Famous Electronics sells TV satellite dishes and has been in business for a number of years. The firm's owner has become concerned about the firm's pricing, advertising, and other competitive strategies. She hired a consulting firm to estimate the demand function for TV dishes. The consulting firm informed her that the demand function was estimated using data gathered from 150 similar firms operating during the past year. Standard deviations of each of the regression coefficients are reported in parenthesis.
Qx = 1500 - 0.8 Px + 20 Pc + 0.032 Y + 0.012 Ax
(240) (0.17) (4.5) (0.007) (0.002)
R2 = 0.25
Standard Error of the estimate = 40.0
where: Qx = annual quantity of dishes sold
Px = the price per dish
Pc = the price of regular cable TV service
Y = average income
Ax = advertising expenditures on dishes
Current values for the independent variables are: Px = 1,500; Pc = 60; Y = 45,000; and Ax = 50,000
Use t-statistic or F-test and null hypothesis wherever applicable:
a. Calculate the expected quantity of dishes to be sold, given the current values of the independent variables.
b. Construct and interpret the meaning of a 95% confidence interval around the estimated quantity of dishes to be sold as forecasted in part a.
c. What proportion of total inter-firm variation in quantity sold is explained by the model? Is this value significantly different from zero, assuming a desired 95% confidence level?
d. Calculate and interpret the economic meaning of the point demand elasticity corresponding to each of the model's independent variables Px, Pc, etc.
Managerial Economics and Business Strategy - 2 Regression Questions
Problem # 10
You are the manager of a firm that sells a leading brand of alkaline batteries. The accompanying Excel file contains data on the demand for your product. Specifically, the file contains data on the natural logarithm of your quantity sold, price, and the average income of consumers in various regions around the world. Use this information to perform a log-linear regression, and then determine the likely impact of a 3 percent decline in global income on the overall demand for your product.
Problem # 15
As a newly appointed "Energy Czar," your goal is to reduce the total demand for residential heating fuel in your state. You must choose one of three legislative proposals designed to accomplish this goal: (a) a tax that would effectively increase the price of residential heating fuel by $2; (b) a subsidy that would effectively reduce the price of natural gas by $1; or (c) a tax that would effectively increase the price of electricity (produced by hydroelectric facilities) by $5. To assist you in your decision, an economist in your office has estimated the demand for residential heating fuel using a linear demand specification. The regression results are presented below. Based on this information, which proposal would you favor? Explain.