In a simple linear regression analysis,the following sums of squares are produced: $\sum \left( Y _ { i } - \bar { Y } \right) ^ { 2 } = 400 , \sum \left( Y _ { i } - Y \right) ^ { 2 } = 80 , \sum \left( \bar { Y } _ { i } - \bar { Y } \right) ^ { 2 } = 320$
The proportion of the variation in Y that is explained by the variation in X is:
A) 20%
B) 80%
C) 25%
D) 50%
E) None of the above

Question

Quizplus · Accepted Answer

The proportion of the variation in Y that is explained by the variation in X is the coefficient of determination, which is equal to the square of the correlation coefficient. The correlation coefficient is equal to the square root of the ratio of the explained variation to the total variation. In this case, the explained variation is 80 and the total variation is 400 + 80 = 480. Therefore, the coefficient of determination is 80/480 = 0.1667, or 16.67%.

In a Simple Linear Regression Analysis,the Following Sums of Squares