The sales manager of a large automotive parts distributor wants to estimate the total annual sales for each of the company’s regions. Three factors appear to be related to regional sales: the number of retail outlets in the region, the total personal income of the region, and the number of cars registered in the region. The following table shows the data for 10 regions that were gathered for last year sales. The excel data file for this problem is: final exam question 6B spring 2021.xlsx Region Annual sales ($ million) Number of retail outlets Number of automobiles registered (million) Personal income ($ billion) 1 37.702 1,739 9.27 85.4 2 24.196 1,221 5.86 60.7 3 32.055 1,846 8.81 68.1 4 3.611 120 4.81 20.1 5 17.625 1,096 10.31 33.8 6 45.919 2,290 11.62 95.1 7 29.600 1,687 8.96 69.3 8 8.114 241 6.28 16.5 9 20.116 649 7.77 34.9 10 12.994 1,427 10.92 15.1 What is the estimated correlation between the annual sales and the number of retail outlet? Enter your answer in percent and in xx.x format. That is, round your answer to one decimal point and use leading and trailing zero as needed to exactly match the xx.x format. Include the negative sign (minus sign) if the coefficient is negative. For example if your answer is 0.6543, first multiply it by 100 to convert it to percent (65.43) and then round it to one decimal and enter 65.4 in the answer text box. If your answer is -0.0436 then enter it as -04.4 (-0.0436*100 = -4.36 which rounded to one decimal is -04.4). Do not include the % sign in your answer. Your answer is: What is the estimated correlation between the annual sales and personal income in the region? Enter your answer in percent and in xx.x format. Follow the instructions under part a. Your answer is: Develop the least square regression line to predict annual sales based on the number of retail outlets, personal income (in $billion), and the number of cars (in million) registered in the region. Enter the regression coefficients in xx.xxxx format. Round your answer to four decimals and use leading and trailing zero to exactly match the format. Include the negative sign (minus sign) if the coefficient is negative. Do not include plus sign in your response. For example, if the coefficient is +6.15634 then enter 06.1563 as your answer, if the coefficient is -0.54765 then enter -00.5477 and if the answer is -1.64335 then enter -01.6434 Ŷ=b0+b1X1+b2X2 +b3X3 Constant/intercept (b0) = Coefficient/slope of number of retail outlets (X1) (b1) = Coefficient/slope of the number of automobiles registered (X2) (b2) = Coefficient/slope of personal income (X3) (b3) =
The sales manager of a large automotive parts distributor wants to estimate the total annual sales for each of the company’s regions. Three factors appear to be related to regional sales: the number of retail outlets in the region, the total personal income of the region, and the number of cars registered in the region. The following table shows the data for 10 regions that were gathered for last year sales.
The excel data file for this problem is:
final exam question 6B spring 2021.xlsx
|
Region |
Annual sales ($ million) |
Number of retail outlets |
Number of automobiles registered (million) |
Personal income ($ billion) |
|
1 |
37.702 |
1,739 |
9.27 |
85.4 |
|
2 |
24.196 |
1,221 |
5.86 |
60.7 |
|
3 |
32.055 |
1,846 |
8.81 |
68.1 |
|
4 |
3.611 |
120 |
4.81 |
20.1 |
|
5 |
17.625 |
1,096 |
10.31 |
33.8 |
|
6 |
45.919 |
2,290 |
11.62 |
95.1 |
|
7 |
29.600 |
1,687 |
8.96 |
69.3 |
|
8 |
8.114 |
241 |
6.28 |
16.5 |
|
9 |
20.116 |
649 |
7.77 |
34.9 |
|
10 |
12.994 |
1,427 |
10.92 |
15.1 |
- What is the estimated
correlation between the annual sales and the number of retail outlet?
Enter your answer in percent and in xx.x format. That is, round your answer to one decimal point and use leading and trailing zero as needed to exactly match the xx.x format. Include the negative sign (minus sign) if the coefficient is negative. For example if your answer is 0.6543, first multiply it by 100 to convert it to percent (65.43) and then round it to one decimal and enter 65.4 in the answer text box. If your answer is -0.0436 then enter it as -04.4 (-0.0436*100 = -4.36 which rounded to one decimal is -04.4). Do not include the % sign in your answer.
Your answer is:
- What is the estimated correlation between the annual sales and personal income in the region?
Enter your answer in percent and in xx.x format. Follow the instructions under part a.
Your answer is:
- Develop the least square regression line to predict annual sales based on the number of retail outlets, personal income (in $billion), and the number of cars (in million) registered in the region.
Enter the regression coefficients in xx.xxxx format. Round your answer to four decimals and use leading and trailing zero to exactly match the format. Include the negative sign (minus sign) if the coefficient is negative. Do not include plus sign in your response. For example, if the coefficient is +6.15634 then enter 06.1563 as your answer, if the coefficient is -0.54765 then enter -00.5477 and if the answer is -1.64335 then enter -01.6434
Ŷ=b0+b1X1+b2X2 +b3X3
Constant/intercept (b0) =
Coefficient/slope of number of retail outlets (X1) (b1) =
Coefficient/slope of the number of automobiles registered (X2) (b2) =
Coefficient/slope of personal income (X3) (b3) =
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