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4. 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=aH'Sc 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: DEPENDENT VARIABLE: LNQ OBSERVATIONS: 53 VARIABLE INTERCEPT LNH LNS PARAMETER ESTIMATE 0.9162 0.3517 0.2550 R-SQUARE 0.5452 STANDARD ERROR 0.2413 0.1021 0.0785 F-RATIO 29.97 T-RATIO 3.80 Q3.44 3.25 P-VALUE 0.0004 0.0012 0.0021 b. How do you interpret coefficients b and c? If the dealership increases the number of salespersons by 20 percent, what will be the percentage increase in daily sales? c. Test the overall model for statistical significance at the 5 percent significance 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 percent level of significance. If Hand S both equal 0, are 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 percent, what is the expected impact on daily sales? page 15

4. 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=aH'Sc 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: DEPENDENT VARIABLE: LNQ OBSERVATIONS: 53 VARIABLE INTERCEPT LNH LNS PARAMETER ESTIMATE 0.9162 0.3517 0.2550 R-SQUARE 0.5452 STANDARD ERROR 0.2413 0.1021 0.0785 F-RATIO 29.97 T-RATIO 3.80 Q3.44 3.25 P-VALUE 0.0004 0.0012 0.0021 b. How do you interpret coefficients b and c? If the dealership increases the number of salespersons by 20 percent, what will be the percentage increase in daily sales? c. Test the overall model for statistical significance at the 5 percent significance 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 percent level of significance. If Hand S both equal 0, are 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 percent, what is the expected impact on daily sales? page 15

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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4. 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=aH*Sc 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: DEPENDENT VARIABLE: LNQ OBSERVATIONS: 53 VARIABLE INTERCEPT LNH LNS PARAMETER ESTIMATE 0.9162 0.3517 0.2550 R-SQUARE 0.5452 STANDARD ERROR 0.2413 0.1021 0.0785 F-RATIO 29.97 T-RATIO 3.80 3.44 3.25 P 0 P-VALUE 0.0004 0.0012 0.0021 b. How do you interpret coefficients b and c? If the dealership increases the number of salespersons by 20 percent, what will be the percentage increase in daily sales? c. Test the overall model for statistical significance at the 5 percent significance 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 percent level of significance. If H and S both equal 0, are 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 percent, what is the expected impact on daily sales? page 157
Transcribed Image Text:4. 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=aH*Sc 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: DEPENDENT VARIABLE: LNQ OBSERVATIONS: 53 VARIABLE INTERCEPT LNH LNS PARAMETER ESTIMATE 0.9162 0.3517 0.2550 R-SQUARE 0.5452 STANDARD ERROR 0.2413 0.1021 0.0785 F-RATIO 29.97 T-RATIO 3.80 3.44 3.25 P 0 P-VALUE 0.0004 0.0012 0.0021 b. How do you interpret coefficients b and c? If the dealership increases the number of salespersons by 20 percent, what will be the percentage increase in daily sales? c. Test the overall model for statistical significance at the 5 percent significance 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 percent level of significance. If H and S both equal 0, are 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 percent, what is the expected impact on daily sales? page 157
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