The following sums of squares are produced: $\Sigma$ $$\left( y _ { i } - \bar { y } \right) ^ { 2 }$$ = 250, $\Sigma$ $\left( y _ { i } - \hat { y } _ { i } \right) ^ { 2 }$ = 100, $\Sigma$ $\left( \hat { y } _ { i } - \bar { y } \right) ^ { 2 }$ = 150.
The percentage of the variation in y that is explained by the variation in x is:
A)60%.
B)75%.
C)40%.
D)50%.

Question

Quizplus · Accepted Answer

The percentage of the variation in y that is explained by the variation in x is calculated using the formula for the coefficient of determination, $R^2 = \frac{SSR}{SST}$, where SSR (regression sum of squares) is $\left( \hat { y } _ { i } - \bar { y } \right) ^ { 2 } = 150$ and SST (total sum of squares) is $\left( y _ { i } - \bar { y } \right) ^ { 2 } = 250$. Thus, $R^2 = \frac{150}{250} = 0.6$ or 60%.

The Following Sums of Squares Are Produced Σ\SigmaΣ (yi−yˉ)2\left( y _ { i } - \bar { y } \right) ^ { 2 }(yi​−yˉ​)2

The Following Sums of Squares Are Produced $\Sigma$ $\left( y _ { i } - \bar { y } \right) ^ { 2 }$