Question

A real estate builder wishes to determine how house size is influenced by family income, family size, and education of the head of household. House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is measured in years. A computer output is shown below.

Regression Statistics
Multiple R	0.865
R Square	0.748
Adjusted R Square	0.726
Standard Error	5.195
Observations	50
ANOVA
	df	SS		MS		F		Signif F
Regression	3	3605.7736		901.4434		33.4081		0.0001
Residual	46	1214.2264		26.9828
	49	4820.0000
	Coeff.	St.Error		t Stat		P-value
Intercept	-1.6335	5.8078		-0.281		0.7798
Family Income	0.4485	0.1137		3.9545		0.0003
Family Size	4.2615	0.8062		5.286		0.0001
Education	-0.6517	0.4319		-1.509		0.1383

What is the predicted house size (in hundreds of square feet) for an individual earning an annual income of 60 (which is measured in thousands of dollars), having a family size of 3, and having 13 years of education?

Select one:

a. 2.42

b. 7.16

c. 48.17

d. 31.22

e. 29.59

At 3% level of significance, which of the following variables can be removed without significantly hurting the model?

Select one:

a. Family income

b. Family size

c. Education

d. Both family income and family size

e. None

Based on the above model, how does increasing family size by 1 member influence the house size, assuming that all other variables remain unchanged?

Select one:

a. House size will increase on average by 426.15 sq. feet

b. House size will increase on average by 5.286 sq. feet

c. House size will change on average by 4.26 sq. feet

d. House size will change on average by 0.865 sq. feet

Answer 1

Let y denotes the house size, x1 denotes family income, x2 denotes family size, x3 denotes education.

The regression equation of y on x1, x2, x3 is:

y = -1.6335 + 0.4485 x1 + 4.2615 x2 - 0.6517 x3.

• when x1 = 60, x2 = 3, x3 = 13

y = -1.6335 + 0.4485*60 + 4.2615*3 - 0.6517*13 = 29.59 (option e).

• Since p-value of education is 0.1383 > 0.03, therefore at 3% level it is insignificant. Hence at 3% level of significance, Education (option c) can be removed without significantly hurting the model.
• Based on the above model, by increasing family size by 1 member house size will change on average by 4.26 sq. feet assuming that all other variables remain unchanged