Statistics 541: Residuals

Admistrivia

• Homework: Do Myers' problem: 3.20 (on page 160, data). Also give me a histogram of the residuals.
• Read all of chapter 5.

Residuals (chapter 5 of Myers)

• Which residuals?
  • Y - Y-hat: don't have the same variance under ideal circumstances. They aren't independent either!
  • (Y - Y-hat)/SD(Y - Y-hat) called studentized residuals: normalizes to common scale.
  • Leave one out statistics: remove the data point--run the regression and refit and standardize. Luckilly no need for doing all this work--its the same as the studentized residual! (related to PRESS = Prediction Sum of Squares)
  • Use variance with value or not? CAlled externally studentized or R-student. Has a known distribution: t_n-p-1.

• Using regression to test outliers
  • Did TMI affect the price of GPU? csv
  • Need a Bonferroni correction if you don't know the cause of the outlier.

• Using regression to test for curvature
  • Is there a non-linear effect caused by X?
  • Test it by putting in X².

• Histogramming the residuals
  • outliers
  • normality

• Plotting residuals vs Y-hat
  • Feel good plot
  • shows off R-sq
  • Might suggest need to transform Y

• Plotting residuals vs X's
  • curvature
  • hetroskadasticity

• Plotting residuals vs partial regression
  • X-axis is X regressed on all other variables
  • Shows leverage effects
  • slope is partial slope in regression