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
|
$55.93
|
4,102,000
|
|
2
|
70.62
|
3,893,000
|
|
3
|
79.58
|
5,299,000
|
|
4
|
58.67
|
4,130,000
|
|
5
|
69.18
|
4,367,000
|
|
6
|
70.14
|
4,111,000
|
|
7
|
73.37
|
3,923,000
|
|
8
|
68.88
|
4,935,000
|
|
9
|
80.99
|
5,276,000
|
|
10
|
75.23
|
4,654,000
|
|
11
|
71.38
|
4,398,000
|
|
12
|
52.90
|
2,967,000
|
|
13
|
61.27
|
3,999,000
|
|
14
|
79.19
|
4,345,000
|
|
15
|
60.03
|
3,834,000
|
|
16
|
78.21
|
4,653,000
|
|
17
|
93.77
|
5,625,000
|
|
18
|
62.53
|
3,978,000
|
|
19
|
78.76
|
4,999,000
|
|
20
|
92.64
|
5,834,000
|
a. Set up a scatter diagram and calculate the associated correlation coefficient. Discuss how strong you think the relationship is between the amount of money spent on television advertising and the number of orders received. Please use the Correlation procedures within Excel under Tools > Data Analysis. The Scatterplot can more easily be generated using the Chart procedure.
b. Assuming there is a statistically significant relationship, use the least squares 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.
c. Interpret the meaning of the slope, b1, in the regression equation.
d. Predict the monthly advertising cost when the number of orders is 4,999,000. (Hint: Be very careful with assigning the dependent variable for this problem)
e. Compute the coefficient of determination, r2, and interpret its meaning.
f. Compute the standard error of estimate, and interpret its meaning.