Question

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 expenditures and sales to those of the leading competitor in the region over the past year. There are two variables: "Promote" reflects Pharmex’s promotional expenditures as a percentage of those of the leading competitor, and "Sales" reflects Pharmex’s sales as a percentage of those of the leading competitor. A portion of the data appears below. Show all work.

Region Promote Sales Region Promote Sales Region Promot Sales
1 77 85 21 103 112 41 100 94
2 110 103 22 95 96 42 96 81
3 110 102 23 103 93 43 88 92
4 93 109 24 89 97 44 109 108
5 90 85 25 97 92 45 109 103
a. Using Excel, create a scatterplot of the data. What do you observe? What type of relationship, if any, is apparent from the scatterplot?
b. Insert a trendline (click on the scatterplot, then click the Layout tab, and choose Trendline). What type of trendline seems to fit best?
c. Under "More Trendline Options," select "Display Equation on chart" and "Display R-squared value on chart." What do you see? What do these numbers mean?

Answer 1

Positive relationship exists

Linear trend line

R² = 0.3522

Explanation:

Given the data :

Promote (X) :

77

110

110

93

90

103

95

103

89

97

100

96

88

109

109

Sales (Y) :

85

103

102

109

85

112

96

93

97

92

94

81

92

108

103

A.) From the resulting plot, tbe slope of the graph is positive, hence, we can conclude that there exist a positive relationship between the variables 'promote' and 'sale'.

The linear trend line gives the best fit for the data with a correlation Coefficient, R value of 0.5935

The R² value is 0.3522. R² is the Coefficient of determination which gives the percentage of explained variation. For this data, about 35% of variation in sales is given by the best fit line.