(--bs-secondary-text-emphasis);--bs-list-group-bg: var(--bs-secondary-bg-subtle);--bs-list-group-border-color: var(--bs-secondary-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-secondary-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-secondary-border-subtle);--bs-list-group-active-color: var(--bs-secondary-bg-subtle);--bs-list-group-active-bg: var(--bs-secondary-text-emphasis);--bs-list-group-active-border-color: var(--bs-secondary-text-emphasis)}.list-group-item-success{--bs-list-group-color: var(--bs-success-text-emphasis);--bs-list-group-bg: var(--bs-success-bg-subtle);--bs-list-group-border-color: var(--bs-success-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-success-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-success-border-subtle);--bs-list-group-active-color: var(--bs-success-bg-subtle);--bs-list-group-active-bg: var(--bs-success-text-emphasis);--bs-list-group-active-border-color: var(--bs-success-text-emphasis)}.list-group-item-info{--bs-list-group-color: var(--bs-info-text-emphasis);--bs-list-group-bg: var(--bs-info-bg-subtle);--bs-list-group-border-color: var(--bs-info-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-info-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-info-border-subtle);--bs-list-group-active-color: var(--bs-info-bg-subtle);--bs-list-group-active-bg: var(--bs-info-text-emphasis);--bs-list-group-active-border-color: var(--bs-info-text-emphasis)}.list-group-item-warning{--bs-list-group-color: var(--bs-warning-text-emphasis);--bs-list-group-bg: var(--bs-warning-bg-subtle);--bs-list-group-border-color: var(--bs-warning-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-warning-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-warning-border-subtle);--bs-list-group-active-color: var(--bs-warning-bg-subtle);--bs-list-group-active-bg: var(--bs-warning-text-emphasis);--bs-list-group-active-border-color: var(--bs-warning-text-emphasis)}.list-group-item-danger{--bs-list-group-color: var(--bs-danger-text-emphasis);--bs-list-group-bg: var(--bs-danger-bg-subtle);--bs-list-group-border-color: var(--bs-danger-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-danger-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-danger-border-subtle);--bs-list-group-active-color: var(--bs-danger-bg-subtle);--bs-list-group-active-bg: var(--bs-danger-text-emphasis);--bs-list-group-active-border-color: var(--bs-danger-text-emphasis)}.list-group-item-light{--bs-list-group-color: var(--bs-light-text-emphasis);--bs-list-group-bg: var(--bs-light-bg-subtle);--bs-list-group-border-color: var(--bs-light-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-light-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-light-border-subtle);--bs-list-group-active-color: var(--bs-light-bg-subtle);--bs-list-group-active-bg: var(--bs-light-text-emphasis);--bs-list-group-active-border-color: var(--bs-light-text-emphasis)}.list-group-item-dark{--bs-list-group-color: var(--bs-dark-text-emphasis);--bs-list-group-bg: var(--bs-dark-bg-subtle);--bs-list-group-border-color: var(--bs-dark-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-dark-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-dark-border-subtle);--bs-list-group-active-color: var(--bs-dark-bg-subtle);--bs-list-group-active-bg: var(--bs-dark-text-emphasis);--bs-list-group-active-border-color: var(--bs-dark-text-emphasis)}.btn-close{--bs-btn-close-color: #000;--bs-btn-close-bg: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%23000'%3e%3cpath d='M.293.293a1 1 0 0 1 1.414 0L8 6.586 14.293.293a1 1 0 1 1 1.414 1.414L9.414 8l6.293 6.293a1 1 0 0 1-1.414 1.414L8 9.414l-6.293 6.293a1 1 0 0 1-1.414-1.414L6.586 8 .293 1.707a1 1 0 0 1 0-1.414z'/%3e%3c/svg%3e");--bs-btn-close-opacity: 0.5;--bs-btn-close-hover-opacity: 0.75;--bs-btn-close-focus-shadow: 0 0 0 0.25rem rgba(13, 110, 253, 0.25);--bs-btn-close-focus-opacity: 1;--bs-btn-close-disabled-opacity: 0.25;--bs-btn-close-white-filter: invert(1) grayscale(100%) brightness(200%);box-sizing:content-box;width:1em;height:1em;padding:.25em .25em;color:var(--bs-btn-close-color);background:rgba(0,0,0,0) var(--bs-btn-close-bg) center/1em auto no-repeat;border:0;border-radius:.25rem;opacity:var(--bs-btn-close-opacity)}.btn-close:hover{color:var(--bs-btn-close-color);text-decoration:none;opacity:var(--bs-btn-close-hover-opacity)}.btn-close:focus{outline:0;box-shadow:var(--bs-btn-close-focus-shadow);opacity:var(--bs-btn-close-focus-opacity)}.btn-close:disabled,.btn-close.disabled{pointer-events:none;user-select:none;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;-o-user-select:none;opacity:var(--bs-btn-close-disabled-opacity)}.btn-close-white{filter:var(--bs-btn-close-white-filter)}[data-bs-theme=dark] .btn-close{filter:var(--bs-btn-close-white-filter)}.toast{--bs-toast-zindex: 1090;--bs-toast-padding-x: 0.75rem;--bs-toast-padding-y: 0.5rem;--bs-toast-spacing: 1.5rem;--bs-toast-max-width: 350px;--bs-toast-font-size:0.875rem;--bs-toast-color: ;--bs-toast-bg: rgba(255, 255, 255, 0.85);--bs-toast-border-width: 1px;--bs-toast-border-color: rgba(0, 0, 0, 0.175);--bs-toast-border-radius: 0.25rem;--bs-toast-box-shadow: 0 0.5rem 1rem rgba(0, 0, 0, 0.15);--bs-toast-header-color: rgba(33, 37, 41, 0.75);--bs-toast-header-bg: rgba(255, 255, 255, 0.85);--bs-toast-header-border-color: rgba(0, 0, 0, 0.175);width:var(--bs-toast-max-width);max-width:100%;font-size:var(--bs-toast-font-size);color:var(--bs-toast-color);pointer-events:auto;background-color:var(--bs-toast-bg);background-clip:padding-box;border:var(--bs-toast-border-width) solid var(--bs-toast-border-color);box-shadow:var(--bs-toast-box-shadow);border-radius:var(--bs-toast-border-radius)}.toast.showing{opacity:0}.toast:not(.show){display:none}.toast-container{--bs-toast-zindex: 1090;position:absolute;z-index:var(--bs-toast-zindex);width:max-content;width:-webkit-max-content;width:-moz-max-content;width:-ms-max-content;width:-o-max-content;max-width:100%;pointer-events:none}.toast-container>:not(:last-child){margin-bottom:var(--bs-toast-spacing)}.toast-header{display:flex;display:-webkit-flex;align-items:center;-webkit-align-items:center;padding:var(--bs-toast-padding-y) var(--bs-toast-padding-x);color:var(--bs-toast-header-color);background-color:var(--bs-toast-header-bg);background-clip:padding-box;border-bottom:var(--bs-toast-border-width) solid var(--bs-toast-header-border-color);border-top-left-radius:calc(var(--bs-toast-border-radius) - var(--bs-toast-border-width));border-top-right-radius:calc(var(--bs-toast-border-radius) - var(--bs-toast-border-width))}.toast-header .btn-close{margin-right:calc(-0.5*var(--bs-toast-padding-x));margin-left:var(--bs-toast-padding-x)}.toast-body{padding:var(--bs-toast-padding-x);word-wrap:break-word}.modal{--bs-modal-zindex: 1055;--bs-modal-width: 500px;--bs-modal-padding: 1rem;--bs-modal-margin: 0.5rem;--bs-modal-color: ;--bs-modal-bg: #ffffff;--bs-modal-border-color: rgba(0, 0, 0, 0.175);--bs-modal-border-width: 1px;--bs-modal-border-radius: 0.5rem;--bs-modal-box-shadow: 0 0.125rem 0.25rem rgba(0, 0, 0, 0.075);--bs-modal-inner-border-radius: calc(0.5rem - 1px);--bs-modal-header-padding-x: 1rem;--bs-modal-header-padding-y: 1rem;--bs-modal-header-padding: 1rem 1rem;--bs-modal-header-border-color: #dee2e6;--bs-modal-header-border-width: 1px;--bs-modal-title-line-height: 1.5;--bs-modal-footer-gap: 0.5rem;--bs-modal-footer-bg: ;--bs-modal-footer-border-color: #dee2e6;--bs-modal-footer-border-width: 1px;position:fixed;top:0;left:0;z-index:var(--bs-modal-zindex);display:none;width:100%;height:100%;overflow-x:hidden;overflow-y:auto;outline:0}.modal-dialog{position:relative;width:auto;margin:var(--bs-modal-margin);pointer-events:none}.modal.fade .modal-dialog{transition:transform .3s ease-out;transform:translate(0, -50px)}@media(prefers-reduced-motion: reduce){.modal.fade .modal-dialog{transition:none}}.modal.show .modal-dialog{transform:none}.modal.modal-static .modal-dialog{transform:scale(1.02)}.modal-dialog-scrollable{height:calc(100% - var(--bs-modal-margin)*2)}.modal-dialog-scrollable .modal-content{max-height:100%;overflow:hidden}.modal-dialog-scrollable .modal-body{overflow-y:auto}.modal-dialog-centered{display:flex;display:-webkit-flex;align-items:center;-webkit-align-items:center;min-height:calc(100% - var(--bs-modal-margin)*2)}.modal-content{position:relative;display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;width:100%;color:var(--bs-modal-color);pointer-events:auto;background-color:var(--bs-modal-bg);background-clip:padding-box;border:var(--bs-modal-border-width) solid var(--bs-modal-border-color);border-radius:var(--bs-modal-border-radius);outline:0}.modal-backdrop{--bs-backdrop-zindex: 1050;--bs-backdrop-bg: #000;--bs-backdrop-opacity: 0.5;position:fixed;top:0;left:0;z-index:var(--bs-backdrop-zindex);width:100vw;height:100vh;background-color:var(--bs-backdrop-bg)}.modal-backdrop.fade{opacity:0}.modal-backdrop.show{opacity:var(--bs-backdrop-opacity)}.modal-header{display:flex;display:-webkit-flex;flex-shrink:0;-webkit-flex-shrink:0;align-items:center;-webkit-align-items:center;justify-content:space-between;-webkit-justify-content:space-between;padding:var(--bs-modal-header-padding);border-bottom:var(--bs-modal-header-border-width) solid 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.modal-content{height:100%;border:0;border-radius:0}.modal-fullscreen-sm-down .modal-header,.modal-fullscreen-sm-down .modal-footer{border-radius:0}.modal-fullscreen-sm-down .modal-body{overflow-y:auto}}@media(max-width: 