Homework SourseManagement is considering opening an additional dealership w
Management is considering opening an additional dealership with 14 sales people. Using linear regression, what is the expected weekly total profit for the new dealership?
Management asks whether using number of sales people to predict total profit is a reasonable approach. Which of the following is the best answer to that question?
Yes, it is intuitively logical that the more sales people the company has, the better it can serve the customers.
No, a correlation coefficient value of 0.02 indicates a bad linear fit to the data
Yes, a correlation coefficient value of 0.02 being positive indicates a positive relationship so the more sales people the better
No, a coefficient of determination value of 0.02 indicates a bad fit to the data.
An old saying in car business is, “the more cars you sell, the higher your total profits will be”. Is this statement accurate for this dealership?
Yes, because the number of new cars sold each week and used cars sold each week both have positive correlation values with total profit.
Yes, because the number of new cars sold each week and used cars sold each week both have positive coefficient of determination values with total profit.
No, number of new cars sold each week has a positive correlation value with total profit, and used cars sold each week has a negative correlation value with total profit.
Yes, number of new cars sold each week and used cars sold each week both have positive intercept values from linear regression with total profit.
Management believes that a new dealership can sell 12 new cars each week. What is the 90% confidence interval for expected total profit?
Management is admitting that number of new cars sold each week is the key to predicting total profit and asks you to confirm their belief. Which of the following statements would you use to answer management?
Yes, everyone knows the more new cars you sell the higher the profit
Yes, number of new cars sold each week is a good predictor of profit because the coefficient of determination is 0.66 and is the population coefficient of determination is statistically different from zero at the 0.05 level.
Yes, number of new cars sold each week is a good predictor of profit because the coefficient of determination is 0.81 and is the population coefficient of determination is statistically different from zero at the 0.05 level.
No, number of new cars sold each week is not a good predictor of profit because the coefficient of determination is 0.05 and it can’t be said that the population coefficient of determination is statistically different from zero at the 0.05 level
Jill, an aggressive member of the management team, has suggested the company should close all their used-car lots. She proposes to simply sell every used car taken in on trade, to the wholesale market. You are asked to analyze the data and worthiness of this suggestion, and offer an opinion based on your analysis. Which of the following is the best response?
| Dealership Identifier | Number of sales people | New Car Brand | Number of New cars sold each week | Number of Used Cars sold each week | Better Business Bureau Rating | Profit from New Car Sales | Profit from Used Car Sales | Total Profit | |
| A1 | 13 | Honda | 7 | 5 | AA | $23,233.00 | $2,350.00 | $25,583.00 | |
| A2 | 12 | VW | 6 | 8 | A | $17,694.00 | $5,888.00 | $23,582.00 | |
| A3 | 16 | Honda | 10 | 8 | AA | $41,430.00 | $10,536.00 | $51,966.00 | |
| A4 | 10 | Dodge | 7 | 5 | AA | $20,132.00 | $5,125.00 | $25,257.00 | |
| A5 | 9 | Dodge | 10 | 2 | AAA | $30,280.00 | $15,226.00 | $45,506.00 | |
| A6 | 19 | VW | 12 | 3 | AAA | $48,576.00 | $16,629.00 | $65,205.00 | |
| A7 | 17 | VW | 15 | 4 | AAA | $52,770.00 | $18,916.00 | $71,686.00 | |
| A8 | 20 | Dodge | 14 | 7 | AAA | $53,074.00 | $18,468.00 | $71,542.00 | |
| A9 | 11 | Dodge | 12 | 2 | A | $46,176.00 | -$2,202.00 | $43,974.00 | |
| A10 | 9 | Toyota | 11 | 4 | A | $40,304.00 | -$708.00 | $39,596.00 | |
| A11 | 17 | Dodge | 10 | 5 | AA+ | $36,940.00 | $13,710.00 | $50,650.00 | |
| A12 | 17 | Toyota | 12 | 4 | AAA | $41,244.00 | $15,608.00 | $56,852.00 | |
| A13 | 16 | VW | 11 | 4 | A | $32,571.00 | $2,448.00 | $35,019.00 | |
| A14 | 18 | Dodge | 4 | 4 | AA+ | $12,048.00 | $12,016.00 | $24,064.00 | |
| A15 | 18 | Toyota | 10 | 3 | AA+ | $35,320.00 | $10,730.00 | $46,050.00 | |
