# Suppose you were given data on the price of a gallon of ice cream

3. Suppose you were given data on the price of a gallon of ice cream and the sales of ice cream (in gallons) for 60 days. The correlation between ads and sales is -0.40. Does this indicate a significant negative relationship between price and sales at the 0.005 level of significance?

A) Yes

B) No

C) Not enough information to determine significance

Situation 7.2.1:

A real estate builder wishes to determine 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 builder randomly selected 50 families and ran the multiple regression. The output is provided below:

 Variable Coefficient t-statistic Constant -1.633 -0.281 Income 0.448 3.954 Size 4.216 5.286 School -0.6517 -1.509 R2 =0.75; Adjusted R2 = 0.73 F = 6.43

12. Referring to Situation 7.2.1, which of the following values for the level of significance is the smallest for which at least two explanatory variables are significant individually?

A) 0.01

B) 0.025

C) 0.05

D) 0.15

13. Referring to Situation 7.2.1, what are the degrees of freedom for this F-statistic?

A) 46 for the numerator, 4 for the denominator

B) 3 for the numerator, 49 for the denominator

C) 46 for the numerator, 49 for the denominator

D) 3 for the numerator, 46 for the denominator

14. Referring to Situation 7.2.1, which of the following values for the level of significance is the smallest for which the regression model as a whole is significant?

A) 0.00005

B) 0.001

C) 0.01

D) 0.05

15. Referring to Situation 7.2.1, what is the predicted house size (in hundreds of square feet) for an individual earning an annual income of \$40,000, having a family size of four, and going to school a total of 13 years?

A) 11.43

B) 15.15

C) 24.68

D) 53.87

16. Referring to Situation 7.2.1, one individual in the sample had an annual income of \$100,000, a family size of 10, and an education of 16 years. This individual 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) 7.40

B) 2.52

C) – 2.52

D) – 4.89

Situation 7.2.2:

A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies. She proceeds to randomly select 26 large corporations and record information in millions of dollars. The output below shows results

 Variable Coefficient Standard Error Constant 15,800 6038.30 Capital 0.124 0.204 Wage 7.7076 1.473 R2 =0.69; Adjusted R2 = 0.66 F = 25.43

17. Referring to Situation 7.2.2, which of the independent variables (capital, wages) in the model are significant at the 5% level? (Hint: the table reports standard errors not t-statistics)

A) Capital, Wages

B) Capital

C) Wages

D) None of the above

18. Referring to Situation 7.2.2, the observed value of the F-statistic is given on the printout as 25.43. What are the degrees of freedom for this F-statistic?

A) 25 for the numerator, 2 for the denominator

B) 2 for the numerator, 23 for the denominator

C) 23 for the numerator, 25 for the denominator

D) 2 for the numerator, 25 for the denominator

Pretty sure the answer is B, but double check for me please

19. The economist in Situation 7.2.2 decided to add a new variable, energy expenditures, to the model. The new results included an R2 = 0.78 and Adjusted R2 = 0.72. How do you interpret these changes?

A) Since R2 increased, the new variable was an important addition to the model.

B) Since Adjusted R2 increased, the new variable was an important addition to the model.

C) One cannot evaluate the importance of the new variable to the model without knowing either the standard error or t-statistic for the variable’s coefficient.

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