767.98px){.modal-fullscreen-md-down{width:100vw;max-width:none;height:100%;margin:0}.modal-fullscreen-md-down .modal-content{height:100%;border:0;border-radius:0}.modal-fullscreen-md-down .modal-header,.modal-fullscreen-md-down .modal-footer{border-radius:0}.modal-fullscreen-md-down .modal-body{overflow-y:auto}}@media(max-width: 991.98px){.modal-fullscreen-lg-down{width:100vw;max-width:none;height:100%;margin:0}.modal-fullscreen-lg-down .modal-content{height:100%;border:0;border-radius:0}.modal-fullscreen-lg-down .modal-header,.modal-fullscreen-lg-down .modal-footer{border-radius:0}.modal-fullscreen-lg-down .modal-body{overflow-y:auto}}@media(max-width: 1199.98px){.modal-fullscreen-xl-down{width:100vw;max-width:none;height:100%;margin:0}.modal-fullscreen-xl-down 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0.4rem;z-index:var(--bs-tooltip-zindex);display:block;margin:var(--bs-tooltip-margin);font-family:system-ui,-apple-system,"Segoe UI",Roboto,"Helvetica Neue","Noto Sans","Liberation Sans",Arial,sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol","Noto Color Emoji";font-style:normal;font-weight:400;line-height:1.5;text-align:left;text-align:start;text-decoration:none;text-shadow:none;text-transform:none;letter-spacing:normal;word-break:normal;white-space:normal;word-spacing:normal;line-break:auto;font-size:var(--bs-tooltip-font-size);word-wrap:break-word;opacity:0}.tooltip.show{opacity:var(--bs-tooltip-opacity)}.tooltip .tooltip-arrow{display:block;width:var(--bs-tooltip-arrow-width);height:var(--bs-tooltip-arrow-height)}.tooltip .tooltip-arrow::before{position:absolute;content:"";border-color:rgba(0,0,0,0);border-style:solid}.bs-tooltip-top .tooltip-arrow,.bs-tooltip-auto[data-popper-placement^=top] 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#094fb6;--bs-navbar-nav-link-padding-x: 0.5rem;--bs-navbar-toggler-padding-y: 0.25;--bs-navbar-toggler-padding-x: 0;--bs-navbar-toggler-font-size: 1.25rem;--bs-navbar-toggler-icon-bg: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 30 30'%3e%3cpath stroke='%23212529' stroke-linecap='round' stroke-miterlimit='10' stroke-width='2' d='M4 7h22M4 15h22M4 23h22'/%3e%3c/svg%3e");--bs-navbar-toggler-border-color: rgba(33, 37, 41, 0);--bs-navbar-toggler-border-radius: 0.25rem;--bs-navbar-toggler-focus-width: 0.25rem;--bs-navbar-toggler-transition: box-shadow 0.15s ease-in-out;position:relative;display:flex;display:-webkit-flex;flex-wrap:wrap;-webkit-flex-wrap:wrap;align-items:center;-webkit-align-items:center;justify-content:space-between;-webkit-justify-content:space-between;padding:var(--bs-navbar-padding-y) 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992px){.navbar-expand-lg{flex-wrap:nowrap;-webkit-flex-wrap:nowrap;justify-content:flex-start;-webkit-justify-content:flex-start}.navbar-expand-lg .navbar-nav{flex-direction:row;-webkit-flex-direction:row}.navbar-expand-lg .navbar-nav .dropdown-menu{position:absolute}.navbar-expand-lg .navbar-nav .nav-link{padding-right:var(--bs-navbar-nav-link-padding-x);padding-left:var(--bs-navbar-nav-link-padding-x)}.navbar-expand-lg .navbar-nav-scroll{overflow:visible}.navbar-expand-lg .navbar-collapse{display:flex !important;display:-webkit-flex !important;flex-basis:auto;-webkit-flex-basis:auto}.navbar-expand-lg .navbar-toggler{display:none}.navbar-expand-lg .offcanvas{position:static;z-index:auto;flex-grow:1;-webkit-flex-grow:1;width:auto !important;height:auto !important;visibility:visible !important;background-color:rgba(0,0,0,0) !important;border:0 !important;transform:none !important;transition:none}.navbar-expand-lg .offcanvas .offcanvas-header{display:none}.navbar-expand-lg .offcanvas 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var(--bs-accordion-border-color)}.accordion-button:not(.collapsed)::after{background-image:var(--bs-accordion-btn-active-icon);transform:var(--bs-accordion-btn-icon-transform)}.accordion-button::after{flex-shrink:0;-webkit-flex-shrink:0;width:var(--bs-accordion-btn-icon-width);height:var(--bs-accordion-btn-icon-width);margin-left:auto;content:"";background-image:var(--bs-accordion-btn-icon);background-repeat:no-repeat;background-size:var(--bs-accordion-btn-icon-width);transition:var(--bs-accordion-btn-icon-transition)}@media(prefers-reduced-motion: reduce){.accordion-button::after{transition:none}}.accordion-button:hover{z-index:2}.accordion-button:focus{z-index:3;border-color:var(--bs-accordion-btn-focus-border-color);outline:0;box-shadow:var(--bs-accordion-btn-focus-box-shadow)}.accordion-header{margin-bottom:0}.accordion-item{color:var(--bs-accordion-color);background-color:var(--bs-accordion-bg);border:var(--bs-accordion-border-width) solid var(--bs-accordion-border-color)}.accordion-item:first-of-type{border-top-left-radius:var(--bs-accordion-border-radius);border-top-right-radius:var(--bs-accordion-border-radius)}.accordion-item:first-of-type .accordion-button{border-top-left-radius:var(--bs-accordion-inner-border-radius);border-top-right-radius:var(--bs-accordion-inner-border-radius)}.accordion-item:not(:first-of-type){border-top:0}.accordion-item:last-of-type{border-bottom-right-radius:var(--bs-accordion-border-radius);border-bottom-left-radius:var(--bs-accordion-border-radius)}.accordion-item:last-of-type .accordion-button.collapsed{border-bottom-right-radius:var(--bs-accordion-inner-border-radius);border-bottom-left-radius:var(--bs-accordion-inner-border-radius)}.accordion-item:last-of-type .accordion-collapse{border-bottom-right-radius:var(--bs-accordion-border-radius);border-bottom-left-radius:var(--bs-accordion-border-radius)}.accordion-body{padding:var(--bs-accordion-body-padding-y) var(--bs-accordion-body-padding-x)}.accordion-flush .accordion-collapse{border-width:0}.accordion-flush .accordion-item{border-right:0;border-left:0;border-radius:0}.accordion-flush .accordion-item:first-child{border-top:0}.accordion-flush .accordion-item:last-child{border-bottom:0}.accordion-flush .accordion-item .accordion-button,.accordion-flush .accordion-item .accordion-button.collapsed{border-radius:0}[data-bs-theme=dark] .accordion-button::after{--bs-accordion-btn-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%236ea8fe'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e");--bs-accordion-btn-active-icon: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%236ea8fe'%3e%3cpath fill-rule='evenodd' d='M1.646 4.646a.5.5 0 0 1 .708 0L8 10.293l5.646-5.647a.5.5 0 0 1 .708.708l-6 6a.5.5 0 0 1-.708 0l-6-6a.5.5 0 0 1 0-.708z'/%3e%3c/svg%3e")}.breadcrumb{--bs-breadcrumb-padding-x: 0;--bs-breadcrumb-padding-y: 0;--bs-breadcrumb-margin-bottom: 1rem;--bs-breadcrumb-bg: ;--bs-breadcrumb-border-radius: ;--bs-breadcrumb-divider-color: rgba(33, 37, 41, 0.75);--bs-breadcrumb-item-padding-x: 0.5rem;--bs-breadcrumb-item-active-color: rgba(33, 37, 41, 0.75);display:flex;display:-webkit-flex;flex-wrap:wrap;-webkit-flex-wrap:wrap;padding:var(--bs-breadcrumb-padding-y) var(--bs-breadcrumb-padding-x);margin-bottom:var(--bs-breadcrumb-margin-bottom);font-size:var(--bs-breadcrumb-font-size);list-style:none;background-color:var(--bs-breadcrumb-bg);border-radius:var(--bs-breadcrumb-border-radius)}.breadcrumb-item+.breadcrumb-item{padding-left:var(--bs-breadcrumb-item-padding-x)}.breadcrumb-item+.breadcrumb-item::before{float:left;padding-right:var(--bs-breadcrumb-item-padding-x);color:var(--bs-breadcrumb-divider-color);content:var(--bs-breadcrumb-divider, ">") /* rtl: var(--bs-breadcrumb-divider, ">") */}.breadcrumb-item.active{color:var(--bs-breadcrumb-item-active-color)}.pagination{--bs-pagination-padding-x: 0.75rem;--bs-pagination-padding-y: 0.375rem;--bs-pagination-font-size:1rem;--bs-pagination-color: #0d6efd;--bs-pagination-bg: #ffffff;--bs-pagination-border-width: 1px;--bs-pagination-border-color: #dee2e6;--bs-pagination-border-radius: 0.25rem;--bs-pagination-hover-color: #0a58ca;--bs-pagination-hover-bg: #f8f9fa;--bs-pagination-hover-border-color: #dee2e6;--bs-pagination-focus-color: #0a58ca;--bs-pagination-focus-bg: #e9ecef;--bs-pagination-focus-box-shadow: 0 0 0 0.25rem rgba(13, 110, 253, 0.25);--bs-pagination-active-color: #ffffff;--bs-pagination-active-bg: #0d6efd;--bs-pagination-active-border-color: #0d6efd;--bs-pagination-disabled-color: rgba(33, 37, 41, 0.75);--bs-pagination-disabled-bg: #e9ecef;--bs-pagination-disabled-border-color: #dee2e6;display:flex;display:-webkit-flex;padding-left:0;list-style:none}.page-link{position:relative;display:block;padding:var(--bs-pagination-padding-y) var(--bs-pagination-padding-x);font-size:var(--bs-pagination-font-size);color:var(--bs-pagination-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background-color:var(--bs-pagination-bg);border:var(--bs-pagination-border-width) solid var(--bs-pagination-border-color);transition:color .15s ease-in-out,background-color .15s ease-in-out,border-color .15s ease-in-out,box-shadow .15s ease-in-out}@media(prefers-reduced-motion: reduce){.page-link{transition:none}}.page-link:hover{z-index:2;color:var(--bs-pagination-hover-color);background-color:var(--bs-pagination-hover-bg);border-color:var(--bs-pagination-hover-border-color)}.page-link:focus{z-index:3;color:var(--bs-pagination-focus-color);background-color:var(--bs-pagination-focus-bg);outline:0;box-shadow:var(--bs-pagination-focus-box-shadow)}.page-link.active,.active>.page-link{z-index:3;color:var(--bs-pagination-active-color);background-color:var(--bs-pagination-active-bg);border-color:var(--bs-pagination-active-border-color)}.page-link.disabled,.disabled>.page-link{color:var(--bs-pagination-disabled-color);pointer-events:none;background-color:var(--bs-pagination-disabled-bg);border-color:var(--bs-pagination-disabled-border-color)}.page-item:not(:first-child) .page-link{margin-left:calc(1px*-1)}.page-item:first-child .page-link{border-top-left-radius:var(--bs-pagination-border-radius);border-bottom-left-radius:var(--bs-pagination-border-radius)}.page-item:last-child .page-link{border-top-right-radius:var(--bs-pagination-border-radius);border-bottom-right-radius:var(--bs-pagination-border-radius)}.pagination-lg{--bs-pagination-padding-x: 1.5rem;--bs-pagination-padding-y: 0.75rem;--bs-pagination-font-size:1.25rem;--bs-pagination-border-radius: 0.5rem}.pagination-sm{--bs-pagination-padding-x: 0.5rem;--bs-pagination-padding-y: 0.25rem;--bs-pagination-font-size:0.875rem;--bs-pagination-border-radius: 0.2em}.badge{--bs-badge-padding-x: 0.65em;--bs-badge-padding-y: 0.35em;--bs-badge-font-size:0.75em;--bs-badge-font-weight: 700;--bs-badge-color: #ffffff;--bs-badge-border-radius: 0.25rem;display:inline-block;padding:var(--bs-badge-padding-y) var(--bs-badge-padding-x);font-size:var(--bs-badge-font-size);font-weight:var(--bs-badge-font-weight);line-height:1;color:var(--bs-badge-color);text-align:center;white-space:nowrap;vertical-align:baseline;border-radius:var(--bs-badge-border-radius)}.badge:empty{display:none}.btn .badge{position:relative;top:-1px}.alert{--bs-alert-bg: transparent;--bs-alert-padding-x: 1rem;--bs-alert-padding-y: 1rem;--bs-alert-margin-bottom: 1rem;--bs-alert-color: inherit;--bs-alert-border-color: transparent;--bs-alert-border: 1px solid var(--bs-alert-border-color);--bs-alert-border-radius: 0.25rem;--bs-alert-link-color: inherit;position:relative;padding:var(--bs-alert-padding-y) var(--bs-alert-padding-x);margin-bottom:var(--bs-alert-margin-bottom);color:var(--bs-alert-color);background-color:var(--bs-alert-bg);border:var(--bs-alert-border);border-radius:var(--bs-alert-border-radius)}.alert-heading{color:inherit}.alert-link{font-weight:700;color:var(--bs-alert-link-color)}.alert-dismissible{padding-right:3rem}.alert-dismissible .btn-close{position:absolute;top:0;right:0;z-index:2;padding:1.25rem 1rem}.alert-default{--bs-alert-color: var(--bs-default-text-emphasis);--bs-alert-bg: var(--bs-default-bg-subtle);--bs-alert-border-color: var(--bs-default-border-subtle);--bs-alert-link-color: var(--bs-default-text-emphasis)}.alert-primary{--bs-alert-color: var(--bs-primary-text-emphasis);--bs-alert-bg: var(--bs-primary-bg-subtle);--bs-alert-border-color: var(--bs-primary-border-subtle);--bs-alert-link-color: var(--bs-primary-text-emphasis)}.alert-secondary{--bs-alert-color: var(--bs-secondary-text-emphasis);--bs-alert-bg: var(--bs-secondary-bg-subtle);--bs-alert-border-color: var(--bs-secondary-border-subtle);--bs-alert-link-color: var(--bs-secondary-text-emphasis)}.alert-success{--bs-alert-color: var(--bs-success-text-emphasis);--bs-alert-bg: var(--bs-success-bg-subtle);--bs-alert-border-color: var(--bs-success-border-subtle);--bs-alert-link-color: var(--bs-success-text-emphasis)}.alert-info{--bs-alert-color: var(--bs-info-text-emphasis);--bs-alert-bg: var(--bs-info-bg-subtle);--bs-alert-border-color: var(--bs-info-border-subtle);--bs-alert-link-color: var(--bs-info-text-emphasis)}.alert-warning{--bs-alert-color: var(--bs-warning-text-emphasis);--bs-alert-bg: var(--bs-warning-bg-subtle);--bs-alert-border-color: var(--bs-warning-border-subtle);--bs-alert-link-color: var(--bs-warning-text-emphasis)}.alert-danger{--bs-alert-color: var(--bs-danger-text-emphasis);--bs-alert-bg: var(--bs-danger-bg-subtle);--bs-alert-border-color: var(--bs-danger-border-subtle);--bs-alert-link-color: var(--bs-danger-text-emphasis)}.alert-light{--bs-alert-color: var(--bs-light-text-emphasis);--bs-alert-bg: var(--bs-light-bg-subtle);--bs-alert-border-color: var(--bs-light-border-subtle);--bs-alert-link-color: var(--bs-light-text-emphasis)}.alert-dark{--bs-alert-color: var(--bs-dark-text-emphasis);--bs-alert-bg: var(--bs-dark-bg-subtle);--bs-alert-border-color: var(--bs-dark-border-subtle);--bs-alert-link-color: var(--bs-dark-text-emphasis)}@keyframes progress-bar-stripes{0%{background-position-x:1rem}}.progress,.progress-stacked{--bs-progress-height: 1rem;--bs-progress-font-size:0.75rem;--bs-progress-bg: #e9ecef;--bs-progress-border-radius: 0.25rem;--bs-progress-box-shadow: inset 0 1px 2px rgba(0, 0, 0, 0.075);--bs-progress-bar-color: #ffffff;--bs-progress-bar-bg: #0d6efd;--bs-progress-bar-transition: width 0.6s ease;display:flex;display:-webkit-flex;height:var(--bs-progress-height);overflow:hidden;font-size:var(--bs-progress-font-size);background-color:var(--bs-progress-bg);border-radius:var(--bs-progress-border-radius)}.progress-bar{display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;justify-content:center;-webkit-justify-content:center;overflow:hidden;color:var(--bs-progress-bar-color);text-align:center;white-space:nowrap;background-color:var(--bs-progress-bar-bg);transition:var(--bs-progress-bar-transition)}@media(prefers-reduced-motion: reduce){.progress-bar{transition:none}}.progress-bar-striped{background-image:linear-gradient(45deg, rgba(255, 255, 255, 0.15) 25%, transparent 25%, transparent 50%, rgba(255, 255, 255, 0.15) 50%, rgba(255, 255, 255, 0.15) 75%, transparent 75%, transparent);background-size:var(--bs-progress-height) var(--bs-progress-height)}.progress-stacked>.progress{overflow:visible}.progress-stacked>.progress>.progress-bar{width:100%}.progress-bar-animated{animation:1s linear infinite progress-bar-stripes}@media(prefers-reduced-motion: reduce){.progress-bar-animated{animation:none}}.list-group{--bs-list-group-color: #212529;--bs-list-group-bg: #ffffff;--bs-list-group-border-color: #dee2e6;--bs-list-group-border-width: 1px;--bs-list-group-border-radius: 0.25rem;--bs-list-group-item-padding-x: 1rem;--bs-list-group-item-padding-y: 0.5rem;--bs-list-group-action-color: rgba(33, 37, 41, 0.75);--bs-list-group-action-hover-color: #000;--bs-list-group-action-hover-bg: #f8f9fa;--bs-list-group-action-active-color: #212529;--bs-list-group-action-active-bg: #e9ecef;--bs-list-group-disabled-color: rgba(33, 37, 41, 0.75);--bs-list-group-disabled-bg: #ffffff;--bs-list-group-active-color: #ffffff;--bs-list-group-active-bg: #0d6efd;--bs-list-group-active-border-color: #0d6efd;display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;padding-left:0;margin-bottom:0;border-radius:var(--bs-list-group-border-radius)}.list-group-numbered{list-style-type:none;counter-reset:section}.list-group-numbered>.list-group-item::before{content:counters(section, ".") ". ";counter-increment:section}.list-group-item-action{width:100%;color:var(--bs-list-group-action-color);text-align:inherit}.list-group-item-action:hover,.list-group-item-action:focus{z-index:1;color:var(--bs-list-group-action-hover-color);text-decoration:none;background-color:var(--bs-list-group-action-hover-bg)}.list-group-item-action:active{color:var(--bs-list-group-action-active-color);background-color:var(--bs-list-group-action-active-bg)}.list-group-item{position:relative;display:block;padding:var(--bs-list-group-item-padding-y) var(--bs-list-group-item-padding-x);color:var(--bs-list-group-color);text-decoration:none;-webkit-text-decoration:none;-moz-text-decoration:none;-ms-text-decoration:none;-o-text-decoration:none;background-color:var(--bs-list-group-bg);border:var(--bs-list-group-border-width) solid var(--bs-list-group-border-color)}.list-group-item:first-child{border-top-left-radius:inherit;border-top-right-radius:inherit}.list-group-item:last-child{border-bottom-right-radius:inherit;border-bottom-left-radius:inherit}.list-group-item.disabled,.list-group-item:disabled{color:var(--bs-list-group-disabled-color);pointer-events:none;background-color:var(--bs-list-group-disabled-bg)}.list-group-item.active{z-index:2;color:var(--bs-list-group-active-color);background-color:var(--bs-list-group-active-bg);border-color:var(--bs-list-group-active-border-color)}.list-group-item+.list-group-item{border-top-width:0}.list-group-item+.list-group-item.active{margin-top:calc(-1*var(--bs-list-group-border-width));border-top-width:var(--bs-list-group-border-width)}.list-group-horizontal{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal>.list-group-item.active{margin-top:0}.list-group-horizontal>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}@media(min-width: 576px){.list-group-horizontal-sm{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-sm>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-sm>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-sm>.list-group-item.active{margin-top:0}.list-group-horizontal-sm>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-sm>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 768px){.list-group-horizontal-md{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-md>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-md>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-md>.list-group-item.active{margin-top:0}.list-group-horizontal-md>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-md>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 992px){.list-group-horizontal-lg{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-lg>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-lg>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-lg>.list-group-item.active{margin-top:0}.list-group-horizontal-lg>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-lg>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 