A Subway franchise consisting of 12 shops wishes to predict its store sales

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(a) A Subway franchise consisting of 12 shops wishes to predict its store sales. The owner has decided to use population size in close proximity to the shops to conduct a regression analysis. Below are the population sizes in thousands and the annual sales in thousands. Solve by excel and mega stat:

Store

Y

X1

(Yearly Sales) (in 000’s)

(Population Size) (in 000’s)

1

722.9

39.2

2

826.3

39.6

3

1090.3

58.4

4

1235.8

64.6

5

548.7

37.5

6

867.2

42.3

7

1040.7

49.9

8

1033.6

55.4

9

810.5

42.1

10

527.1

20.8

11

1058.7

63.5

12

963.4

38.6

 

  1. Is the regression model statistically significant? Use alpha = .05
  2. If it is, how do you know?
  3. What is the regression equation?
  4. If X1= 40 (in 000's) what is an estimate ofin (000’s)?
  5. What is the 95% prediction interval for Y hat when X1 = 40 (in 000’s)?
  6. What are the coefficient of determinationand the standard error of the estimate?
  7. What is the degree of association between population size, X1, and yearly sales, Y?
  8. Approximately how much of sales, Y, is attributable to population size, X1?

(b)  The owner of the franchise believes that sales might also be affected by the proximity of other business and shopping locations near a sandwich shop's site. He decides to conduct a multiple regression adding this variable. The following are the data for sales Y, population size, X1 and abusiness proximity rating, X2. Solve by excel and mega stat. 

 

Store

Y

X1

X2

(Yearly Sales) (in 000’s)

(Population Size) (in 000’s)

(Business Rating)

1

722.9

39.2

5

2

826.3

39.6

6

3

1090.3

58.4

8

4

1235.8

64.6

9

5

548.7

37.5

2

6

867.2

42.3

6

7

1040.7

49.9

9

8

1033.6

55.4

9

9

810.5

42.1

3

10

527.1

20.8

3

11

1058.7

63.5

5

12

963.4

38.6

5

 

 

  1. Is the multiple regression model statistically significant at alpha=.05?
  2. How do you know?
  3. Does the addition of Business Rating, X2, improve the model?
  4. How can you tell?
  5. What is the multiple regression equation?

 

  1. Approximately what percent of yearly sales, Y1, is explained by population size, X1 and Business Rating, X2? 
  2.  What is the 95% prediction interval for a new proposed shop if the population size is, X1 =40 (000) and business rating is,  X2 = 6?
  • 9 years ago
A Subway franchise consisting of 12 shops wishes to predict its store sales
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