A microeconomist wants to determine how corporate sales are influenced by capita

Question

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

I. referring to above, 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

II. Referring to above, 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

III. The economist in above 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.

IV. There are several reasons why choices between alternative regression models should NOT be based on which model has the highest R2. Which of the following is NOT one of those reasons?

A) Models using time series data will have higher R2 than models using cross-sectional data.
B) Some variables are inherently more unstable and thus harder to predict.
C) R2 indicates relationships not causality.
D) R2 captures the individual effects of variables but not the effects of all variables.

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

Explanation / Answer

I. Correct Answer Option (c)

Since Capital t = 0.124/0.204 = 0.608

           Wage t = 7.7076 / 1.473 = 5.232

The critical value of t = 2.059 at 25df and 5%los from t-tables

Here Capital t= 0.608 < tcrit we accept H0. i.e. there is no significant

Here Wage t= 5.232 > tcrit we do no accept H0. i.e. there is significant

II. Correct Answer: Option (D)

   In Regression analysis, The df of F is (no. of indpendent variables, sample size -1) = (2,25)

III. Correct Answer: Option (C)

IV. Correct Answer: Option (A)

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