You have been presented with the following data and asked to fit statistical dem

Question

You have been presented with the following data and asked to fit statistical 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  

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.

v. Compute the price elasticity of demand and income elasticity of demand in period 10. Elaborate your answers.

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.

Explanation / Answer

i.

Dependent variable: SALES (Y) (‘000 gallons)
Independent variables: ADVERTISING EXPENSES (A) ($’000), SELLING PRICE (P) ($/gallon), DISPOSABLE INCOME (M) ($’000)

ii. Below are regression results;

iii. We can look at adjusted R2 which 0.71. That is, 71% of variation in sales is explain by the above independent variable. Overall its a pretty decent model.

We can also look at the joint significance of coefficients-

The last column shows the p-value which is less than 5%. It means that these coefficients are jointly significant at 5% level of significance.

In terms of individual significance, only selling price is statistically significant variable at 5% critical level. Other 2 variables - Disposable income and advertising expenses are not statistically significant.

iv. Advertising expenses do not have any statistically significant effect on Sales. Likewise, even income has no significant effect. However, in terms of their signs both have positive sign which is consistent with the known facts.

Coefficient of price is negative implying that as price increases by $1, the sales fall by $12.44. It has a statistically significant variable as well.

PS: According to chegg guidelines in event of multiple parts, only first four are attempted. However, you may repost the qsn asking for solution of specific questions/parts.

Dependent var: Sales Coefficients Standard Error t Stat P-value Intercept 321.24 91.80 3.50 0.01 ADVERTISING EXPENSES (A) ($’000) 0.03 0.19 0.16 0.88 SELLING PRICE (P) ($/gallon)    -12.44 4.31 -2.89 0.03 DISPOSABLE INCOME (M) ($’000) 2.08 3.02 0.69 0.52

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