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.

Variable	Coefficient	Standard Error	t-Stat	P-value
Intercept	128.93746	2.6205302	49.203	8.93E-20
Size		1.2072436	11.439	2.09E-09
FP	6.47601954	1.9803612	3.27	0.004512

Which statement is supported by the regression output?

a. At α = .05, FP is not a significant predictor in a two-tailed test.

b. A large house with no fireplace will sell for more than a small house with a fireplace.

c. FP is a more significant predictor than Size.

d. A fireplace adds around $6476 to the selling price of the average house.

Answer 1

Statement d. is supported by the regression output. As the regression coefficient of fireplace is 6.47601954, so existence of fireplace would increase selling price of the average house approximately by 6.476 units (thousands of dollars) i.e. by $6476

Also note that statement a. is false as FP is a significant predictor which is reflected in its p-value = 0.004512 < 0.05

Also statement c. is false as size is the more significant predictor than FP as p-value for size is less than that for FP
Also from regression output we can't say anything about statement b. since large house and small house can't be compared unless exact difference in their size and regression coefficient of size are known.