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:
Regression Statistics
Multiple R 0.865
R Square 0.748
Adjusted R Square 0.726
Standard Error 5.195
Observations 50
SUMMARY OUTPUT
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
ANOVA
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?
A. Income, Size, School
B. Income, School
C. Size, School
D. Income, Size (Correct)
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)?
A) 11.43
B)53.86
C) 24.88
D)15.15
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?
A) 2.52
B)-2.52
C)-5.40
D)7.40
E) 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?
5.286
3.9545
0.1383
-1.509 (correct)
0.7798

Answer 1

Answer:

Check the explanation

Step-by-step explanation:

(a)

P-value of income and size is 0.0003 and 0.0001 respectively. Both are less than 0.05 level of significance. So these are significant ot the model. Option D is correct.

(b)

The model is

House_size = -1.6335+0.4485*income + 4.2615*family_size -0.6517*school

Here we have income = 85600/1000 = 85.6

family_size = 6

school = 13

So the predicted house size is

House_size = -1.6335+0.4485*85.6 + 4.2615*6 -0.6517*13=53.855

the predicted house size (in hundreds of square feet) is 53.86. hence, option B is correct.

3)

Here we have income = 100000/1000 = 100

family_size = 10

school = 16

So the predicted house size is

House_size = -1.6335+0.4485*100 + 4.2615*10 -0.6517*16=75.40

Residual : observed value- predicted value = 70 - 75.40 = -5.40

Option C is correct.