Question 1. A consumer-product marketing experiment involved different ad- vertising and promotion strategies in eight sales regions. TV advertising, newspaper advertising, and a retailer incentive were systematically varied. TV advertising (2₁) was either reduced by 10% compared with the previous quarter, kept the same, or increased by 10%. These advertising levels are coded as -1, 0, or 1. Similar changes were made to the level of newspaper advertising (x2), again coded as -1, 0, or 1. The retailer incentive (23) is either used or not, coded as 1 or 0. The response variable (Y) is the change in market share in percentage points relative to the precious quarter. Suppose the model under consideration is Y₁ =B₁ + B₁x1i + B₂x2¡ + B3X3i + €¡, i = 1, ..., 8, where random errors ; are independent and identically-distributed N (0, ²). a. Compute the least square estimates of B₁, j = 0, 1, 2, 3. b. Derive the ANOVA table for the data and compute R². c. Carry out a t test and construct a 95% confidence interval for each ; (j = 1,2,3). TV advertising -1 0 0 1 -1 0 0 1 Newspaper Retailer Change in advertising incentive market share 0 0 -1 0 1 0 0 -1 1 0 1 1 1 1.2 1.5 2.2 2.3 1.9 1.4 2.8 2.3 d. Suppose that the Vice President for marketing is considering the following company-wide strategy: keep TV advertising at level 0 on the coded scale, set news- paper advertising to level 1 on the coded scale, and do not use the retailer incentive. Give a 95% confidence interval for the mean value of the market-share change.
Question 1. A consumer-product marketing experiment involved different ad- vertising and promotion strategies in eight sales regions. TV advertising, newspaper advertising, and a retailer incentive were systematically varied. TV advertising (2₁) was either reduced by 10% compared with the previous quarter, kept the same, or increased by 10%. These advertising levels are coded as -1, 0, or 1. Similar changes were made to the level of newspaper advertising (x2), again coded as -1, 0, or 1. The retailer incentive (23) is either used or not, coded as 1 or 0. The response variable (Y) is the change in market share in percentage points relative to the precious quarter. Suppose the model under consideration is Y₁ =B₁ + B₁x1i + B₂x2¡ + B3X3i + €¡, i = 1, ..., 8, where random errors ; are independent and identically-distributed N (0, ²). a. Compute the least square estimates of B₁, j = 0, 1, 2, 3. b. Derive the ANOVA table for the data and compute R². c. Carry out a t test and construct a 95% confidence interval for each ; (j = 1,2,3). TV advertising -1 0 0 1 -1 0 0 1 Newspaper Retailer Change in advertising incentive market share 0 0 -1 0 1 0 0 -1 1 0 1 1 1 1.2 1.5 2.2 2.3 1.9 1.4 2.8 2.3 d. Suppose that the Vice President for marketing is considering the following company-wide strategy: keep TV advertising at level 0 on the coded scale, set news- paper advertising to level 1 on the coded scale, and do not use the retailer incentive. Give a 95% confidence interval for the mean value of the market-share change.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Transcribed Image Text:Question 1. A consumer-product marketing experiment involved different ad-
vertising and promotion strategies in eight sales regions. TV advertising, newspaper
advertising, and a retailer incentive were systematically varied. TV advertising (1)
was either reduced by 10% compared with the previous quarter, kept the same, or
increased by 10%. These advertising levels are coded as -1, 0, or 1. Similar changes
were made to the level of newspaper advertising (22), again coded as -1, 0, or 1. The
retailer incentive (23) is either used or not, coded as 1 or 0. The response variable (Y)
is the change in market share in percentage points relative to the precious quarter.
Suppose the model under consideration is
Y₁ = Bo + B₁x₁₁+ B₂x2; + B3X3i + €₁, i= 1,...,8,
where random errors €; are independent and identically-distributed N (0, 2).
a. Compute the least square estimates of ß;, j = 0, 1, 2, 3.
b. Derive the ANOVA table for the data and compute R².
c. Carry out a t test and construct a 95% confidence interval for each B; (j = 1, 2, 3).
TV
advertising
-1
0
0
1
0
1
Newspaper
advertising
0
-1
0
-1
1
0
Retailer
incentive
0
0
0
1
1
1
1
Change in
market share
1.2
1.5
2.2
2.3
1.9
1.4
2.8
2.3
d. Suppose that the Vice President for marketing is considering the following
company-wide strategy: keep TV advertising at level 0 on the coded scale, set news-
paper advertising to level 1 on the coded scale, and do not use the retailer incentive.
Give a 95% confidence interval for the mean value of the market-share change.
Expert Solution
Step 1
Given the consumer-product marketing experiment involved in different advertising and promotion strategies in eight sales regions as
| TV advertising | Newspaper advertising | Retailer incentive | Change in market share |
| -1 | 0 | 0 | 1.2 |
| 0 | -1 | 0 | 1.5 |
| 0 | 1 | 0 | 2.2 |
| 1 | 0 | 0 | 2.3 |
| -1 | 0 | 1 | 1.9 |
| 0 | -1 | 1 | 1.4 |
| 0 | 1 | 1 | 2.8 |
| 1 | 0 | 1 | 2.3 |
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