You want to analyze y = house selling price and x = number of bathrooms (1, 2, or 3) by testing whether x and y are independent.
a. You could conduct a test of independence using
(i) The ANOVA F test for a multiple regression model with two indicator variables or
(ii) A regression t test for the coefficient of the number of bathrooms when it is treated as a quantitative predictor in a straight-line regression model. Explain the difference between these two ways of treating the number of bathrooms in the analysis.
b. What do you think are the advantages and disadvantages of the straight-line regression approach to conducting the test?
c. Give an example of three population means for which the straight-line regression model would be less appropriate than the model with indicator variables.