Question

In: Statistics and Probability

A marketing manager for Country Kitchen Corporation (CKC), which sells snack food product "Nature -Bar" in...

A marketing manager for Country Kitchen Corporation (CKC), which sells snack food product "Nature -Bar" in dif- ferent regions, was interested in how its sales (denoted Sales) are influenced by the sales of its main competitor (denoted Csales.) She gathered last year data on Sales and Csales for a 15 randomly selected sales regions and ob- tained the regression model of Sales on Csales. Both Sales and Csales are measured in millions of dollars. To answer questions below use your own Minitab output.

The data are in Excel file Nature-Bar.

a) Is the regression of Sales on Csales statistically significant at a= 0.02? (State the hypothesis test, rejection rule and your conclusion)

Region

Sales

Advertising

Promotions

Csales

Selkirk

101.8

1.3

0.2

20.4

Csales=main competitor's sales

Susquehanna

44.4

0.7

0.2

30.5

Sales=sales of company's Nature -Bar

Kittery

108.3

1.4

0.3

24.6

Acton

85.1

0.5

0.4

19.6

Finger Lakes

77.1

0.5

0.6

25.5

Berkshires

158.7

1.9

0.4

21.7

Central

180.4

1.2

1

6.8

all variables are in millions of dollars

Providence

64.2

0.4

0.4

12.6

Nashua

74.6

0.6

0.5

31.3

Dunster

143.4

1.3

0.6

18.6

Endicott

120.6

1.6

0.8

19.9

Five-Towns

69.7

1

0.3

25.6

Waldeboro

67.8

0.8

0.2

27.4

Jackson

106.7

0.6

0.5

24.3

Stowe

119.6

1.1

0.3

13.7

Solutions

Expert Solution

Regression Analysis
r² 0.390 n   15
r   -0.625 k   1
Std. Error   30.932 Dep. Var. Sales
ANOVA table
Source SS   df   MS F p-value
Regression 7,966.4886 1   7,966.4886 8.33 .0128
Residual 12,438.5207 13   956.8093
Total 20,405.0093 14  
Regression output confidence interval
variables coefficients std. error    t (df=13) p-value 95% lower 95% upper std. coeff.
Intercept 177.7012 0.000
Csales -3.5446 1.2284 -2.885 .0128 -6.1984 -0.8908 -0.625

The regression equation is Sales = 177.7012 - 3.5446 * Csales

Hypotheses: β1 = 0 versus Ha: β1 ≠ 0

Critical t- score (α = 0.02, Df = 13) = ± 2.6503

p- value = 0.0128

Since 0.0128 < 0.02, we reject Ho

Conclusion: Sales is significantly affected by Csales.

orchestra answered 1 year ago
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