Question

In: Statistics and Probability

In a study to identify factors that influence territory sales and to assess the relative importance...

In a study to identify factors that influence territory sales and to assess the relative importance of the factors, four predictor variables were chosen, as defined below. Data from a random sample of 25 sales territories of a firm's national sales organization were analyzed. The first order linear model is: The purpose of this exercise is to build a multiple regression model to predict y. Y = sales credited to territory salesman X1 = length of time in the territory in months X2 = industry sales, in units, of products sold in territory. X3 = advertising dollars in territory X4 = weighted average of past market share magnitudes for 4 previous years

y

x1

x2

x3

x4

3670

43.1

74065

4583

2.51

3474

108.1

58117

5540

5.51

2295

13.8

21119

2950

10.91

4676

186.2

68521

2243

8.27

6126

161.8

57805

7747

9.15

5032

365

50935

3141

8.54

3368

220.3

65602

2086

7.07

6520

127.6

46177

8846

12.54

4876

105.7

42053

5673

8.85

2468

57.7

36830

2762

5.38

2533

23.6

33613

1992

5.43

2408

13.8

21413

1972

8.48

2337

13.8

20417

1737

7.8

4587

87

36272

10694

10.34

2729

165.9

23093

8619

5.15

3289

116.3

26879

7748

6.64

2801

42.3

39572

4566

5.45

3264

52.8

51866

6023

6.31

3454

165

58750

3721

6.35

1741

10.6

23991

861

7.37

2036

13.8

25695

3572

8.39

1578

8.1

23736

2846

5.15

4167

58.5

34314

5060

12.88

2800

21.1

22810

3552

9.14

2135

8.9

37807

402

5.51

a)Write a first order model for sales, y, as a function of advertising dollars in a territory.

b) Write a second order model for sales, y, as a function of advertising dollars in a territory.

c) Test to determine if there is a curvilinear relationship between worldwide gross revenues and movie budget.

d)Is there evidence to indicate there is a curvilinear relationship between worldwide gross revenues and movie budget?

e) What is the value of test statistics?

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