Posted by **Ed** on Monday, June 4, 2007 at 7:32pm.

4) The manager of Collins Import Autos

believes that the number of cars

sold in a day (Q) depends on two

factor: (1) the number of hours the

dealership is open (H) and (2) the

number of salespersons working that

day (S). After collecting the data

for two months (53 days), the

manager estimates the following log-

linear model:

b c

Q = aH S

a) Explain how to transform this log-

linear model into a linear form

that can be estimated using

multiple regression analysis.

The computer output for the multiple regression analysis is shown below:

Dependant Variable: LNQ

R-Square: 0.5452 F-Ratio: 29.97

P-Value on F: 0.0001

Observations: 53

Variable: Intercept

Parameter Est: o.9162

Standard Error: 0.2413

T-Ratio: 3.80

P-Value: 0.0004

Variable: LNH

Parameter Estimate: 0.3517

Standard Error: 0.1021

T-Ratio: 3.44

P-Value: 0.0012

Variable: LNS

Parameter Est: 0.2550

Standard Error: 0.0785

T-Ratio: 3.25

P-Value: 0.0021

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?

c) Test the overall model for

statistical significance at the 5%

level?

d) What percent of the total variation

in daily auto sales is explained by

this equation?

What could you suggest to increase

this percentage?

e) Test the intercept for statistical

significance at the 5% level

Significance. If H and S both equal

0, are the sales expected to be 0?

Explain why or why not…..

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?

Thanks,

EY

a) transform natural log values to linear values using e^x.

b) Parameter estimates in a log-linear function are elasticities.

c) what does the F statistic tell you?

d) what does the R^2 statistic tell you.

e) what does the T-ratio statistics on the parameter estimates tell you?

f) re-examine answers b and e

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