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:
[tex]r=\dfrac{\sum{XY}}{\sqrt{\sum{X^2}\sum{Y^2}}}--------------(1)[/tex]
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 Â Â Â 67 Â Â Â -20 Â Â Â Â Â Â -95 Â Â Â Â Â 1900 Â Â 400 Â Â Â 9025
25 Â Â 122 Â Â Â -10 Â Â Â Â Â Â -40 Â Â Â Â Â Â 400 Â Â Â 100 Â Â Â 1600
35 Â Â 164 Â Â Â Â 0 Â Â Â Â Â Â Â 2 Â Â Â Â Â Â Â 0 Â Â Â Â Â 0 Â Â Â Â Â Â 4
45 Â Â 210 Â Â Â 10 Â Â Â Â Â Â 48 Â Â Â Â Â Â 480 Â Â Â 100 Â Â Â 2304
55 Â Â 247 Â Â Â 20 Â Â Â Â Â Â 85 Â Â Â Â Â 1700 Â Â Â 400 Â Â Â 7225
x' be the mean of the data of the x-values.
[tex]x'=\dfrac{15+25+35+45+55}{5}\\\\\\x'=\dfrac{175}{5}\\\\\\x'=35[/tex]
Also let y' denote the mean of the y-values.
[tex]y'=\dfrac{67+122+164+210+247}{5}\\\\\\y'=\dfrac{810}{5}\\\\\\y'=162[/tex]
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
