Question

Graph using the scatter plot diagram and interpret the following data.

71-80. The owner of a chain of fruit shake stores would like to study the correlation between atmospheric temperature and sales during the summer season. Suppose a random sample of 12 days is selected with the results given as follows:

 

Day

Temperature(F⁰)

(x)

Total Sales (Units)

(y)

1

79

147

2

76

143

3

78

147

4

84

168

5

90

206

6

83

155

7

93

192

8

94

211

9

97

209

10

85

187

11

88

200

12

82

150

 

Answer 1

A scatter diagram for the data given is obtained from entering the following commands in $R$

> x=c(79,76,78,84,90,83,93,94,97,85,88,82)

> y=c(147,143,147,168,206,155,192,211,209,187,200,150)

> plot(x,y,main="Scatter plot of sales against temperature")

These commands produces the scatter diagram below.

Clearly, the values of sales increases with increase in temperature. We can therefore predict that there is a strong positive correlation between sales and temperature. To verify this, we need to determine the correlation coefficient $r$.

To obtain the value of the correlation coefficient, we enter the following commands in $R$

> x=c(79,76,78,84,90,83,93,94,97,85,88,82)

> y=c(147,143,147,168,206,155,192,211,209,187,200,150)

> cor(x,y)

[1] 0.9270573

The value of $r=0.9270573$ shows that there is a strong positive correlation between sales and temperature.