In a simple linear regression problem, the following sum of squares are produced: . The percentage of the variation in y that is explained by the variation in x is:

A) 25%
B) 75%
C) 33%
D) 50%
E) 150%

The percentage of variation in y that is explained by the variation in x is given by the coefficient of determination, which is the ratio of the explained variation to the total variation. The explained variation is the sum of squares of regression (SSR), and the total variation is the sum of squares total (SST). Therefore, the coefficient of determination is:

$R^2 = SSR/SST = (SST - SSE)/SST = 1 - SSE/SST$

where SSE is the sum of squares error.

Since only the SSR is given in the problem, we cannot directly calculate R^2. However, we do know that SSE + SSR = SST. Therefore, we can calculate SSE by subtracting SSR from SST:

SSE = SST - SSR =

Now we can calculate R^2:

$R^2 = 1 - SSE/SST = 1 - 11eb6b9e_0615_3536_8d9d_f1ad2453b7cd_TB8220_12 /11eb6b9e_0615_3536_8d9d_f1ad2453b7cd_TB8220_11 = 0.75$

Therefore, the percentage of variation in y that is explained by the variation in x is 75%, which corresponds to choice B.