Question

"Find the coefficient of determination given that the correlation coefficient = -.39"

(Give your answer as a decimal rounded to the ten thousandth decimal place.)

Answer 1

`r = -0.39`

And the determination coeffcient is just the correlation coeffcient square and we got:

`R = r^2 = (-0.39)^2 =0.1521`

And rounded to the nearest tenth thousand would be 0.1521

Explanation:

The correlation coefficient is a measure of variability and is given by this formula:

`r=(n(\sum xy)-(\sum x)(\sum y))/(√([n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]))`

For this case we have

`r = -0.39`

And the determination coeffcient is just the correlation coeffcient square and we got:

`R = r^2 = (-0.39)^2 =0.1521`

And rounded to the nearest tenth thousand would be 0.1521