Question

doroteo determined that the correlation coefficient for a set data was -0.9. what percent of the total variation in the y-values is not explained by the regression line?

Answer 1

19% of the total variation in the y-values is not explained by the regression line

Explanation:

The correlation coefficient, r, is a measure of the degree of association between two variables. It gives information on the direction and strength of the relationship.

On the other hand,
`R^(2)` is the coefficient of determination and is a measure of the percent of the total variation in the y-values explained by the regression line.

`R^(2)` is simply the square of r;

`R^(2)=r^(2)=(-0.9)^(2)=0.81`

This implies that 81% of the total variation in the y-values is explained by the regression line. Therefore, only 19% is not explained.