The manager of Collins Import Autos believes the numbers of cars sold in a day (
ID: 1091472 • Letter: T
Question
The manager of Collins Import Autos believes the numbers of cars sold in a day (Q) depends on 2 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 2 months (53 days) the manager estimates the following log-linear model:
Q=aH^bS^c
The linear equation is: Q = a + bH + cS 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
1. If H and S both equal 0, are the sales expected to be 0? Explain why or why not
2. Test the estimated coefficient b for statistical significance. If th dealership decreases its hours of operation by 10 percent, what is the expected impact on daily sales?
Explanation / Answer
a. Since its already given in the question dat
Q = a* (H^b) * (S^c)
Hence if H and S are Zero , than definitely Q must also be Zero..
b. The value of cofficient b is significant at 5% level..
hence if H decreses by 10 % than Q ll decrese automatically be = (10%*(0.3517)) = 3.517%
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.