Your company is considering marketing a new product that it has just completed developing Your market research department has just completed an analysis of the sales volume you could expect at various retail prices and advertising levels in selected markets. The results of its survey are as follows: Retail Price/Unit Ad Spending (S1000s Sales (S1000s) $8.00 100 1434 $10.00 100 1119 $12.00 100 1005 $8.00 100 1419 S10.00 100 1074 $12.00 100 987 $8.00 100 1038 $10.00 100 1080 $12.00 100 966 $8.00 100 1311 S10.00 100 1095 $12.00 100 1026 $8.00 250 2430 $10.00 250 1959 $12.00 250 1035 $8.00 250 2496 S10.00 250 1923 $12.00 250 1116 $8.00 250 2400 $10.00 250 1860 $12.00 250 1170 $8.00 250 2370 S10.00 250 2010 $12.00 250 1179 A Without considering any possible interaction between the price and advertising spending level what is your first order inear regression equation and what % of the variation does this model provide you with? B. A colleague expresses some concern that the retail sales level may have a different sensitivity to the advertising level at the different prices. Run a linear regression that takes that possibility into consideration. Develop a regression equation that takes that possibility into account. What % of the variation does this model provide you with? C. Which model would you recommend that the company use? Why? D. What would the mean percentage error should the company expect if it choose to use the model that you recommend?
Your company is considering marketing a new product that it has just completed developing Your market research department has just completed an analysis of the sales volume you could expect at various retail prices and advertising levels in selected markets. The results of its survey are as follows: Retail Price/Unit Ad Spending (S1000s Sales (S1000s) $8.00 100 1434 $10.00 100 1119 $12.00 100 1005 $8.00 100 1419 S10.00 100 1074 $12.00 100 987 $8.00 100 1038 $10.00 100 1080 $12.00 100 966 $8.00 100 1311 S10.00 100 1095 $12.00 100 1026 $8.00 250 2430 $10.00 250 1959 $12.00 250 1035 $8.00 250 2496 S10.00 250 1923 $12.00 250 1116 $8.00 250 2400 $10.00 250 1860 $12.00 250 1170 $8.00 250 2370 S10.00 250 2010 $12.00 250 1179 A Without considering any possible interaction between the price and advertising spending level what is your first order inear regression equation and what % of the variation does this model provide you with? B. A colleague expresses some concern that the retail sales level may have a different sensitivity to the advertising level at the different prices. Run a linear regression that takes that possibility into consideration. Develop a regression equation that takes that possibility into account. What % of the variation does this model provide you with? C. Which model would you recommend that the company use? Why? D. What would the mean percentage error should the company expect if it choose to use the model that you recommend?
Linear Algebra: A Modern Introduction
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ISBN:9781285463247
Author:David Poole
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Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 22EQ
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Your company is considering marketing a new product that it has just completed developing. Your market research department has just completed an analysis of the sales volume
6
you could expect at various retail prices and advertising levels in selected markets. The results of its survey are as follows:
Sales ($1000s)
Retail Price/Unit Ad Spending (S1000s
$8.00
8
100
1434
$10.00
100
1119
10
$12.00
100
1005
11
$8.00
100
1419
$10.00
$12.00
12
100
1074
13
100
987
14
$8.00
100
1038
15
$10.00
100
1080
16
$12.00
100
966
17
$8.00
100
1311
18
$10.00
100
1095
19
$12.00
100
1026
20
$8.00
250
2430
21
$10.00
250
1959
22
$12.00
250
1035
23
$8.00
250
2496
24
$10.00
250
1923
25
$12.00
250
1116
26
$8.00
250
2400
27
$10.00
250
1860
28
$12.00
250
1170
29
$8.00
250
2370
30
$10.00
250
2010
31
$12.00
250
1179
32
33
34
A. Without considering any possible interaction between the price and advertising spending level what is your first order inear regression equation
35
and what % of the variation does this model provide you with?
36
B. A colleague expresses some concern that the retail sales level may have a different sensitivity to the advertising level at the different prices.
37
Run a linear regression that takes that possibility into consideration. Develop a regression equation that takes that possibility into account.
38
What % of the variation does this model provide you with?
C. Which model would you recommend that the company use? Why?
D. What would the mean percentage error should the company expect if it choose to use the model that you recommend?
39
40
41
42
43
44
16
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