Managerial Economics 13th Edition by James McGuigan,Charles Moyer,Frederick Harris

Exercise 11

The county assessor (see Exercise 9 of Chapter 4) is concerned about possible multicollinearity between the size (X 1 ) and total number of rooms (X 2 ) variables. Calculate the correlation coefficient between these two variables and diagnose the magnitude of the collinearity problem.
Exercise 9
The county assessor (see Exercise 4) feels that the use of more independent variables in the regression equation might improve the overall explanatory power of the model. In addition to size, the assessor feels that the total number of rooms, age, and whether or not the house has an attached garage might be important variables affecting selling price. The data for the 15 randomly selected dwellings are shown in the following table.
a. Using a computer regression program, determine the estimated regression equation with the four explanatory variables shown in the following table.
b. Give an economic interpretation of each of the estimated regression coefficients.
c. Which of the independent variables (if any) is statistically significant (at the 0.05 level) in explaining selling price
d. What proportion of the total variation in selling price is explained by the regression model
e. Perform an F-test (at the 5 percent significance level) of the overall explanatory power of the model.
f. Construct an approximate 95 percent prediction interval for the selling price of a 15-year-old house having 1,800 sq. ft., 7 rooms, and an attached garage.

Exercise 4
Cascade Pharmaceuticals Company developed the following regression model, using time-series data from the past 33 quarters, for one of its nonprescription cold remedies:
Y = -1:04 + 0:24X 1 - 0:27X 2
where Y = quarterly sales (in thousands of cases) of the cold remedy
X 1 = Cascade's quarterly advertising (× $1,000) for the cold remedy
X 2 = competitors' advertising for similar products (× $10,000)
Here is additional information concerning the regression model:
s b1 = 0:032 s b2 = 0:070
R 2 = 0:64 s e = 1:63 F-statistic = 31:402
Durbin-Watson (d) statistic = 0.4995
a. Which of the independent variables (if any) appears to be statistically significant (at the 0.05 level) in explaining sales of the cold remedy
b. What proportion of the total variation in sales is explained by the regression equation
c. Perform an F-test (at the 0.05 level) of the overall explanatory power of the model.
d. What additional statistical information (if any) would you find useful in the evaluation of this model