2/1/2017

Diagnostics and remedial measures

• Residuals
• Standardized residuals
• Checking model assumptions with residual plots
  • Nonconstant variance
  • Nonlinear relationship
  • Dependence
  • Outliers
  • Normality (normal quantile plot) - use qqplot and qqline in R
• Tests for normality
  1. Correlation test for normality - based on expected value of ordered residuals
     • Compute the expected value of the ordered residual (see p. 111)
     • Find correlation coefficient between ordered residuals and their expected values.
  2. Use Shapiro-Wilk test, Kolmogorov test, or one of the other tests from norm.test
• Return to model for Toluca Company - toluca-Ch3.R
• Tests for constant variance
  1. Modified Levene Test (Brown-Forythe Test)
     • Form 2 or more groups, based on the value of x
     • Find the medians of the residuals for both groups
     • Form the absolute deviations (from their respective median) of the residuals
     • Use the pooled t-test to see if the absolute deviations differ, on average, for the two groups.
  2. Breusch-Pagan Test
     • Assume that the natural log of the variance has a linear relationship with x (i.e., the variance increases or decreases with x)
     • Regress the squared residuals against x
     • Form the test statistic on p. 119

In Class Exercise

• Exercise 3.4 on p. 147

Please read Sections 3.7 - 3.11 for class on Wednesday.