Question

If the formula were used to find the r-value of the following data, what would be the value of to three decimal places?

x
y
3 2
5 7
9 10
11 14
14 18
A. 6.181
B. 5.528
C. 3.980
D. 4.450

Answer 1

0.0017947

Explanation:

x y xy
`x^2`
`y^2`

3 2 6 9 4

5 7 35 25 49

9 10 90 81 100

11 14 154 121 196

14 18 252 196 324

N = 5

`\sum x=3+5+9+11+14=42`

`\sum y=2+7+10+14+18=51`

`\sum (xy)=6+35+90+154+252=537`

`\sum x^2=9+25+81+121+196=432`

`\sum y^2=4+49+100+196+324=673`

Now to find r we will use the formula:

`r =(N\sum(xy)-\sum x \sum y)/((N \sum x^2 -(\sum x)^2)(N \sum y^2 -(\sum y)^2))`

Substitute the values to find value of r

`r =(5(537)-(42 * 51))/((5 (432) -(42)^2)(5(673) -(51)^2))`

`r =0.0017947`

Thus the value of r is 0.0017947

Answer 2

I think it is D. 4.450.