1200px){.list-group-horizontal-xl{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-xl>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-xl>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-xl>.list-group-item.active{margin-top:0}.list-group-horizontal-xl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xl>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}@media(min-width: 1400px){.list-group-horizontal-xxl{flex-direction:row;-webkit-flex-direction:row}.list-group-horizontal-xxl>.list-group-item:first-child:not(:last-child){border-bottom-left-radius:var(--bs-list-group-border-radius);border-top-right-radius:0}.list-group-horizontal-xxl>.list-group-item:last-child:not(:first-child){border-top-right-radius:var(--bs-list-group-border-radius);border-bottom-left-radius:0}.list-group-horizontal-xxl>.list-group-item.active{margin-top:0}.list-group-horizontal-xxl>.list-group-item+.list-group-item{border-top-width:var(--bs-list-group-border-width);border-left-width:0}.list-group-horizontal-xxl>.list-group-item+.list-group-item.active{margin-left:calc(-1*var(--bs-list-group-border-width));border-left-width:var(--bs-list-group-border-width)}}.list-group-flush{border-radius:0}.list-group-flush>.list-group-item{border-width:0 0 var(--bs-list-group-border-width)}.list-group-flush>.list-group-item:last-child{border-bottom-width:0}.list-group-item-default{--bs-list-group-color: var(--bs-default-text-emphasis);--bs-list-group-bg: var(--bs-default-bg-subtle);--bs-list-group-border-color: var(--bs-default-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-default-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-default-border-subtle);--bs-list-group-active-color: var(--bs-default-bg-subtle);--bs-list-group-active-bg: var(--bs-default-text-emphasis);--bs-list-group-active-border-color: var(--bs-default-text-emphasis)}.list-group-item-primary{--bs-list-group-color: var(--bs-primary-text-emphasis);--bs-list-group-bg: var(--bs-primary-bg-subtle);--bs-list-group-border-color: var(--bs-primary-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-primary-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-primary-border-subtle);--bs-list-group-active-color: var(--bs-primary-bg-subtle);--bs-list-group-active-bg: var(--bs-primary-text-emphasis);--bs-list-group-active-border-color: var(--bs-primary-text-emphasis)}.list-group-item-secondary{--bs-list-group-color: var(--bs-secondary-text-emphasis);--bs-list-group-bg: var(--bs-secondary-bg-subtle);--bs-list-group-border-color: var(--bs-secondary-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-secondary-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-secondary-border-subtle);--bs-list-group-active-color: var(--bs-secondary-bg-subtle);--bs-list-group-active-bg: var(--bs-secondary-text-emphasis);--bs-list-group-active-border-color: var(--bs-secondary-text-emphasis)}.list-group-item-success{--bs-list-group-color: var(--bs-success-text-emphasis);--bs-list-group-bg: var(--bs-success-bg-subtle);--bs-list-group-border-color: var(--bs-success-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-success-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-success-border-subtle);--bs-list-group-active-color: var(--bs-success-bg-subtle);--bs-list-group-active-bg: var(--bs-success-text-emphasis);--bs-list-group-active-border-color: var(--bs-success-text-emphasis)}.list-group-item-info{--bs-list-group-color: var(--bs-info-text-emphasis);--bs-list-group-bg: var(--bs-info-bg-subtle);--bs-list-group-border-color: var(--bs-info-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-info-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-info-border-subtle);--bs-list-group-active-color: var(--bs-info-bg-subtle);--bs-list-group-active-bg: var(--bs-info-text-emphasis);--bs-list-group-active-border-color: var(--bs-info-text-emphasis)}.list-group-item-warning{--bs-list-group-color: var(--bs-warning-text-emphasis);--bs-list-group-bg: var(--bs-warning-bg-subtle);--bs-list-group-border-color: var(--bs-warning-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-warning-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-warning-border-subtle);--bs-list-group-active-color: var(--bs-warning-bg-subtle);--bs-list-group-active-bg: var(--bs-warning-text-emphasis);--bs-list-group-active-border-color: var(--bs-warning-text-emphasis)}.list-group-item-danger{--bs-list-group-color: var(--bs-danger-text-emphasis);--bs-list-group-bg: var(--bs-danger-bg-subtle);--bs-list-group-border-color: var(--bs-danger-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-danger-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-danger-border-subtle);--bs-list-group-active-color: var(--bs-danger-bg-subtle);--bs-list-group-active-bg: var(--bs-danger-text-emphasis);--bs-list-group-active-border-color: var(--bs-danger-text-emphasis)}.list-group-item-light{--bs-list-group-color: var(--bs-light-text-emphasis);--bs-list-group-bg: var(--bs-light-bg-subtle);--bs-list-group-border-color: var(--bs-light-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-light-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-light-border-subtle);--bs-list-group-active-color: var(--bs-light-bg-subtle);--bs-list-group-active-bg: var(--bs-light-text-emphasis);--bs-list-group-active-border-color: var(--bs-light-text-emphasis)}.list-group-item-dark{--bs-list-group-color: var(--bs-dark-text-emphasis);--bs-list-group-bg: var(--bs-dark-bg-subtle);--bs-list-group-border-color: var(--bs-dark-border-subtle);--bs-list-group-action-hover-color: var(--bs-emphasis-color);--bs-list-group-action-hover-bg: var(--bs-dark-border-subtle);--bs-list-group-action-active-color: var(--bs-emphasis-color);--bs-list-group-action-active-bg: var(--bs-dark-border-subtle);--bs-list-group-active-color: var(--bs-dark-bg-subtle);--bs-list-group-active-bg: var(--bs-dark-text-emphasis);--bs-list-group-active-border-color: var(--bs-dark-text-emphasis)}.btn-close{--bs-btn-close-color: #000;--bs-btn-close-bg: url("data:image/svg+xml,%3csvg xmlns='http://www.w3.org/2000/svg' viewBox='0 0 16 16' fill='%23000'%3e%3cpath d='M.293.293a1 1 0 0 1 1.414 0L8 6.586 14.293.293a1 1 0 1 1 1.414 1.414L9.414 8l6.293 6.293a1 1 0 0 1-1.414 1.414L8 9.414l-6.293 6.293a1 1 0 0 1-1.414-1.414L6.586 8 .293 1.707a1 1 0 0 1 0-1.414z'/%3e%3c/svg%3e");--bs-btn-close-opacity: 0.5;--bs-btn-close-hover-opacity: 0.75;--bs-btn-close-focus-shadow: 0 0 0 0.25rem rgba(13, 110, 253, 0.25);--bs-btn-close-focus-opacity: 1;--bs-btn-close-disabled-opacity: 0.25;--bs-btn-close-white-filter: invert(1) grayscale(100%) brightness(200%);box-sizing:content-box;width:1em;height:1em;padding:.25em .25em;color:var(--bs-btn-close-color);background:rgba(0,0,0,0) var(--bs-btn-close-bg) center/1em auto no-repeat;border:0;border-radius:.25rem;opacity:var(--bs-btn-close-opacity)}.btn-close:hover{color:var(--bs-btn-close-color);text-decoration:none;opacity:var(--bs-btn-close-hover-opacity)}.btn-close:focus{outline:0;box-shadow:var(--bs-btn-close-focus-shadow);opacity:var(--bs-btn-close-focus-opacity)}.btn-close:disabled,.btn-close.disabled{pointer-events:none;user-select:none;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;-o-user-select:none;opacity:var(--bs-btn-close-disabled-opacity)}.btn-close-white{filter:var(--bs-btn-close-white-filter)}[data-bs-theme=dark] .btn-close{filter:var(--bs-btn-close-white-filter)}.toast{--bs-toast-zindex: 1090;--bs-toast-padding-x: 0.75rem;--bs-toast-padding-y: 0.5rem;--bs-toast-spacing: 1.5rem;--bs-toast-max-width: 350px;--bs-toast-font-size:0.875rem;--bs-toast-color: ;--bs-toast-bg: rgba(255, 255, 255, 0.85);--bs-toast-border-width: 1px;--bs-toast-border-color: rgba(0, 0, 0, 0.175);--bs-toast-border-radius: 0.25rem;--bs-toast-box-shadow: 0 0.5rem 1rem rgba(0, 0, 0, 0.15);--bs-toast-header-color: rgba(33, 37, 41, 0.75);--bs-toast-header-bg: rgba(255, 255, 255, 0.85);--bs-toast-header-border-color: rgba(0, 0, 0, 0.175);width:var(--bs-toast-max-width);max-width:100%;font-size:var(--bs-toast-font-size);color:var(--bs-toast-color);pointer-events:auto;background-color:var(--bs-toast-bg);background-clip:padding-box;border:var(--bs-toast-border-width) solid var(--bs-toast-border-color);box-shadow:var(--bs-toast-box-shadow);border-radius:var(--bs-toast-border-radius)}.toast.showing{opacity:0}.toast:not(.show){display:none}.toast-container{--bs-toast-zindex: 1090;position:absolute;z-index:var(--bs-toast-zindex);width:max-content;width:-webkit-max-content;width:-moz-max-content;width:-ms-max-content;width:-o-max-content;max-width:100%;pointer-events:none}.toast-container>:not(:last-child){margin-bottom:var(--bs-toast-spacing)}.toast-header{display:flex;display:-webkit-flex;align-items:center;-webkit-align-items:center;padding:var(--bs-toast-padding-y) var(--bs-toast-padding-x);color:var(--bs-toast-header-color);background-color:var(--bs-toast-header-bg);background-clip:padding-box;border-bottom:var(--bs-toast-border-width) solid var(--bs-toast-header-border-color);border-top-left-radius:calc(var(--bs-toast-border-radius) - var(--bs-toast-border-width));border-top-right-radius:calc(var(--bs-toast-border-radius) - var(--bs-toast-border-width))}.toast-header .btn-close{margin-right:calc(-0.5*var(--bs-toast-padding-x));margin-left:var(--bs-toast-padding-x)}.toast-body{padding:var(--bs-toast-padding-x);word-wrap:break-word}.modal{--bs-modal-zindex: 1055;--bs-modal-width: 500px;--bs-modal-padding: 1rem;--bs-modal-margin: 0.5rem;--bs-modal-color: ;--bs-modal-bg: #ffffff;--bs-modal-border-color: rgba(0, 0, 0, 0.175);--bs-modal-border-width: 