Question

Use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage of the total variation that can be explained by the linear relationship between the two variables. requals0.952 What is the value of the coefficient of​ determination?

Answer 1

Explanation:

Given that
`r = 0.952`

We have coefficient of determination

`r^2 =0.952^2\\=0.906304`

=90.63%

This implies that nearly 91% of variation in change in dependent variable is due to the change in x.

The coefficient of determination is the square of the correlation (r) between predicted y scores and actual y scores; thus, it ranges from 0 to 1.

An R2 of 0 means that the dependent variable cannot be predicted from the independent variable.

An R2 of 1 means the dependent variable can be predicted without error from the independent variable.