A realtor used the regression model Y =β 0 + β 1X1 + β 2X2 + e to predict selling prices of homes (in the thousands of $). The variable X1 represents home size (square feet) and X2 represents number of bedrooms. The following information is available:
Predictor
Constant: coefficient 26.28 Standard Error 22.88
Size: coefficient 0.12352 Standard Error 0.02435
Bedrooms: coefficient 20.183 Standard Error 6.697
ANOVA
Source DF SS F
Regression: F 293.29
Residual: SS 219.6
Total: DF 10
a. Testing at the .01 level of significance if the size of the home is a useful predictor of the selling prices of homes (after accounting for the effect of bedrooms), what is the value of the test statistic?
b. Test to see if a house with more bedrooms sells for more.
(i) State Ho and Ha
(ii) Calculate the value of the test statistic
(iii) What is your conclusion? Use 5% level of significance.
c. Using the regression results from above what is the predicted selling price of a home with 6 bedrooms and 3200 feet?
d. Is the overall model significant?