1px;--bs-modal-border-radius: 0.5rem;--bs-modal-box-shadow: 0 0.125rem 0.25rem rgba(0, 0, 0, 0.075);--bs-modal-inner-border-radius: calc(0.5rem - 1px);--bs-modal-header-padding-x: 1rem;--bs-modal-header-padding-y: 1rem;--bs-modal-header-padding: 1rem 1rem;--bs-modal-header-border-color: #dee2e6;--bs-modal-header-border-width: 1px;--bs-modal-title-line-height: 1.5;--bs-modal-footer-gap: 0.5rem;--bs-modal-footer-bg: ;--bs-modal-footer-border-color: #dee2e6;--bs-modal-footer-border-width: 1px;position:fixed;top:0;left:0;z-index:var(--bs-modal-zindex);display:none;width:100%;height:100%;overflow-x:hidden;overflow-y:auto;outline:0}.modal-dialog{position:relative;width:auto;margin:var(--bs-modal-margin);pointer-events:none}.modal.fade .modal-dialog{transition:transform .3s ease-out;transform:translate(0, -50px)}@media(prefers-reduced-motion: reduce){.modal.fade .modal-dialog{transition:none}}.modal.show .modal-dialog{transform:none}.modal.modal-static .modal-dialog{transform:scale(1.02)}.modal-dialog-scrollable{height:calc(100% - var(--bs-modal-margin)*2)}.modal-dialog-scrollable .modal-content{max-height:100%;overflow:hidden}.modal-dialog-scrollable .modal-body{overflow-y:auto}.modal-dialog-centered{display:flex;display:-webkit-flex;align-items:center;-webkit-align-items:center;min-height:calc(100% - var(--bs-modal-margin)*2)}.modal-content{position:relative;display:flex;display:-webkit-flex;flex-direction:column;-webkit-flex-direction:column;width:100%;color:var(--bs-modal-color);pointer-events:auto;background-color:var(--bs-modal-bg);background-clip:padding-box;border:var(--bs-modal-border-width) solid var(--bs-modal-border-color);border-radius:var(--bs-modal-border-radius);outline:0}.modal-backdrop{--bs-backdrop-zindex: 1050;--bs-backdrop-bg: #000;--bs-backdrop-opacity: 0.5;position:fixed;top:0;left:0;z-index:var(--bs-backdrop-zindex);width:100vw;height:100vh;background-color:var(--bs-backdrop-bg)}.modal-backdrop.fade{opacity:0}.modal-backdrop.show{opacity:var(--bs-backdrop-opacity)}.modal-header{display:flex;display:-webkit-flex;flex-shrink:0;-webkit-flex-shrink:0;align-items:center;-webkit-align-items:center;justify-content:space-between;-webkit-justify-content:space-between;padding:var(--bs-modal-header-padding);border-bottom:var(--bs-modal-header-border-width) solid var(--bs-modal-header-border-color);border-top-left-radius:var(--bs-modal-inner-border-radius);border-top-right-radius:var(--bs-modal-inner-border-radius)}.modal-header .btn-close{padding:calc(var(--bs-modal-header-padding-y)*.5) calc(var(--bs-modal-header-padding-x)*.5);margin:calc(-0.5*var(--bs-modal-header-padding-y)) calc(-0.5*var(--bs-modal-header-padding-x)) calc(-0.5*var(--bs-modal-header-padding-y)) auto}.modal-title{margin-bottom:0;line-height:var(--bs-modal-title-line-height)}.modal-body{position:relative;flex:1 1 auto;-webkit-flex:1 1 auto;padding:var(--bs-modal-padding)}.modal-footer{display:flex;display:-webkit-flex;flex-shrink:0;-webkit-flex-shrink:0;flex-wrap:wrap;-webkit-flex-wrap:wrap;align-items:center;-webkit-align-items:center;justify-content:flex-end;-webkit-justify-content:flex-end;padding:calc(var(--bs-modal-padding) - var(--bs-modal-footer-gap)*.5);background-color:var(--bs-modal-footer-bg);border-top:var(--bs-modal-footer-border-width) solid var(--bs-modal-footer-border-color);border-bottom-right-radius:var(--bs-modal-inner-border-radius);border-bottom-left-radius:var(--bs-modal-inner-border-radius)}.modal-footer>*{margin:calc(var(--bs-modal-footer-gap)*.5)}@media(min-width: 576px){.modal{--bs-modal-margin: 1.75rem;--bs-modal-box-shadow: 0 0.5rem 1rem rgba(0, 0, 0, 0.15)}.modal-dialog{max-width:var(--bs-modal-width);margin-right:auto;margin-left:auto}.modal-sm{--bs-modal-width: 300px}}@media(min-width: 992px){.modal-lg,.modal-xl{--bs-modal-width: 800px}}@media(min-width: 1200px){.modal-xl{--bs-modal-width: 1140px}}.modal-fullscreen{width:100vw;max-width:none;height:100%;margin:0}.modal-fullscreen .modal-content{height:100%;border:0;border-radius:0}.modal-fullscreen .modal-header,.modal-fullscreen .modal-footer{border-radius:0}.modal-fullscreen .modal-body{overflow-y:auto}@media(max-width: 575.98px){.modal-fullscreen-sm-down{width:100vw;max-width:none;height:100%;margin:0}.modal-fullscreen-sm-down .modal-content{height:100%;border:0;border-radius:0}.modal-fullscreen-sm-down .modal-header,.modal-fullscreen-sm-down .modal-footer{border-radius:0}.modal-fullscreen-sm-down .modal-body{overflow-y:auto}}@media(max-width: 767.98px){.modal-fullscreen-md-down{width:100vw;max-width:none;height:100%;margin:0}.modal-fullscreen-md-down .modal-content{height:100%;border:0;border-radius:0}.modal-fullscreen-md-down .modal-header,.modal-fullscreen-md-down .modal-footer{border-radius:0}.modal-fullscreen-md-down .modal-body{overflow-y:auto}}@media(max-width: 991.98px){.modal-fullscreen-lg-down{width:100vw;max-width:none;height:100%;margin:0}.modal-fullscreen-lg-down .modal-content{height:100%;border:0;border-radius:0}.modal-fullscreen-lg-down .modal-header,.modal-fullscreen-lg-down .modal-footer{border-radius:0}.modal-fullscreen-lg-down .modal-body{overflow-y:auto}}@media(max-width: 1199.98px){.modal-fullscreen-xl-down{width:100vw;max-width:none;height:100%;margin:0}.modal-fullscreen-xl-down .modal-content{height:100%;border:0;border-radius:0}.modal-fullscreen-xl-down .modal-header,.modal-fullscreen-xl-down .modal-footer{border-radius:0}.modal-fullscreen-xl-down .modal-body{overflow-y:auto}}@media(max-width: 1399.98px){.modal-fullscreen-xxl-down{width:100vw;max-width:none;height:100%;margin:0}.modal-fullscreen-xxl-down .modal-content{height:100%;border:0;border-radius:0}.modal-fullscreen-xxl-down .modal-header,.modal-fullscreen-xxl-down .modal-footer{border-radius:0}.modal-fullscreen-xxl-down .modal-body{overflow-y:auto}}.tooltip{--bs-tooltip-zindex: 1080;--bs-tooltip-max-width: 200px;--bs-tooltip-padding-x: 0.5rem;--bs-tooltip-padding-y: 0.25rem;--bs-tooltip-margin: ;--bs-tooltip-font-size:0.875rem;--bs-tooltip-color: #ffffff;--bs-tooltip-bg: #000;--bs-tooltip-border-radius: 0.25rem;--bs-tooltip-opacity: 0.9;--bs-tooltip-arrow-width: 0.8rem;--bs-tooltip-arrow-height: 0.4rem;z-index:var(--bs-tooltip-zindex);display:block;margin:var(--bs-tooltip-margin);font-family:system-ui,-apple-system,"Segoe UI",Roboto,"Helvetica Neue","Noto Sans","Liberation Sans",Arial,sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol","Noto Color Emoji";font-style:normal;font-weight:400;line-height:1.5;text-align:left;text-align:start;text-decoration:none;text-shadow:none;text-transform:none;letter-spacing:normal;word-break:normal;white-space:normal;word-spacing:normal;line-break:auto;font-size:var(--bs-tooltip-font-size);word-wrap:break-word;opacity:0}.tooltip.show{opacity:var(--bs-tooltip-opacity)}.tooltip .tooltip-arrow{display:block;width:var(--bs-tooltip-arrow-width);height:var(--bs-tooltip-arrow-height)}.tooltip .tooltip-arrow::before{position:absolute;content:"";border-color:rgba(0,0,0,0);border-style:solid}.bs-tooltip-top .tooltip-arrow,.bs-tooltip-auto[data-popper-placement^=top] .tooltip-arrow{bottom:calc(-1*var(--bs-tooltip-arrow-height))}.bs-tooltip-top .tooltip-arrow::before,.bs-tooltip-auto[data-popper-placement^=top] .tooltip-arrow::before{top:-1px;border-width:var(--bs-tooltip-arrow-height) calc(var(--bs-tooltip-arrow-width)*.5) 0;border-top-color:var(--bs-tooltip-bg)}.bs-tooltip-end .tooltip-arrow,.bs-tooltip-auto[data-popper-placement^=right] .tooltip-arrow{left:calc(-1*var(--bs-tooltip-arrow-height));width:var(--bs-tooltip-arrow-height);height:var(--bs-tooltip-arrow-width)}.bs-tooltip-end .tooltip-arrow::before,.bs-tooltip-auto[data-popper-placement^=right] .tooltip-arrow::before{right:-1px;border-width:calc(var(--bs-tooltip-arrow-width)*.5) var(--bs-tooltip-arrow-height) calc(var(--bs-tooltip-arrow-width)*.5) 0;border-right-color:var(--bs-tooltip-bg)}.bs-tooltip-bottom .tooltip-arrow,.bs-tooltip-auto[data-popper-placement^=bottom] .tooltip-arrow{top:calc(-1*var(--bs-tooltip-arrow-height))}.bs-tooltip-bottom 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.accordion-header{font-size:1.65rem}}.accordion .accordion-icon:not(:empty){margin-right:.75rem;display:flex}.accordion .accordion-button:not(.collapsed){box-shadow:none}.accordion .accordion-button:not(.collapsed):focus{box-shadow:var(--bs-accordion-btn-focus-box-shadow)}.bslib-card{overflow:auto}.bslib-card .card-body+.card-body{padding-top:0}.bslib-card .card-body{overflow:auto}.bslib-card .card-body p{margin-top:0}.bslib-card .card-body p:last-child{margin-bottom:0}.bslib-card .card-body{max-height:var(--bslib-card-body-max-height, none)}.bslib-card[data-full-screen=true]>.card-body{max-height:var(--bslib-card-body-max-height-full-screen, none)}.bslib-card .card-header .form-group{margin-bottom:0}.bslib-card .card-header .selectize-control{margin-bottom:0}.bslib-card .card-header .selectize-control .item{margin-right:1.15rem}.bslib-card .card-footer{margin-top:auto}.bslib-card 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color: #00e0e0; } /* Other */ + code span.pp { color: #dcc6e0; } /* Preprocessor */ + code span.re { color: #00e0e0; background-color: #f8f8f2; } /* RegionMarker */ + code span.sc { color: #abe338; } /* SpecialChar */ + code span.ss { color: #abe338; } /* SpecialString */ + code span.st { color: #abe338; } /* String */ + code span.va { color: #00e0e0; } /* Variable */ + code span.vs { color: #abe338; } /* VerbatimString */ + code span.wa { color: #dcc6e0; } /* Warning */ @@ -327,7 +392,7 @@
-