| A16 | 6 | Dodge | 3 | 4 | A | $9,774.00 | $2,560.00 | $12,334.00 | |
| A17 | 13 | Dodge | 3 | 5 | AAA | $9,951.00 | $20,295.00 | $30,246.00 | |
| A18 | 15 | Honda | 13 | 4 | AAA | $53,261.00 | $15,688.00 | $68,949.00 | |
| A19 | 13 | Toyota | 8 | 7 | AA+ | $27,248.00 | $14,552.00 | $41,800.00 | |
| A20 | 11 | Ford | 6 | 5 | AAA | $21,270.00 | $19,250.00 | $40,520.00 | |
| A21 | 10 | Honda | 13 | 6 | AAA | $53,950.00 | $19,578.00 | $73,528.00 | |
| A22 | 14 | Toyota | 12 | 3 | AA+ | $45,852.00 | $13,265.00 | $59,117.00 | |
| A23 | 16 | VW | 10 | 7 | A | $32,680.00 | $6,241.00 | $38,921.00 | |
| A24 | 19 | Honda | 4 | 3 | AAA | $11,700.00 | $15,279.00 | $26,979.00 | |
| A25 | 18 | Dodge | 12 | 8 | A | $36,852.00 | $4,360.00 | $41,212.00 | |
| A26 | 19 | Ford | 5 | 7 | AA+ | $15,180.00 | $20,201.00 | $35,381.00 | |
| A27 | 9 | Toyota | 10 | 4 | AA+ | $39,140.00 | $12,656.00 | $51,796.00 | |
| A28 | 7 | Dodge | 15 | 2 | AA | $54,885.00 | $766.00 | $55,651.00 | |
| A29 | 9 | Honda | 3 | 7 | A | $10,827.00 | $5,415.00 | $16,242.00 | |
| A30 | 16 | VW | 7 | 6 | A | $25,333.00 | $5,642.00 | $30,975.00 | |
| A31 | 6 | Honda | 3 | 8 | AA+ | $11,325.00 | $18,208.00 | $29,533.00 | |
| A32 | 5 | Toyota | 10 | 3 | AAA | $36,260.00 | $15,111.00 | $51,371.00 | |
| A33 | 12 | Ford | 11 | 8 | A | $35,145.00 | $6,120.00 | $41,265.00 | |
| A34 | 17 | Honda | 13 | 4 | AAA | $51,454.00 | $18,756.00 | $70,210.00 | |
| A35 | 12 | Toyota | 11 | 3 | A | $31,449.00 | $713.00 | $32,162.00 | |
| A36 | 5 | Ford | 12 | 3 | A | $39,684.00 | -$697.00 | $38,987.00 | |
| A37 | 11 | Honda | 4 | 7 | AA | $14,132.00 | $6,484.00 | $20,616.00 | |
| A38 | 6 | Dodge | 10 | 7 | A | $40,620.00 | $6,493.00 | $47,113.00 | |
| A39 | 8 | Honda | 10 | 6 | A | $31,480.00 | $4,004.00 | $35,484.00 | |
| A40 | 13 | VW | 14 | 4 | AA | $54,754.00 | $2,924.00 | $57,678.00 | |
| A41 | 5 | Dodge | 14 | 3 | AA | $41,720.00 | $1,018.00 | $42,738.00 | |
| A42 | 19 | VW | 4 | 6 | A | $14,832.00 | $1,592.00 | $16,424.00 | |
| A43 | 11 | Honda | 8 | 6 | AA | $31,624.00 | $7,714.00 | $39,338.00 | |
| A44 | 5 | Ford | 9 | 6 | AA | $37,080.00 | $5,692.00 | $42,772.00 | |
| A45 | 19 | Toyota | 15 | 3 | AA | $53,130.00 | $3,250.00 | $56,380.00 | |
| A46 | 9 | Toyota | 4 | 2 | AAA | $13,880.00 | $13,726.00 | $27,606.00 | |
| A47 | 12 | Dodge | 9 | 7 | AA | $30,195.00 | $7,352.00 | $37,547.00 | |
| A48 | 19 | Honda | 12 | 3 | AA+ | $41,412.00 | $11,936.00 | $53,348.00 | |
| A49 | 17 | Dodge | 7 | 2 | AAA | $25,207.00 | $15,404.00 | $40,611.00 | |
| A50 | 18 | Honda | 8 | 3 | AA | $31,112.00 | $2,182.00 | $33,294.00 | |
| A51 | 5 | VW | 15 | 2 | A | $60,705.00 | -$980.00 | $59,725.00 | |
| A52 | 8 | VW | 5 | 7 | AA+ | $16,540.00 | $20,145.00 | $36,685.00 | |
| A53 | 7 | VW | 6 | 4 | AA+ | $17,466.00 | $12,060.00 | $29,526.00 | |
| A54 | 12 | Toyota | 11 | 2 | AAA | $32,032.00 | $15,066.00 | $47,098.00 | |
| A55 | 16 | Ford | 11 | 4 | A | $32,670.00 | $2,944.00 | $35,614.00 | |
| A56 | 8 | Ford | 5 | 8 | AAA | $19,205.00 | $24,016.00 | $43,221.00 | |
| A57 | 5 | Ford | 11 | 4 | A | $37,807.00 | $1,976.00 | $39,783.00 | |
| A58 | 16 | Toyota | 9 | 7 | AAA | $26,100.00 | $21,723.00 | $47,823.00 | |
| A59 | 7 | Toyota | 12 | 5 | AA | $43,116.00 | $5,950.00 | $49,066.00 | |
| A60 | 8 | Dodge | 14 | 2 | AA+ | $47,992.00 | $9,640.00 | $57,632.00 |
Solution
a) Now first we need to find the correlation between number of sales and total profit
Now the correlation coefficient
Hence correlation coefficient is 0.154 and r sqaure value is 0.02. Hence there is 2% variation is due to total profit. No, a coefficient of determination value of 0.02 indicates a bad fit to the data.
2) since r=0.154. Yes, because the number of new cars sold each week and used cars sold each week both have positive correlation values with total profit.
3) 90% confidence interval for Total Profit
Confidence interval for total profit is (-0.0000203,0.00012)
4) Ho: The model is not significant
H1: Model is not significant
Level of significance:5%
Test statistic:
F =1.422 and P value=0.2378
Conclusion : P > 0.05 we accept the null hypothesis. Hence we conclude that the model is not significant at 5% level
| SUMMARY OUTPUT | |
| Regression Statistics | |
| Multiple R | 0.154739 |
| R Square | 0.023944 |
| Adjusted R Square | 0.007116 |
| Standard Error | 4.735581 |
| Observations | 60 |
