For a multiple regression model, $\sum \left( y _ { i } - \bar { y } \right) ^ { 2 } = 250$ , and $\sum \left( y _ { i } - \hat { y } _ { i } \right) ^ { 2 } = 60$ , then the proportion of the total variation in the observed $y _ { i}$ 's that is not explained by the model is
A) .76
B) .24
C) 310
D) 190
E) .52

Question

Quizplus · Accepted Answer

The proportion of the total variation not explained by the model is given by the ratio of the sum of squares of residuals ($\sum (y_i - \hat{y}_i)^2$) to the total sum of squares ($\sum (y_i - \bar{y})^2$). Thus, it is $\frac{60}{250} = 0.24$.

For a Multiple Regression Model ∑(yi−yˉ)2=250\sum \left( y _ { i } - \bar { y } \right) ^ { 2 } = 250∑(yi​−yˉ​)2=250

For a Multiple Regression Model $\sum \left( y _ { i } - \bar { y } \right) ^ { 2 } = 250$