Econ

Question 1

a. Explain how to transform this log-linear model into a linear form that can be estimated using multiple regression analysis.

ANSWER:

Logarithms must be taken of the equation to transform the log-linear model into a non-linear equation:

Q = aHbSc

In Y = (In a) = b (In H) + c (In S)

Therefore:

Q’ = In Q

H’ = In H

S’ = In S

The linear equation is: Q = a’ + bH’ + cS’

b. How do you interpret coefficients b and c? If the dealership increases the number of salespersons by 20 percent, what will the percentage increase in daily sales?

ANSWER:

The estimated elasticity of car sales (Q) to sales people (S) is .225. So if S goes up by 20%, we would expect Q to INCREASE by 20%*.225 = 4.5%

c. Test the overall model for statistical significance at the 5% level.

ANSWER:

For the overall significance of a model, we look at the P-value on the F-statistic. Since the P value is not high, we can say the model is significant.

d. What percent of the total variation in daily auto sales is explained by this equation? What could you suggest to increase this percentage?

ANSWER:

54% of the daily auto sales is explained by the equation. If pricing of the product is reconsidered, the percentage could be increased.

e. Test the intercept for statistical significance at the 5% level of significance. If H and S both equal 0, are the sales expected to be 0? Explain why or why not.

ANSWER:

Values are significant at the 5% level.

Original specification is Q=aHS. Therefore, if H and S are zero, then Q must be zero.

f. Test the estimated coefficient b for statistical significance. If the Dealership decreases its hours of operation by 10%, what is the expected impact on daily sales?

ANSWER:

The coefficient b is statistically significant at the 5% level. If H goes down by 10%, then Q decreases by 10%*.3517 = 3.517%.

Question 2

More choice means there will be greater aggregate satisfaction from the benefits available. Although depending on your...