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Estimation of linear regression model
A CEO of a large pharmaceutical company would like to determine if he should be placing more money allotted in the budget next year for television advertising of a new drug marketed for controlling asthma. He wonders whether there is a strong relationship between the amount of money spent on television advertising for this new drug called XBC and the number of orders received. The manufacturing process of this drug is very difficult and requires stability so the CEO would prefer to generate a stable number of orders. The cost of advertising is always an important consideration in the phase I roll-out of a new drug. Data that have been collected over the past 20 months indicate the amount of money spent of television advertising and the number of orders received.
The use of linear regression is a critical tool for a manager's decision-making ability. Please carefully read the example below and try to answer the questions in terms of the problem context. The results are as follows:
Month
Advertising Cost (thousands of dollars)
Number of Orders
1
$68.93
4,902,000
2
72.62
3,893,000
3
79.58
5,299,000
4
58.67
4,130,000
5
69.18
4,367,000
6
70.14
5,111,000
7
83.37
3,923,000
8
68.88
4,935,000
9
82.99
5,276,000
10
75.23
4,654,000
11
81.38
4,598,000
12
52.90
2,967,000
13
61.27
3,999,000
14
79.19
4,345,000
15
80.03
4,934,000
16
78.21
4,653,000
17
83.77
5,625,000
18
62.53
3,978,000
19
88.76
4,999,000
20
72.64
5,834,000
Assuming there is a statistically significant relationship. Use the least square method to find the regression equation to predict the advertising costs based on the number of orders received. Please use the regression procedure within Excel under Tools > Data Analysis to construct this equation.
Solve the equations using linear algebra
Consider the following estimated regression equation, based on 10 observations.
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