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
