STATS PROBLEM HOMEWORK 9 ASSIGNMENT 2015

| August 30, 2017

Question

(a) A Subway franchise consisting of 12 shops wishes to predict its sales. It has decided to use population size in close proximity to the shops to conduct the 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 Revenue) (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

767.2

32.3

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. .0/msohtmlclip1/01/clip_image001.gif”>Is the regression model statistically significant? Use alpha = .05

2. .0/msohtmlclip1/01/clip_image002.gif”>If it is, how do you know?

3. .0/msohtmlclip1/01/clip_image003.gif”>What is the regression equation?

4. .0/msohtmlclip1/01/clip_image004.gif”>If X1= 40 (in 000’s) what is an estimate of .0/msohtmlclip1/01/clip_image006.gif”>in (000’s)?

5. What is the 95% prediction interval for Y when X1 = 40 (in 000’s)?

.0/msohtmlclip1/01/clip_image007.gif”>

6. .0/msohtmlclip1/01/clip_image008.gif”>What is the coefficient of determination?

7. What is the degree of association betweenpopulation size, X1, and yearly revenue, Y?

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8. Approximately how much of sales, Y, is attributable topopulation size, X1?

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(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. The following are the data for sales Y, population size, X1 and a business proximity rating, X2. Solve by excel and mega stat.

Store

Y

X1

X2

(Yearly Revenue) (in 000’s)

(Population Size) (in 000’s)

(Business Rating)

1

722.9

39.2

5

2

826.3

39.6

8

3

1090.3

58.4

4

4

1235.8

64.6

7

5

548.7

37.5

2

6

767.2

32.3

6

7

1040.7

49.9

9

8

1033.6

55.4

5

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?

.0/msohtmlclip1/01/clip_image011.gif”>

2. .0/msohtmlclip1/01/clip_image012.gif”>How do you know?

3. Does the addition of Business Rating, X2, improve the model?

.0/msohtmlclip1/01/clip_image013.gif”>

4. .0/msohtmlclip1/01/clip_image014.gif”>How can you tell?

5. What is the multiple regression equation?

.0/msohtmlclip1/01/clip_image015.gif”>

6. .0/msohtmlclip1/01/clip_image016.gif”>Approximately what percent of yearly revenue, Y1, is explained bypopulation size, X1 and Business Rating, X2?

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