In: Statistics and Probability
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?