Question

If the r-value or correlation coefficient of a data set is 0.827, what is the coefficient of determination to three decimal places?

A. 0.884
B. 0.627
C. 0.684
D. 0.827

Answer 1

Answer: Option C

`r ^ 2 = 0.684`

Explanation:

The correlation coefficient r is a measure of how strong the relationship between two variables x and y is.

If the value of r is positive then the correlation is positive and that implies that the variable x grows together with the variable y.

If the value of r is negative that means that the correlation is negative and that implies that when the variable x grows then the variable y decreases.

Then for a relationship, the coefficient of determination
`r ^ 2` is a measure of how well the model fit the data or how accurate the model is. While r is closer to 1, better is the precision of the model.

The coefficient of determination
`r ^ 2` for a linear relationship is calculated as the square of the correlation coefficient.

In this problem we have that the correlation coefficient r is

`r = 0.827`

then the coefficient of determination is:

`r ^ 2 = 0.827 ^ 2`

`r ^ 2 = 0.684`

The answer is option C