The accompanying SAS computer output relates to the house price data of Problem 10 in Chapter 8. Use this output and, if necessary, the output associated with Problem 9 in Chapter 9 to answer the following questions.
a. Determine r2Y|X1,X2, the squared multiple correlation between house price (Y) and the independent variables house size (X1) and number of bedrooms (X2).
b. Determine rYX2|X1, the partial correlation of Y with X2 given that X1 is in the model.
c. Determine rYX1|X2, the partial correlation of Y with X1 given that X2 is in the model.
d. Using the t test technique of Problem 2, test H0: ρYX2|X1 = 0. Compare your test statistic value with the partial t test statistic for X2 shown on the SAS output here.
e. Using the t test technique of Problem 2, test H0: ρYX1|X2 = 0. Compare your test statistic value with the partial t test statistic for X1 shown on the SAS output here.
f. Based on your answers to parts (a) through (e), which variables (if any) should be included in the regression model, and what is their order of importance?