Residential real estate prices depend, in part, on property size and number of bedrooms. The house size X1 (in hundreds of square feet), number of bedrooms X2, and house price Y (in thousands of dollars) of a random sample of houses in a certain county were observed. The data are listed in the following table.

Use the accompanying output to answer the following questions.
a. Determine the least-squares estimates for the model in which house price is regressed on both house size and number of bedrooms. Find the predicted average price of a 2,500-square-foot home that has four bedrooms.
b. Compare the R2-value for the regression in part (a) with the r2 value for the data in Problem 16 of Chapter 5. Does adding X2 to a model that already contains X1 appear to be useful in predicting the house price?

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House 19 17 18 20 25 House size (Xi) Number of bedrooms (X) House price (X) 104 110 175 85 89 95 Regression of Y on X1 and X2 F ValuePr> F 2866.66064520.03 0.0082 DF Sum of Squares Mean Square Source Model Error Corrected Total 5733.321290 572.392996 6 6305.714286 143.098249 Parameter Intercept X1 X2 Estimate Standard Error t Value Pr>It 16.09338521 24.64693805 0.65 0.5494 5.72178988 1.82778969 3.13 0.0352 11731517 13.8993701 0.09 0.9344