Homework SourseA pharmaceutical company is investigating the relationship b
A pharmaceutical company is investigating the relationship between advertising expenditures and the sales of some over-the-counter (OTC) drugs. The following data represents a sample of 10 common OTC drugs. Find the equation of the regression line, using Advertising dollars as the independent variable and Sales as the dependent variable. Interpret the slope of the line in the words of the problem. Find r2 and interpret it in the words of the problem. Use the line to predict the Sales if Advertising dollars = $50 million. Note that AD = Advertising dollars in millions and S = Sales in millions $.
AD
S
22
64
25
74
29
82
35
90
38
100
42
120
46
120
52
142
65
180
88
230
| AD | S |
| 22 | 64 |
| 25 | 74 |
| 29 | 82 |
| 35 | 90 |
| 38 | 100 |
| 42 | 120 |
| 46 | 120 |
| 52 | 142 |
| 65 | 180 |
| 88 | 230 |
Solution
Calculator Output
a = 6.629, b = 2.569, r = .996
y-hat = 6.629 + 2.569x
The slope = 2.569 means that for every increase of $1 million Advertising, sales increases $2.569 million on average.
r2 = .993 so there is a 99.3% reduction in error for predicting Sales using advertising dollars.
y-hat = 6.629 + 2.596(50) = 135.079
