STAT 541: Residuals

# Statistics 541: Residuals

• 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: tn-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