You have been presented with the following data and asked to fit statisti¬cal demand functions: REGION SALES (Y) (‘000 gallons) ADVERTISING EXPENSES (A) ($’000) SELLING PRICE (P) ($/gallon) DISPOSABLE INCOME (M) ($’000) 1 160 150 15.00 19.0 2 220 160 13.50 17.5 3 140 50 16.50 14.0 4 190 190 14.50 21.0 5 130 90 17.00 15.5 6 160 60 16.00 14.5 7 200 140 13.00 21.5 8 150 110 18.00 18.0 9 210 200 12.00 18.5 10 190 100 15.50 20.0 Use any multiple regression packages to estimate a linear relationship between the dependent variable and the independent variables. Use any multiple regression packages to estimate a linear relationship between the dependent variable and the independent variables. a. Linear Relationship i. Identify the dependent and independent variables. ii. Estimate a linear relationship between the dependent variable and all the independent variables. iii. What are the tests that you would use to determine the ‘goodness-of-fit’ of the estimated demand function? Conduct the tests and explain the results. iv. Discuss the economic implications of the various coefficients. b. Non-linear relationship. i. Estimate a logarithmic form of the demand function. ii. Is the estimated demand function ‘good’? Explain your answer. iii. Compare with the linear form above. Elaborate.
You have been presented with the following data and asked to fit statisti¬cal demand
REGION SALES (Y)
(‘000 gallons) ADVERTISING EXPENSES (A)
($’000) SELLING PRICE (P)
($/gallon) DISPOSABLE INCOME (M)
($’000)
1 160 150 15.00 19.0
2 220 160 13.50 17.5
3 140 50 16.50 14.0
4 190 190 14.50 21.0
5 130 90 17.00 15.5
6 160 60 16.00 14.5
7 200 140 13.00 21.5
8 150 110 18.00 18.0
9 210 200 12.00 18.5
10 190 100 15.50 20.0
Use any multiple regression packages to estimate a linear relationship between the dependent variable and the independent variables. Use any multiple regression packages to estimate a linear relationship between the dependent variable and the independent variables.
a. Linear Relationship
i. Identify the dependent and independent variables.
ii. Estimate a linear relationship between the dependent variable and all the independent variables.
iii. What are the tests that you would use to determine the ‘goodness-of-fit’ of the estimated demand function? Conduct the tests and explain the results.
iv. Discuss the economic implications of the various coefficients.
b. Non-linear relationship.
i. Estimate a logarithmic form of the demand function.
ii. Is the estimated demand function ‘good’? Explain your answer.
iii. Compare with the linear form above. Elaborate.
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