This chapter has considered many aspects of regression analysis. Let’s consider several of them at once by using software with the House Selling Prices OR data file on the text CD to conduct a multiple regression analysis of y = selling price of home, x1 = size of home, x2 = number of bedrooms, x3 = number of bathrooms.
a. Construct a scatterplot matrix. Identify the plots that pertain to selling price as a response variable. Interpret, and explain how the highly discrete nature of x2 and x3 affects the plots.
b. Fit the model. Write down the prediction equation, and interpret the coefficient of size of home by its effect when x2 and x3 are fixed.
c. Show how to calculate R2 from SS values in the ANOVA table. Interpret its value in the context of these variables.
d. Find and interpret the multiple correlation.
e. Show all steps of the F test that selling price is independent of these predictors. Explain how to obtain the F statistic from the mean squares in the ANOVA table.
f. Report the t statistic for testing H0: β2 = 0. Report the P-value for Ha: β2 < 0, and interpret. Why do you think this effect is not significant? Does this imply that the number of bedrooms is not associated with selling price?
g. Construct and examine the histogram of the residuals for the multiple regression model. What does this describe, and what does it suggest?
h. Construct and examine the plot of the residuals plotted against size of home. What does this describe, and what does it suggest?