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. $$\begin{array} { l c r c c }
\hline \text { Source of variation } & \text { SS } & d f & \text { MS } & F \
\hline \text { Regression } & 3177.17 & 2 & 1588.584 & \
\text { Residual } & & 17 & 17.71713 & \
\text { Total } & 3478.36 & 19 & & \
\hline
\end{array}$$ Which of the following conclusions can be made based on the F-test?
A)The p-value on the F-test will be very high.
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 estimates were based on a sample of 19 houses.

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. $$\begin{array} { l c r c c } 
\hline \text { Source of variation } & \text { SS } & d f & \text { MS } & F \
\hline \text { Regression } & 3177.17 & 2 & 1588.584 & \
\text { Residual } & & 17 & 17.71713 & \
\text { Total } & 3478.36 & 19 & & \
\hline
\end{array}$$ Which of the following conclusions can be made based on the F-test?
A)The p-value on the F-test will be very high.
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 estimates were based on a sample of 19 houses.

Quizplus · Accepted Answer

The F-test tests the null hypothesis that all regression coefficients are equal to zero, versus the alternative that at least one of the coefficients is non-zero, in other words, at least one predictor is useful in explaining Y. Therefore, since the null hypothesis can be rejected (given that the MS for Regression is much larger than the MS for Residual), we can conclude that at least one of the predictors is useful in predicting the selling price of houses. We cannot make any conclusions about the p-value, the usefulness of the model, or the sample size based solely on the F-test.

A Realtor Is Trying to Predict the Selling Price of Houses