The marketing manager of a large supermarket chain would lik

The marketing manager of a large supermarket chain would like to use shelf space to predict the sales of pet food. For a random sample of 12 similar stores, she gathered the following information regarding the shelf space, in feet, devoted to pet food and the weekly sales in hundreds of dollars. Use these data to answer questions 9 through 11.

Store

1

2

3

4

5

6

Shelf Space

5

5

5

10

10

10

Weekly Sales

1.6

2.2

1.4

1.9

2.4

2.6

Store

7

8

9

10

11

12

Shelf Space

15

15

15

20

20

20

Weekly Sales

2.3

2.7

2.8

2.6

2.9

3.1

What is the equation for the least squares line?

What is the coefficient of determination?

Construct a 95% predicition interval estimate for the weekly sales, in hundreds of dollars, for a store with 8 feet of shelf space devoted to pet food.

Please show the steps to solve this problem.

Solution

he marketing manager of a large supermarket chain would like to use shelf space to predict the sales of pet food. For a random sample of 12 similar stores, she gathered the following information regarding the shelf space, in feet, devoted to pet food and the weekly sales in hundreds of dollars. Use these data to answer questions 1 through 3.
Store 1 2 3 4 5 6
Shelf Space 5 5 15 20 20 20
Weekly Sales 1.6 2.2 1.4 1.9 2.4 2.6
Store 7 8 9 10 11 12
Shelf Space 25 25 25 30 30 30
Weekly Sales 2.3 2.7 2.8 2.6 2.9 3.1
Question 1: Compute the value of the sample correlation coefficient between weekly sales and shelf space. Possible answers A. 0.6234 B. 0.827 C. 0.652 D. 0.741 I answered D
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Using the LinReg function on my TI-84 I get r = 0.3835
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Question 2: Is the correlation between weekly sales and shelf space significant at the .01 level of significance? Possible answers: A. No, the sample correlation coefficient does not exceed the critical value. B. Yes, the p-value of the test for significance is not than .01. C. Yes, the value of the test statistic does exceed the critical value. D. Yes, the computed t-test statistic is less than the critical value.
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Using the A-6 Table for linear correlation I find the critical value
for n = 6 is r = 0.917
Since \"r\" for the data set is 0.3835 we fail to reject Ho:
Ho: no linear correlation.
Ha: significant linear correlation
Answer: A
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Question 3: What is the estimated regression equation? A. = 1.45 + 0.044x B. = 1.45 + 0.724x C. = 1.45 - 0.074x D. = 2.63 - 0.174x I answered A.
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I get y = 0.024x + 1.67