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). Part of the regression output is provided below, based on a sample of 20 homes. Some of the information has been omitted. $$\begin{array} { l r r r r }
\hline \text { Variable } & \text { Coefficients } & \text { Standard Error } & \text { t-Stat } & \text { P-value } \
\hline \text { Intercept } & 128.93746 & 2.6205302 & 49.203 & 8.93 \mathrm { E } - 20 \
\text { Size } & & 1.2072436 & 11.439 & 2.09 \mathrm { E } - 09 \
\text { FP } & 6.47601954 & 1.9803612 & 3.27 & 0.004512 \
\hline
\end{array}$$ Which statement is supported by the regression output?
A)At ? = .05, FP is not a significant predictor in a two-tailed test.
B)A fireplace adds around $6476 to the selling price of the average house.
C)A large house with no fireplace will sell for more than a small house with a fireplace.
D)FP is a more significant predictor than Size.

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). Part of the regression output is provided below, based on a sample of 20 homes. Some of the information has been omitted. $$\begin{array} { l r r r r } 
\hline \text { Variable } & \text { Coefficients } & \text { Standard Error } & \text { t-Stat } & \text { P-value } \
\hline \text { Intercept } & 128.93746 & 2.6205302 & 49.203 & 8.93 \mathrm { E } - 20 \
\text { Size } & & 1.2072436 & 11.439 & 2.09 \mathrm { E } - 09 \
\text { FP } & 6.47601954 & 1.9803612 & 3.27 & 0.004512 \
\hline
\end{array}$$ Which statement is supported by the regression output?
A)At ? = .05, FP is not a significant predictor in a two-tailed test.
B)A fireplace adds around $6476 to the selling price of the average house.
C)A large house with no fireplace will sell for more than a small house with a fireplace.
D)FP is a more significant predictor than Size.

Quizplus · Accepted Answer

The coefficient of FP is 6.47601954, which means that on average, houses with a fireplace sell for $6,476 more than houses without a fireplace, all else being equal. The t-statistic of 3.27 and p-value of 0.004512 indicate that FP is a significant predictor in the regression model, even at α = 0.05. However, we cannot determine whether a large house with no fireplace will sell for more than a small house with a fireplace based on the information provided. We also cannot determine whether FP is a more significant predictor than Size, as these variables are not directly comparable in terms of their coefficients or t-statistics.

A Realtor Is Trying to Predict the Selling Price of Houses