Given that SSE = 150 and SSR = 450, the proportion of the variation in y that is explained by the variation in x is 0.75.

Question

Quizplus · Accepted Answer

The proportion of the variation in y explained by the variation in x is given by the coefficient of determination (R^2), which is defined as:

R^2 = SSR/SSE

Substituting the given values, we get:

R^2 = 450/150 = 3

This means that 300% of the variation in y is explained by the variation in x, which is more than 100% and therefore technically impossible. It is likely that one or both of the given values are incorrect.

However, since the given options do not include "uncertain" or "cannot be determined", we can only go by the calculations and say that R^2 cannot be 0.75, as this would require SSR to be 112.5 (since SSR/SSE = 0.75 and SSE = 150). Therefore, the only valid option is A.

Given That SSE = 150 and SSR = 450, the Proportion