Question

An executive in the home construction industry is interested in how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is in years. The executive randomly selected 50 families and ran the multiple regression. Excel output is provided below:

SUMMARY OUTPUT

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	1201.9245	45.5340	0.0000
Residual	46	1214.2264	26.3962
Total	49	4820.0000

	Coeff	Std Error	t Stat	P-value
Intercept	-1.6335	5.8078	-0.281	0.7798
Income	0.4485	0.1137	3.9545	0.0003
Size	4.2615	0.8062	5.286	0.0001
School	-0.6517	0.4319	-1.509	0.1383

Use the output shown above to answer the following questions.

Question 1. Which of the explanatory variables in the model are significant?

Income, Size, SchoolIncome, School    Income, SizeSize, School

Question 2. For a family of size 6 with a head of household earning an annual income of $85,600 with an education of 13 years, what is the predicted house size (in hundreds of square feet)?

24.8811.43    53.8615.15

Question 3. One family in the sample had a head-of-household with an education of 16 years and who provided the sole annual family income of $100,000; the family size was 10. The family owned a home with an area of 7,000 square feet (House = 70.00). What is the residual (in hundreds of square feet) for this data point?

2.525.40    -2.52-5.407.40

Question 4. Suppose the executive wants to test whether the coefficient on School is significantly different from 0. What is the value of the relevant t-statistic?

0.77985.286    3.9545-1.5090.1383

Answer 1

Question 1. Which of the explanatory variables in the model are significant?

Income, Size

Question 2. For a family of size 6 with a head of household earning an annual income of $85,600 with an education of 13 years, what is the predicted house size (in hundreds of square feet)?

53.86

Question 3. One family in the sample had a head-of-household with an education of 16 years and who provided the sole annual family income of $100,000; the family size was 10. The family owned a home with an area of 7,000 square feet (House = 70.00). What is the residual (in hundreds of square feet) for this data point?

-5.40

Question 4. Suppose the executive wants to test whether the coefficient on School is significantly different from 0. What is the value of the relevant t-statistic?

-1.509

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