linear-regression.Rmd

# Linear Regression

## Learning Objectives {-#objectives-linear-regression}

1. Explain what is meant by response and explanatory variables.
2. State the simple regression model (with a single explanatory variable).
3. Derive the least squares estimates of the slope and intercept parameters in a simple linear regression model.
4. Use `R` to fit a simple linear regression model to a data set and interpret the output.
  - Perform statistical inference on the slope parameter.
  - Describe the use of measures of goodness of fit of a linear regression model.
  - Use a fitted linear relationship to predict a mean response or an individual response with confidence limits.
  - Use residuals to check the suitability and validity of a linear regression model.
5. State the multiple linear regression model (with several explanatory variables).
6. Use `R` to fit a multiple linear regression model to a data set and interpret the output.
7. Use measures of model fit to select an appropriate set of explanatory variables.

## Theory {-#theory-linear-regression}

## `R` Practice {-#practice-linear-regression}