For a multiple regression model, SSR = 600 and SSE = 200.The multiple coefficient of determination is

A) .333.
B) .275.
C) .30.
D) .75.

The multiple coefficient of determination, denoted as R-squared (R²), is defined as the proportion of variation in the dependent variable (y) that is explained by the independent variables (x's) in the multiple regression model. It ranges from 0 to 1, with higher values indicating a better fit of the model to the data.

R² is calculated as:

R² = SSR / SST

where SST (total sum of squares) is the sum of the squared differences between the observed y values and the mean of y. In other words, SST measures the total variation in y.

Since the model has k independent variables and n observations, we can write:

SST = SSR + SSE

where SSE (error sum of squares) is the sum of the squared differences between the observed y values and the predicted y values from the model. In other words, SSE measures the unexplained variation in y.

Substituting the given values, we get:

SST = 600 + 200 = 800

R² = SSR / SST = 600 / 800 = 0.75

Therefore, the multiple coefficient of determination is 0.75, which means that 75% of the variation in the dependent variable is explained by the independent variables in the model. The best choice is D.