Texts: [Please explain each step and what was done to get the answer.] Pharmex is a chain of drugstores that operate around the country. To see how effective its advertising and other promotional activities are, the company has collected data from 50 randomly selected metropolitan regions. In each region, it has compared its own promotional expenditure and sales to those of the leading competitor in the region over the past year. The data include two variables: PROMOTE: Pharmex’s promotional expenditures as a percentage of those of the leading competitor. SALES: Pharmex’s sales as a percentage of those of the leading competitor. At the end of this problem, you will find the computer output that is relevant to this problem.
1. What is the response variable? ___________
2. From the scatter plot, does there seem to be a linear relationship between the two? YES/NO (circle). If not, sketch the type of relationship that you see (if any).
3. What is the variance of SALES? _____________.
4. Complete the missing numbers in the regression output.
5. How does an increase of 10 units in PROMOTE manifest itself in SALES? ___________________________________
6. The null hypothesis that the slope is 0 (vs. the alternative of not zero) can be tested using the _____ statistic. Its value is ________ and its p-value is _____________.
7. Based on (6.), we fail to reject/reject (circle) the null hypothesis at a 5% significance level.
8. State your conclusion in non-statistical words: ___________________________ ________________________________________________________________
9. Using only the Sales data, if in a certain month Pharmex spends 110 (percentage relative to competitors), what would be your best prediction of their sales? _________
10. Using the information on both Sales and Promote, if in a certain month Pharmex spends 110 (percentage relative to competitors), what would be your best prediction of their sales? _________
11. Which prediction is more accurate? __________ Why? ___________________________________
COMPUTER OUTPUT FOR PROBLEM 1
Regression Plot: Sales = 25.1264 + 0.762296 Promote
S = 7.39473
R-Sq = 45.3%
R-Sq(adj) = 44.2%
20
110
Sales 100
100 Promote
110
120
Regression Analysis: Sales versus Promote
The regression equation is Sales = 25.13 + Promote
Estimate
Std. Error
t value
Pr(>|t)
(Intercept)
0.040
Promote
0.000
25.13
2.11
0.7623
0.1209
Analysis of Variance Table
Response: Sales
Df
F value
Pr(>F)
Promote
1
39.74
0.000
Residuals
48
Sum Sq.
Mean Sq.
2172.9
2172.9
54.7