A multiple regression analysis involving three independent variables and 25 data points results in a value of 0.769 for the unadjusted multiple coefficient of determination. Then, the adjusted multiple coefficient of determination is:
A) 0.385
B) 0.877
C) 0.591
D) 0.736
E) 0.819

Question

Quizplus · Accepted Answer

The adjusted multiple coefficient of determination is calculated to account for the number of predictors in the model relative to the number of observations. It is given by the formula: $1 - [(1 - R^2)(n - 1) / (n - k - 1)]$, where $R^2$ is the unadjusted coefficient of determination, $n$ is the number of observations, and $k$ is the number of predictors. Plugging in the given values ($R^2 = 0.769$, $n = 25$, $k = 3$), the calculation yields an adjusted $R^2$ value of approximately 0.736.

A Multiple Regression Analysis Involving Three Independent Variables and 25