Question

The manager of Collins Import Autos believes the number of cars sold in a day (Q) depends on two factors: (1) the number of hours the dealership is open (H) and (2) the number of salespersons working that day (S).

After collecting data for two months (53 days), the manager estimates the following log-linear model:
Q = aHbSc
(a) Explain how to transform the 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:

Dependent Variable: LNQ
R-Square: 0.5452
F-Ratio:29.97
P-Value on F: 0.0001
Observations: 53
Variable: Parameter Estimate Standard Error TRatio PValue
Intercept: 0.9162 0.2413 3.80 0.0004
lnH 0.3517 0.1021 3.44 0.0012
lnS 0.2550 0.0785 3.25 0.0021

Answer 1

Step-by-step explanation:

In order to be able to transform the log-linear model into a linear form that can be estimated using multiple regression analysis, we will have to multiply the equation by the natural logarithm (㏑).

Q = aHᵇSˣ

㏑ Q = ㏑a + b㏑H + x㏑S

Q* = a + bH* + xS*