Question

The information below represents the relationship between the selling price (Y, in $1,000) of a home, the square footage of the home (X1), and the number of rooms in the home (X2). The data represents 60 homes sold in a particular area of East Lansing, Michigan and was analyzed using multiple linear regression and simple regression for each independent variable. The first two tables relate to the multiple regression analysis.

Summary measures
Multiple R	0.9408
R-Square	0.8851
Adj R-Square	0.8660
StErr of Estimate	20.8430

Regression coefficients
	Coefficient	Std Err	t-value	p-value
Constant	-13.9705	49.1585	-0.2842	0.7811
Size	7.4336	1.0092	7.3657	0.0000
Number of Rooms	5.3055	8.2767	0.6410	0.5336

The following table is for a simple regression model using only size. (R^2 = 0.8812)

	Coefficient	Std Err	t-value	p-value
Constant	14.771	19.691	0.7502	0.4665
Size	7.816	0.796	9.8190	0.0000

The following table is for a simple regression model using only number of rooms. (R^2= 0.3657)

	Coefficient	Std Err	t-value	p-value
Constant	-93.460	108.269	-0.8632	0.4037
Number of Rooms	41.292	15.082	2.7379	0.0169

(A) Use the information related to the multiple regression model to determine whether each of the regression coefficients are statistically different from 0 at a 5% significance level. Summarize your findings.

(B) Test at the 5% significance level the relationship between Y and X in each of the simple linear regression models. How does this compare to your answer in (A)? Explain.

(C) Is there evidence of multicollinearity in this situation? Explain why or why not.

Answer 1