Analysis of Covariance

1
Analysis of Covariance

• Dingcai Cao
• University of Chicago
• April 18, 2006

2
Linear Regression

• Statistical model Least squares Estimates
• Diagnosis
• Model selection
• Model comparison

3
Linear regression vs. ANOVA
4
Example Oyster growth data
5
Example ANOVA
6
ANCOVA
7
Example Test of homogeneity of slope
8
Homework

• Here is a simulated dataset with variables of X1,
  X2, X3, Y1 and Y2. For the homework, X1, X2 and
  X3 are explanatory variables, and Y1 and Y2 are
  the outcome variables.
• 1) Regress Y1 on X1X2, report the results.
  Are the fits good? Why or why not?
• Regress Y1 on X1X2X3X1X3, compare the results
  with those in 1). Any difference? Why?
• Regress Y2 on X1X3, report the results. Are the
  fits good? Why or why not? Consider a
  transformation, run the model again.

• Homework is due on April 27. The homework and
  the dataset (in SAS format or CSV format) can be
  downloaded at
• http//ccp.uchicago.edu/dcao/links.html