Finding Coefficient of Determination

[Tchao]

Homework Statement

If the slope of the regression line is negative and the correlation coefficient is -0.5, coefficient of determination is:

Homework Equations

coefficient of determination: r² = 1 - SSE/SST

correlation coefficient: r = S_xy / (√S_xx * √S_yy )

The Attempt at a Solution

r = -0.5
r² = 0.25 but because slope of regression line is negative, then coefficient of determination would be also negative.
r² = -0.25

I am not sure if my though process in determining the correct answer is right or not.

 

[I like Serena]

Homework Statement

If the slope of the regression line is negative and the correlation coefficient is -0.5, coefficient of determination is:

Homework Equations

coefficient of determination: r² = 1 - SSE/SST

correlation coefficient: r = S_xy / (√S_xx * √S_yy )

The Attempt at a Solution

r = -0.5
r² = 0.25 but because slope of regression line is negative, then coefficient of determination would be also negative.
r² = -0.25

I am not sure if my though process in determining the correct answer is right or not.

Hi Tchao,

Indeed, the coefficient of determination is $r^2=0.25$.
And it is positive, since a square is always positive.
It means that the coefficient of determination doesn't tell us whether the slope is upward or downward, only that there is a correlation.