Testiranje hipoteza o proporcijama

+

Testiranje hipoteza o učestalostima

@@ -337,25 +402,1622 @@

Testiranje hipoteza o proporcijama

-

2024-09-24

+

2024-11-12

-
-

+
+

Problem očekivanih proporcija

+
+
+
+

Da li mogu da proverim da li su me prevarili za boju M&M bombona ako očekujem da ih u kesici ima međusobno jednak broj?

+
+
+
+ + + + + + tinytable_kzc6k0z0o1vd7uzjjjn8 + + + + + + + +
+ + + + + + + + + + + + + + + + + + + + + + + +
BojaBroj
Crvene30
Plave 33
Zelene37
+
+ + + + + + +
+
+
+

+
+
-
-

Hi-kvardrat simulacija

+
+

Pirsonov hi-kvardrat test slaganja

-
-
     [,1] [,2] [,3]
-[1,]   63   41   54
-[2,]  106  107  129
+
+ + + + + + tinytable_zdna6ctd5r45c5bc92tz + + + + + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
BojaBrojOčekivanjeKv. razlikaHi-kvadrat promenljiva
Crvene3033.33311.1090.333
Plave 3333.333 0.1110.003
Zelene3733.33313.4470.403
+
+ + + + + + +
+
+
+

\[ \chi^2 = \sum\frac{(O_i - E_i)^2}{E_i} = 0.333 + 0.003 + 0.403 = 0.739\]

+
+
+
+

Hi-kvadrat raspodela

+
+
+
+
+
+

+
+
+
+
+
+
+
+
+
+

+
+
+
+
+
+
+
+
+
+
+

+
+
+
+
+
+
+
+

Interpretacija hi-kvadratnog testa slaganja

+
+
chisq.test(x = c(30, 33, 37), p = c(33, 33, 33), rescale.p = TRUE)

-    Pearson's Chi-squared test
+    Chi-squared test for given probabilities
+
+data:  c(30, 33, 37)
+X-squared = 0.74, df = 2, p-value = 0.6907
+
+
+

\(H_0:\) Proporcije opserviranih kategorija se ne razlikuju od teoretskih proporcija.

+

\(H_1:\) Proporcije opserviranih kategorija se razlikuju od teoretskih proporcija.

+
+

“Proporcije testiranih kategorija se statistički značajno ne razlikuju od teoretskih proporcija.”

+
+
+
+

Vežba: očekivane vrednosti ABO krvne grupe

+
    +
  • Proveriti da li se opservirane učestalosti ABO krvnih grupa datih u tabeli razlikuju od očvekivanih
    • +
+
+
+ + + + + + tinytable_aj53uh4tqvrh16b6gtsj + + + + + + + +
+ + + + + + + + + + + + + + + + + + + + + +
ABABO
Učestalost5919755
+
+ + + + + + +
+
+

Očekivane učestalosti su:

+
+

O: 44.5%, A: 38.9%, B: 12.1%, AB: 4.5%

+
+
+
+

Asocijacija između dve kategorije?

+
+
+
+

Problem: Da li je nodularnost konture jetre povezana sa konzumiranjem alkohola?

+
+
+

+
+
+
+
+

Tabela kontigencije kao preduslov za test

+
    +

  • Standardan način prikazivanja kategorijalnih podataka je preko tabele kontigencije.

    • +

  • Predstavlja broj (ili proporciju) opservacija koje pripadaju svim mogućim kombinacijama kategorija.

    • +
+
+
+ + + + + + tinytable_sifw512kijvwxxatwezs + + + + + + + +
+ + + + + + + + + + + + + + + + + + + + + + +
Nodularne promeneAlkohol: DaAlkohol: Ne
Ne1679
Da1013
+
+ + + + + + +
+
+
+
+

Obično je lakše tumačiti proporcije

+
+
+ + + + + + tinytable_pwyjz5ufz0a8ir5mdc6s + + + + + + + +
+ + + + + + + + + + + + + + + + + + + + + + +
Nodularne promeneAlkohol: DaAlkohol: Ne
Ne1679
Da1013
+
+ + + + + + +
+
+ + + + + + tinytable_c007d7d7av5ja6i2lzl8 + + + + + + + +
+ + + + + + + + + + + + + + + + + + + + + + +
Nodularne promeneAlkohol: Da (proporcija)Alkohol: Ne (proporcija)
Ne0.170.83
Da0.430.57
+
+ + + + + + +
+
+
+
+

Kako da odredimo očekivane učestalosti

+
    +
  • Pirsonov hi-kvadrat test nam omogućava da testiramo da li se opservirane učestalosti razlikuju od očekivanih
    • +
  • Treba da odredimo koje učestalosti očekujemo ako kategorije nisu međusobno povezane (nezavisne su)
    • +
+

Možemo se poslužiti osobinom verovatnoće:

+

\[ P(X \cap Y) = P(X) \times P(Y) \]

+
+
+

Ručno računanje očekivanih učestalosti

+
+
+ + + + + + tinytable_vsjsa8apgl4aa5pxp9g0 + + + + + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Nodularne promeneAlkohol: DaAlkohol: NeMargina
Ne P(Bez nodularnih)*P(Alkohol)P(Bez nodularnih)*P(Bez Alkohola)P(Bez nodularnih)
Da P(Nodularne)*P(Alkohol) P(Nodularne)*P(Bez Alkohola) P(Nodularne)
MarginaP(Alkohol) P(Bez Alkohola) Ukupno
+
+ + + + + + +
+
+
+
+

Interpretacija Pirsonovog hi-kvadrat testa za r \(\times\) k tabele (1)

+
+
rezultati <- chisq.test(nodularnost_dat, correct = FALSE)
+rezultati
+
+

+    Pearson's Chi-squared test
+
+data:  nodularnost_dat
+X-squared = 7.6474, df = 1, p-value = 0.005685
+
+
+
+

“Postoji statistički značajna asocijacija između nodularne konture jetre i konzumiranja alkohola.”

