Question

The table contains data on the mileage displayed on a bicycle odometer as it relates to the number of days since the bicycle was purchased. Using the Scatter Plot tool, find the value of the correlation coefficient for this data set.

0.8

1.0

0.3

0.1

Answer 1

Hence, the correlation coefficient is:

r=1.0

Explanation:

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

`r=\frac{\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'=(15+25+35+45+55)/(5)\\\\\\x'=(175)/(5)\\\\\\x'=35`

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

`y'=(67+122+164+210+247)/(5)\\\\\\y'=(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

Answer 2

Based on the given table above, and using the scatter plot tool, the value of the correlation coefficient for this data set would be r = 0.997, so if you round this off, you will get 1.0. So the answer for this would be the second option which is 1.0. I hope this is the answer that you are looking for.