Respuesta :
Answer:
0.953081279
Step-by-step 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
Answer:
The value of r is 0.953.
Step-by-step explanation:
The correlation coefficient i.e. r is calculated by the formula,
[tex]r=\dfrac{n\sum{xy}-(\sum x)(\sum y)}{\sqrt{(n\sum x^2-(\sum x)^2)(n\sum y^2-(\sum y)^2)}}[/tex]
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,
[tex]r=\dfrac{5\times 540-(39)\cdot (56)}{\sqrt{(5\times 355-(39)^2)(5\times 858-(56)^2)}}[/tex]
[tex]r=\dfrac{2700-2184}{\sqrt{(254)(1154)}}[/tex]
[tex]r=\dfrac{516}{\sqrt{293116}}[/tex]
[tex]r=\dfrac{516}{541.4018}[/tex]
[tex]r=0.9530[/tex]
Therefore, the value of r is 0.953.
