regression.md

Predicting with Regression

Setup

library(caret)

## Loading required package: lattice

## Loading required package: ggplot2

data("faithful")

Separate Train and Test sets

inTrain <- createDataPartition(y = faithful$waiting, p = 0.5, list = FALSE)
trainFaith <- faithful[inTrain,]
testFaith <- faithful[-inTrain,]
head(trainFaith)

##   eruptions waiting
## 2     1.800      54
## 4     2.283      62
## 5     4.533      85
## 6     2.883      55
## 7     4.700      88
## 8     3.600      85

EDA

plot(trainFaith$waiting, trainFaith$eruptions, pch = 19, col = "blue", xlab = "Waiting", ylab = "Duration")

Fit a Linear Model

lm1 <- lm(eruptions ~ waiting, data = trainFaith)
summary(lm1)$coef

##                Estimate  Std. Error   t value     Pr(>|t|)
## (Intercept) -1.81835963 0.225281595 -8.071497 3.384665e-13
## waiting      0.07521069 0.003119093 24.113000 8.986641e-51

with(trainFaith, plot(waiting, eruptions, pch = 19, col = "blue", xlab = "Waiting", ylab = "Duration"))
lines(trainFaith$waiting, lm1$fitted, lwd = 3)

Predict a New Value

Simulation of the prediction using lm coefficients

# Y = b0 + b1 * X
coef(lm1)[1] + coef(lm1)[2] * 80

## (Intercept) 
##    4.198496

Actual prediction value

newdata <- data.frame(waiting = 80)
predict(lm1, newdata)

##        1 
## 4.198496

Plotting the prediction of training and test sets

par(mfrow = c(1, 2))
plotVals <- function(df){with(df, plot(waiting, eruptions, pch = 19, col = "blue", xlab = "Waiting", ylab = "Duration"))}
plotVals(trainFaith)
lines(trainFaith$waiting, predict(lm1), lwd = 3)
plotVals(testFaith)
lines(testFaith$waiting, predict(lm1, newdata = testFaith), lwd = 3)

Get training and test set Errors

RMSE on Training

sqrt(sum((lm1$fitted - trainFaith$eruptions)^2))

## [1] 5.865756

RMSE on Testing

sqrt(sum((predict(lm1, newdata = testFaith) - testFaith$eruptions)^2))

## [1] 5.687559

Prediction Intervals

pred1 <- predict(lm1, newdata = testFaith, interval = "prediction")
ord <- order(testFaith$waiting)

plot(testFaith$waiting, testFaith$eruptions, pch = 19, col = "blue")
matlines(testFaith$waiting[ord], pred1[ord,], type = "l", col = c(1, 2, 2), lty = c(1, 1, 1), lwd = 3)

Fit model using CARET package

modFit <- train(eruptions ~ waiting, data = trainFaith, method = "lm")
summary(modFit$finalModel)$coef

##                Estimate  Std. Error   t value     Pr(>|t|)
## (Intercept) -1.81835963 0.225281595 -8.071497 3.384665e-13
## waiting      0.07521069 0.003119093 24.113000 8.986641e-51