+
+
+
+

Interpretacija Pirsonovog hi-kvadrat testa za r \(\times\) k tabele (2)

+

Opservacije (originalni podaci):

+
+
+
           Alkohol
+Nodularnost Da Ne
+         Ne 16 79
+         Da 10 13
+
+
+

Očekivani podaci (svi moraju biti \(>5\)):

+
+
+
           Alkohol
+Nodularnost        Da      Ne
+         Ne 20.932203 74.0678
+         Da  5.067797 17.9322
+
+
+ +
+
+

Vežba: Pirsonov hi-kvadrat test za r \(\times\) k tabele

+
    +
  • Uneti sledeće opservacije i interpretirati rezultat
    • +
+
+
+ + + + + + tinytable_0t07byi81rf5c723g9ae + + + + + + + +
+ + + + + + + + + + + + + + + + + + + + + + +
PacijentTonzilektomijaBez tonzilektomije
Hodžkinova bolest4144
Kontrola 3352
+
+ + + + + + +
+
+
+
+

McNemarov test

+
+
+
    +
  • McNemarov test je metod za testiranje dva vezana (zavisna) uzorka
    • +
  • Iste jedinice su opservirane više puta
    • +
  • Mečovane jedinice dva uzorka
    • +
+
+
+
+ + + + + + tinytable_dffd30624q5q5v45qkml + + + + + + + +
+ + + + + + + + + + + + + + + + + + + + + + +
Test 2 +Test 2 -
Test 1 +ab
Test 1 -cd
+
+ + + + + + +
+
+

\[ \chi^2 = \frac{(b - c)^2}{b + c} \]

+
+
+
+
+

Interpretacija McNemarovog testa

+

\(H_0:\) Tabela kontigencije je simetrična.

+

\(H_1:\) Tabela kontigencije nije simetrična.

+
+
+
+
+ + + + + + tinytable_7okhu56gr6jhsgw11cn2 + + + + + + + +
+ + + + + + + + + + + + + + + + + + + + + + + +
preposle
01
11
01
+
+ + + + + + +
+
+
+

Tabela kontigencije za parove:

+
+
+
   posle
+pre  0  1
+  0 18 35
+  1 13 34
+
+
+

Rezultat:

+
+
+

+    McNemar's Chi-squared test
+
+data:  .
+McNemar's chi-squared = 10.083, df = 1, p-value = 0.001496
+
+
+
+
+
+
+

Vežba: McNemarov test

+
    +
  • Preuzeti i analizirati bazu podataka Aritmije.xlsx
    • +
  • Interpretirati rezultat
    • +
+
+
+

Fisherov test tačne verovatnoće

+
+
+
    +
  • Može se koristiti uvek
    • +
  • Konzervativan je, te se koristi samo ako se ne može upotrebiti hi-kvadrat test
    • +
  • Uslovljen je marginama*
    • +
+

\[ p = \frac{(a+b)!\,(c+d)!\,(a+c)!\,(b+d)!}{n!\,a!\,b!\,c!\,d!} \]

+
+

+
+
+
+
+

Žena koja pije čaj

+
+
+
+
+ + + + + + tinytable_lflswu7ntmvgpmpz7ez2 + + + + + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Mleko prvoČaj prvoUkupno
Pogađala Mleko404
Pogađala Čaj 044
Ukupno 448
+
+ + + + + + +
+
+
+
+

+    Fisher's Exact Test for Count Data
+
+data:  tea_data
+p-value = 0.01429
+alternative hypothesis: true odds ratio is greater than 1
+95 percent confidence interval:
+ 2.003768      Inf
+sample estimates:
+odds ratio 
+       Inf
+
+
+
+

+
+
+
+
+

Vežba: Fisherov test tačne verovatnoće

+
    +
  1. Preuzeti i analizirati bazu podataka Alkohol i hipertenzija.xlsx
    2. +
  2. Interpretirati rezultat
    3. +
+
+
+

Biranje testa (do sad)

+
+
+ + + + + + tinytable_zqm2e6xuhhy8eg6t708y + + + + + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + +
Tip testaParametarskiNeparametarski
Jedan uzorak t-test za jedan uzorakhi-kvadrat test slaganja
Dva nezavisnat-test hi-kvadrat/Fisherov test
Dva zavisna t-test za zavisne McNemarov test
+
+ + + + + -data: simulated_data_matrix -X-squared = 3.9314, df = 2, p-value = 0.1401
@@ -368,10 +2030,10 @@

Struktura kursa

- tinytable_ziop86xci30ttofnaj2s + tinytable_cycd3osf8llndtu7d0mp @@ -389,7 +2051,7 @@

Struktura kursa

- +
@@ -464,12 +2126,12 @@

Struktura kursa

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zv`8oM|GwF*SQFYy_K5KR;|=0{|F@j~?au$0?f+}C^GKNQu%oo_I1>c?c`hOUv{+2v G|NjA>Jy%`; literal 0 HcmV?d00001 diff --git a/docs/slides/09_korelacija/prezentacija.html b/docs/slides/09_korelacija/prezentacija.html new file mode 100644 index 0000000..3c0d6ca --- /dev/null +++ b/docs/slides/09_korelacija/prezentacija.html @@ -0,0 +1,1701 @@ + + + + + + + + + + + + + + + Medicinska statistika i informatika - Korelacija i regresija + + + + + + + + + + + + + + + +

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      Korelacija i regresija

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      +Dr Nikola Grubor +
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      2024-11-11

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      Korelacija

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      Korelacija i kauzalnost

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      Netačna pretpostavka da korelacija podrazumeva uzročnu vezu je verovatno jedna od dve ili tri najveće greške u čovekovom zaključivanju.

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      — Stephen Jay Gould (1941 - 2002)

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      Ljudi su prirodno dobri

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      u kauzalnom zaključivaju.

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      Korelacija \(\not =\) Kauzalnost

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      Neverovatne povezanosti

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      Julski efekat

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      Vrste povezanosti

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      Varljivi podaci

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      Primer: lipidi i insulinska rezistencija (1)

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      \(H:\) Lipidni sastav membrane skeletnih mišićih ćelija utiče na insulinsku rezistenciju.

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      Borkman et al. (1993)

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      Primer: lipidi i insulinska rezistencija (2)

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      • Scatterplot (dijagram rasturanja)
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      • Kako da opišemo odnos ove dve varijable?
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      • Korelacija
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      Karakteristike linearne povezanosti

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      • Smer (pozitivan \(+\), negativan \(-\))
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      • Stepen (od \(-1\) do \(+1\), “jačina” povezanosti)
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      • Oblik (Linearan, nelinearan)
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      • Scatterplot (dijagram rasturanja)
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      Vežba: napraviti dijagram rasturanja

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      Učitati bazu DZ.

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      Prikazati grafički vezu između starosti i ukupnog holesterola?

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      Prikazati grafički vezu između triglicerida i stepena uhranjenosti?

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      Korelacioni koeficijent

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      Definicija
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      +Koeficijent korelacije je statistika koja kvantifikuje jačinu povezanosti varijabli. +
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      • Pearsonov koeficijent korelacije (r)
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      • Spearmanov koeficijent korelacije ranga (\(\rho\))
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      Simetričnost korelacija

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      Masne kiseline predviđaju insulinsku senzitivnost.
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      Insulinska senzitivnost predviđa masne kiseline.
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      Pearsonov koeficijent korelacije

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      \(H_0:\) Ispitivane varijable nisu linearno povezane.

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      Uslovi:

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      • Nezavisne opservacije
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      • Normalna raspodela u populaciji
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      • Svaka varijabla mora da ima svog para
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      • Pretpostavlja linearan odnos varijabli
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      Tumačenje rezultata Pearsonove korelacije

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      cor.test(~ insulin + c20, data = bork, method = "pearson")
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+    Pearson's product-moment correlation
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+data:  insulin and c20
+t = 4.9612, df = 18, p-value = 0.000101
+alternative hypothesis: true correlation is not equal to 0
+95 percent confidence interval:
+ 0.4783589 0.8998777
+sample estimates:
+ cor 
+0.76
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      Svi ovi podaci imaju iste numeričke osobine, ali…

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      + + + + + + tinytable_8md5q0pgspqk6pj5tusg + + + + + + + +
      +

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+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
datasetmean_xsd_xmean_ysd_ycor
away 54174827-0.06
bullseye 54174827-0.07
circle 54174827-0.07
dino 54174827-0.06
dots 54174827-0.06
h_lines 54174827-0.06
high_lines54174827-0.07
slant_down54174827-0.07
slant_up 54174827-0.07
star 54174827-0.06
v_lines 54174827-0.07
wide_lines54174827-0.07
x_shape 54174827-0.07
+
+ + + + + + +
+ + +
+

Uvek vizualizovati podatke!

+ +
+
+

Spearmanov koeficijent korelacije

+

\(H_0:\) Ispitivane varijable nisu monotono povezane.

+
+
+
+
+ +
+

Savet

+
+
+

Daje verodostojnije rezultate kada podaci neispunjavaju uslove linearnosti ili normalne raspodele.

+
+
+
+

Uslovi:

+
    +
  1. Varijabla nema normalnu raspodelu
    2. +
  2. Podaci su ordinalni ili rangovi
    3. +
  3. Svaka varijabla mora da ima svog para
    4. +
  4. Nelinearan odnos varijabli (scatterplot)
    5. +
  5. Monotoničnost*
    6. +
+
+
+

Tumačenje rezultata Spearmanove korelacije

+
+
cor.test(~ insulin + c20, data = bork, method = "spearman")
+
+

+    Spearman's rank correlation rho
+
+data:  insulin and c20
+S = 372, p-value = 0.0004998
+alternative hypothesis: true rho is not equal to 0
+sample estimates:
+      rho 
+0.7203008
+
+
+
+
+

Interpretacija koeficijenta korelacije

+ +
+
+

Šta ako se ne slažu korelacije?

+
+
+
+
x <- 0:20
+y <- exp(x)
+
+
+
+
+
+

+
+
+
+
+
+

Pearsonova korelacija:

+
+
+
     cor 
+0.527173
+
+
+

Spearmanova korelacija:

+
+
+
rho 
+  1
+
+
+

Ako je Spearman \(\gt\) Pearson, znači da imamo monotonu (uzlaznu ili silaznu) povezanost, a ne linearnu povezanost.

