Question

For y = number of times used public transportation in previous week and x = number of cars in family (which takes value 0, 1, or 2 for the given sample), explain the difference between conducting a test of independence of the variables using the ANOVA F test for comparing three means and using a regression t test for the coefficient of the number of cars in an ordinary regression model with a linear effect for the number of cars (e.g. treating number of cars as a numeric variable). Give an example of three population means for which the regression test would be less appropriate than the ANOVA test. (Hint: What does the regression linear model with numeric number of cars assume that the ANOVA F test does not?). Need a detailed reasoning.

Answer 1