Question

A realtor is trying to predict the selling price of houses in Greenville (in thousands of dollars) as a function of Size (measured in thousands of square feet) and whether or not there is a fireplace (FP is 0 if there is no fireplace, 1 if there is a fireplace). The regression output is provided below. Some of the information has been omitted.
Source of variation SS df MS F
Regression 3177.17 2 1588.584
Residual 17 17.7 17 13
Total 3478.36 19
Which of the following conclusions can be made based on the F-test?
A) The estimates were based on a sample of 19 houses.
B) At least one of the predictors is useful in explaining Y.
C) The model is of no use in predicting selling prices of houses.
D) The p-value on the F-test will be very high.

Answer 1

Answer:

The correct option is B.

Step-by-step explanation:

The ANOVA table is as follows:

Source of variation          SS            df             MS                F

   Regression               3177.17         2         1588.584          ___

     Residual                    ___           17          17.71713

        Total                    3478.36       19

The complete table is as follows:

Source of variation          SS                  df             MS                  F

   Regression               3177.17               2         1588.584        89.663

     Residual                   301.1941           17          17.7173

        Total                    3478.36             19

The critical value of F is:

$F_{\alpha, (\eta_{1}, \eta_{2})}=F_{0.05, (2,17)}=3.5915$

Decision rule:

If the calculated value of the F test statistic is more than or equal to the critical value.

$F=89.663\geq F_{2,17}=3.5915$

The null hypothesis will be rejected.

Conclusion:

At least one of the predictors is useful in explaining Y.

Thus, the correct option is B.