Question

What is the r value of the following data to three decimal places x y 4 2 5 9 8 10 9 12 13 23

Answer 1

The value of r is 0.953.

Explanation:

The correlation coefficient i.e. r is calculated by the formula,

`r=\frac{n\sum{xy}-(\sum x)(\sum y)}{√((n\sum x^2-(\sum x)^2)(n\sum y^2-(\sum y)^2))}`

where n=5 is the sample size.

We create a table of required values,

x y x² y² xy

4 2 16 4 8

5 9 25 81 45

8 10 64 100 80

9 12 81 144 108

13 23 169 529 299

∑ 39 56 355 858 540

Substitute the values in the formula,

`r=(5* 540-(39)\cdot (56))/(√((5* 355-(39)^2)(5* 858-(56)^2)))`

`r=(2700-2184)/(√((254)(1154)))`

`r=(516)/(√(293116))`

`r=(516)/(541.4018)`

`r=0.9530`

Therefore, the value of r is 0.953.

Answer 2

0.953081279

Explanation:

we have been given the following data set;

x; 4, 5, 8, 9, 13

y; 2, 9, 10, 12, 23

We are required to determine the r value of the data set.The r-value is the correlation coefficient that is used to measure the degree of association between two variables. It gives us information on the strength and direction of the association.

We can easily compute r in Ms. Excel;

We first enter the data into any two adjacent columns of an excel workbook.

Then we proceed to type;

=CORREL

into any blank cell. This is an in-built function that computes the correlation coefficient. Ms. Excel returns a value of 0.953081279

as the r value