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