Answer:

Hence, the correlation coefficient is:

               r=1.0

Step-by-step explanation:

We know that the correlation coefficient ”r” is calculated by the formula:

r=dfrac{sum{XY}}{sqrt{sum{X^2}sum{Y^2}}}--------------(1)

Let x denote the data point (Number of days since purchase)

Let y denote the data point (Mileage Displayed on odometer)

x         y        X=x-x’       Y=y-y’        XY         X²          Y²

15      67       -20            -95           1900     400      9025

25     122      -10            -40            400       100       1600

35     164        0               2               0           0            4

45     210       10             48             480       100       2304

55     247      20             85           1700       400      7225

x’ be the mean of the data of the x-values.

x'=dfrac{15+25+35+45+55}{5}\\\x'=dfrac{175}{5}\\\x'=35

Also let y’ denote the mean of the y-values.

y'=dfrac{67+122+164+210+247}{5}\\\y'=dfrac{810}{5}\\\y'=162

Now we have:

∑ XY=4480

∑ X²=1000

∑ Y²=20158

Hence, we put all the  values in the formula (1) to obtain:

r=0.997 which is close to 1.0

Also from the scatter plot we could observe that the relationship is linear and also strong positive relationship.

Hence, the correlation coefficient is 1.0