MULTIPLE CHOICE/EASY I ONLY NEED 2 and 3 NEED BY TUESDAY MARCH 20 An executive i

Question

MULTIPLE CHOICE/EASY

I ONLY NEED 2 and 3

NEED BY TUESDAY MARCH 20

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:

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

SUMMARY OUTPUT Regression Statistics Multiple R 0.865 R Square 0.748 Adjusted R Square 0.726 Standard Error 5.195 Observations 50

Explanation / Answer

(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.

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