For the values of the coefficient of determination listed below, which one yields the greatest value of sum of squares for regression given that the total sum of squares is 200?
A) 0.90
B) -0.90
C) 0.00
D) 0.98
E) -0.98

Question

Quizplus · Accepted Answer

The coefficient of determination (R-squared) is defined as the ratio of the explained variance to the total variance. Therefore, the higher the R-squared value, the greater the proportion of variance that is explained by the regression model.

The sum of squares for regression measures how much of the total variation in the response variable is explained by the regression model. It is calculated as SST - SSE, where SST is the total sum of squares and SSE is the sum of squared errors.

Given that the total sum of squares is 200, we want to choose the coefficient of determination that yields the greatest sum of squares for regression.

We know that SST = SSR + SSE, where SSR is the sum of squares for regression. Therefore, for a given value of R-squared, the larger the SSR, the smaller the SSE, and the greater the sum of squares for regression.

Among the choices given, the highest R-squared value is 0.98, which means that 98% of the variance in the response variable is explained by the regression model. Therefore, we expect the sum of squares for regression to be the highest for this choice, assuming that the regression model is a good fit for the data.

Choices A, B, C, and E have lower R-squared values and therefore would yield smaller sums of squares for regression.

For the Values of the Coefficient of Determination Listed Below