4) The manager of Collins Import Autos believes that the number of cars sold in a day (Q) depends o

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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