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Homework answers / question archive / The manager of Collins Import Auto 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 od salespersons working that day (S)
The manager of Collins Import Auto 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 od salespersons working that day (S). After collecting data for two months (53 days), the manager estimates the following log-linear model: Q=aHbSc.The computer output for the multiple regression analysis is below: Obs: 53R-Square: 0.5452F-Ratio 29.97P-Value on F: 0.0001Vaiable ParameterEstimate Std Error T-Ratio P-ValueIntercept 0.9162 0.2413 3.80 0.0004 LNH 0.3517 0.1021 3.44 0.0012LNS 0.2550 0.0785 3.25 0.0021b. How d you interpret coefficients b and c? If the dealership increases the number of salespersons by 20% , what will be the % increase in daily sales? c. Test the overall model for statistical significance at the 5% significance level.d. What percent of the total variation in daily auto sales is explained by this equation? what could you suggest to increase the percentage? e. Test the intercept for statistical significance at the 5% level of significance. If H and S both equal zero, are sales expected to be zero? 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?
a.
By duplicating the condition by common logarithm (ln), we get a straight connection:
b.
The parameters b and c show the elasticity of demand in a log relation equation. If number of sales person (S) increase by 20 percent, then daily sale will go up by:
The sales would go up by 5.1% if thre is increase in sales person by 20%.
c.
The overall model can be tested with the help of F-test:
• The calculated value of F given in table is 29.97 for low values of p value.
• Therefore, the test is significant for major confidence level of interval.
d.
The explained part of variation is shown by the value of R2. Therefore, the independent variables explain around 54.52% of variation in the dependent variable.
e.
The intercept “a” could be tested at 95% confidence interval with the help of t test:
• The calculated value of t is 3.79 (.9162/.2413).
• The table value of t with 51 degrees of freedom (53-2) is between 2.0 and 2.02.
• The calculated value is greater than table value. Hence the intercept is significant
If H and S both are equal to zero, then the value of Q would be equal to zero and not the value of intercept as the equation is exponential and not linear.
f.
The intercept “b” could be tested at 95% confidence interval with the help of t-test:
- The calculated value of t is 3.44 (.3517/.1021).
- The table value of t with 51 degrees of freedom (53-2) is between 2.0 and 2.02.
- The calculated value is greater than table value. Hence the coefficient is significant.
If dealership (H) decreases by 10%, then the change in sales would be:
Thus, the sales (Q) will decrease by 3.517% if the dealership (H) decreases by 10%.