+
+
+
+
+

Vežba: izračunavanje korelacije

+
    +
  1. Proveriti normalnost (koeficijent varijacije)
    2. +
  2. Pearson ili Spearman
    3. +
+
+

Učitati bazu DZ.

+

Da li postoji povezanost između starosti i ukupnog holesterola?

+

Da li postoji povezanost između triglicerida i stepena uhranjenosti?

+
+
+
+

+
+
+

Struktura kursa

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+ + + + + + tinytable_wtx1jdo6yulflswu7ntm + + + + + + + +
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NedeljaTema
1Uvod u medicinsku statistiku
2Sređivanje podataka
3Statističko opisivanje podataka
4Verovatnoća i raspodele verovatnoća
5Populacija i uzorak
6Testiranje hipoteza o populacionim prosečnim vrednostima i proporcijama
7Testiranje hipoteza o učestalostima
8Testiranje hipoteza o rangovima
9Korelacija
10Regresija / Kolokvijum
11Podaci, informacije i znanje
12Zdravstveni informacioni sistem
13Mere dijagnostičke tačnosti
14Medicinsko odlučivanje
15Bioinformatika
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inline-block; text-indent: -5em; padding-left: 5em; } + pre > code.sourceCode > span { text-indent: -5em; padding-left: 5em; } } pre.numberSource code { counter-reset: source-line 0; } @@ -392,7 +392,7 @@
-

Korelacija i regresija

+

Regresija

@@ -402,57 +402,8 @@

Korelacija i regresija

-

2024-11-08

+

2024-11-11

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Korelacija

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Korelacija i kauzalnost

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Netačna pretpostavka da korelacija podrazumeva uzročnu vezu je verovatno jedna od dve ili tri najveće greške u čovekovom zaključivanju.

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— Stephen Jay Gould (1941 - 2002)

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Ljudi su prirodno dobri

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u kauzalnom zaključivaju.

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Korelacija \(\not =\) Kauzalnost

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Neverovatne povezanosti

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Julski efekat

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Vrste povezanosti

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Vrste povezanosti

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Varljivi podaci

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Primer: lipidi i insulinska rezistencija (1)

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\(H:\) Lipidni sastav membrane skeletnih mišićih ćelija utiče na insulinsku rezistenciju.

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Borkman et al. (1993)

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Primer: lipidi i insulinska rezistencija (2)

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  • Scatterplot (dijagram rasturanja)
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  • Kako da opišemo odnos ove dve varijable?
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  • Korelacija
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Karakteristike linearne povezanosti

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  • Smer (pozitivan \(+\), negativan \(-\))
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  • Stepen (od \(-1\) do \(+1\), “jačina” povezanosti)
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  • Oblik (Linearan, nelinearan)
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Vežba: napraviti dijagram rasturanja

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Učitati bazu DZ.

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Prikazati grafički vezu između starosti i ukupnog holesterola?

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Prikazati grafički vezu između triglicerida i stepena uhranjenosti?

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Korelacioni koeficijent

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Definicija
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-Koeficijent korelacije je statistika koja kvantifikuje jačinu povezanosti varijabli. -
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  • Pearsonov koeficijent korelacije (r)
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  • Spearmanov koeficijent korelacije ranga (\(\rho\))
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Simetričnost korelacija

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Masne kiseline predviđaju insulinsku senzitivnost.
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Insulinska senzitivnost predviđa masne kiseline.
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Pearsonov koeficijent korelacije

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\(H_0:\) Ispitivane varijable nisu linearno povezane.

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Uslovi:

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  • Nezavisne opservacije
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Tumačenje rezultata Pearsonove korelacije

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cor.test(~ insulin + c20, data = bork, method = "pearson")
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-    Pearson's product-moment correlation
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-data:  insulin and c20
-t = 4.9612, df = 18, p-value = 0.000101
-alternative hypothesis: true correlation is not equal to 0
-95 percent confidence interval:
- 0.4783589 0.8998777
-sample estimates:
- cor 
-0.76
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Svi ovi podaci imaju iste numeričke osobine, ali…

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- - - - - - tinytable_tenm6sempv6q45fnvkaz - - - - - - - -
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datasetmean_xsd_xmean_ysd_ycor
away 54174827-0.06
bullseye 54174827-0.07
circle 54174827-0.07
dino 54174827-0.06
dots 54174827-0.06
h_lines 54174827-0.06
high_lines54174827-0.07
slant_down54174827-0.07
slant_up 54174827-0.07
star 54174827-0.06
v_lines 54174827-0.07
wide_lines54174827-0.07
x_shape 54174827-0.07
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Uvek vizualizovati podatke!

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Spearmanov koeficijent korelacije

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\(H_0:\) Ispitivane varijable nisu monotono povezane.

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Savet

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Daje verodostojnije rezultate kada podaci neispunjavaju uslove linearnosti ili normalne raspodele.

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Uslovi:

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  1. Varijabla nema normalnu raspodelu
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  2. Podaci su ordinalni ili rangovi
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  3. Svaka varijabla mora da ima svog para
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  4. Nelinearan odnos varijabli (scatterplot)
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  5. Monotoničnost*
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Tumačenje rezultata Spearmanove korelacije

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cor.test(~ insulin + c20, data = bork, method = "spearman")
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-    Spearman's rank correlation rho
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-data:  insulin and c20
-S = 372, p-value = 0.0004998
-alternative hypothesis: true rho is not equal to 0
-sample estimates:
-      rho 
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Interpretacija koeficijenta korelacije

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Vežba: izračunavanje korelacije

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Učitati bazu DZ.

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Da li postoji povezanost između starosti i ukupnog holesterola?

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Da li postoji povezanost između triglicerida i stepena uhranjenosti?

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Šta ako se ne slažu korelacije?

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x <- 0:20
-y <- exp(x)
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Pearsonova korelacija:

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     cor 
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Spearmanova korelacija:

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rho 
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Ako je Spearman \(\gt\) Pearson, znači da imamo monotonu (uzlaznu ili silaznu) povezanost, a ne linearnu povezanost.

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Regresija

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Metematički model

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Metematički model

\(y = \text{komplikovano...}\)
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Anatomija regresione jednačine (1)

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Anatomija regresione jednačine (1)

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Anatomija regresione jednačine (1)

  • \(\beta\), regresioni koeficijent (promena \(y\) ako \(x+1\))
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    Anatomija regresione jednačine (2)

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    Anatomija regresione jednačine (2)

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    Anatomija regresione jednačine (2)

  • $ r^2 = 50 % $
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    Anatomija regresione jednačine (3)

    @@ -1118,11 +532,11 @@

    Anatomija regresione jednačine (3)

    - tinytable_xkgbtyto2hvgvpcjjsjt + tinytable_8md5q0pgspqk6pj5tusg @@ -1140,7 +554,7 @@

    Anatomija regresione jednačine (3)

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    @@ -1172,12 +586,12 @@

    Anatomija regresione jednačine (3)

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    Anatomija regresione jednačine (3)

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    Anatomija regresione jednačine (3)

    \[ y = \alpha + \beta x \]

    \[ \text{insulin} = -1220 + 76 \times \text{%C20-22} \]

    $ R^2 = $ 0.5776

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    Pretpostavke linearne regresije

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    Pretpostavke linearne regresije

    Gde su pretpostavke ispunjene?

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    Šta je statistička kontrola?

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    N <- 300
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-primer <- tibble(
-  pridruzena_varijabla = sample(0:1, N, replace = TRUE),
-  prediktor = runif(N, 0 , 1) + (0.3 * pridruzena_varijabla),
-  ishod = 2.0 + (0.5 * prediktor) + (0.25 * pridruzena_varijabla)
-)
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    N <- 300
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+primer <- tibble(
+  pridruzena_varijabla = sample(0:1, N, replace = TRUE),
+  prediktor = runif(N, 0 , 1) + (0.3 * pridruzena_varijabla),
+  ishod = 2.0 + (0.5 * prediktor) + (0.25 * pridruzena_varijabla)
+)
    @@ -1292,11 +707,11 @@

    Šta je statistička kontrola?

    - tinytable_zcecthpzz2oatfavu1lg + tinytable_f1xdtrkmto5329rb20wz @@ -1314,7 +729,7 @@

    Šta je statistička kontrola?

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    +
    @@ -1327,45 +742,45 @@

    Šta je statistička kontrola?

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    00.16180922.080905
    00.40541652.2027080.93369652.466848
    10.64181442.5709070.84253162.671266
    00.41525752.2076290.21942252.109711
    10.60405252.5520260.78942782.644714
    00.56028052.28014011.10114872.800574
    10.70763072.603815
    @@ -1436,7 +851,7 @@

    Šta je statistička kontrola?

    Kontrolisanje putem regresije

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    lm(ishod ~ prediktor, data = primer)
    
 Call:
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    Kontrolisanje putem regresije
    
 
 Coefficients:
 (Intercept)    prediktor  
-     2.0054       0.6846
    + 2.0076 0.6929
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    lm(ishod ~ prediktor + pridruzena_varijabla, data = primer)
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    lm(ishod ~ prediktor + pridruzena_varijabla, data = primer)
    
 Call:
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    Korelacija vs. regresija
    
 
  • Kod regresije \(Y\) \(\rightarrow\) \(X\) \(\not =\) \(Y\) \(\leftarrow\) \(X\)
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    -
    +

    @@ -1494,10 +909,10 @@

    Struktura kursa

    - tinytable_2h0e5w9xph4y5s8ljtds + tinytable_s34u8ireasgobi6ae8ni @@ -1515,7 +930,7 @@

    Struktura kursa

    - +
    @@ -1590,12 +1005,12 @@

    Struktura kursa

    @@ -1679,7 +1094,7 @@

    Struktura kursa

    - + @@ -1892,43 +1307,81 @@

    Struktura kursa

    }); + + +