Finding Coefficient of Determination

1. Apr 23, 2017

Tchao

1. The problem statement, all variables and given/known data

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

2. Relevant equations

coefficient of determination: r2 = 1 - SSE/SST

correlation coefficient: r = Sxy / (√Sxx * √Syy )

3. 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.

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2. Apr 24, 2017

I like Serena

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.