Correlation coefficient and scatter plot.
A CEO of a large pharmaceutical company would like to conclude if he has to 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 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 point to 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 instance 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
|
Set up a scatter diagram and calculate the associated correlation coefficient. Examine how strong you think the relationship is between the amounts of money spent on television advertising and the number of orders received. Please use the Correlation procedures within Excel under Tools > Data Analysis. The Scatter plot can more easily be generated using the Chart procedure.
Interpret the meaning of the slope, b1, in the regression equation.
Predict the monthly advertising cost when the number of orders is 5,100,000.
Compute the coefficient of determination, r2, and interpret its meaning.
Compute the standard error of estimate, and interpret its meaning.