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

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.