Question

George is interested in how the average sale price of homes in Albemarle County is related to (1) the size of a home in square feet and (2) whether a home is new or not new.   To incorporate the new/not new categorical variable into his regression model, he creates a dummy variable = 1 if a home is new and 0 if it is not new. He estimates two models, one without interaction, and one that includes an interaction term equal to New X Size. The following tables show his results.

Model 1 (without interaction):

	Coefficient	Std. Error	t	p
Intercept	-40,230.867	14,696.140	-2.738	0.007
Size	116.132	8.795	13.204	0.000
New	57,736.283	18,653.041	3.095	0.003

Model 2 (with interaction):

	Coefficient	Std. Error	t	p
Intercept	-22,227.808	15,521.110	-1.432	0.155
Size	104.438	9.424	11.082	0.000
New	-78,527.502	51,007.642	-1.540	0.127
New X Size	61.916	21.686	2.855	0.005

1. Interpret the coefficients in Model 2. Should George be worried because the coefficient for “New” is no longer statistically significant in Model 2, although it was significant in Model 1? Explain.

Answer 1

Answer to the question)

Interpretation of coefficients of model 2 are as follows:

Size: the coefficient for size is 104.438 , which implies that if the size of the home is increased by one unit, the price increases by 104.438 times . Since the P value for size is 0.000 this implies size has a significant effect on the price of the home

New: The coefficient of new is -78,527.502 , hence this implies if the house is not new, its price decreases by 78,527.502 times. The p value for the factor new is : 0.127. Since the P value is larger than alpha 0.05 we conclude that the factor new doesnot have a significant effect on the price value of the home

New x Size denotes the interaction effect of the two factors. It has a coefficient of 61.916 , which implies that with increase in one unit of New and Size the increase in price is 61.916 times. The P value for the interaction effect is 0.005. Since this P value is less than alpha 0.05, it concludes that the interaction effect of the two factors is significant.

.

Yes, the model 2 has changed the significance level of the factor new house. It tells us that it is the interaction effect of new with the size of house that is actually influencing the price of the home significantly. So yes George must consider this aspect.