A multiple regression analysis based on a data set that consists of 30 observations yielded the following estimated equation:
Q = 120 - 1.1P + 3.7I + 0.90A
Where P is price, I is income, and A is advertising. If the coefficient of determination is 0.80, then the adjusted coefficient of determination is
A) 0.84.
B) 0.78.
C) 0.62.
D) 1.04.

Question

Quizplus · Accepted Answer

The adjusted 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: $ \bar{R}^2 = 1 - [(1 - R^2)(n - 1) / (n - k - 1)] $, where $ R^2 $ is the coefficient of determination, $ n $ is the number of observations, and $ k $ is the number of predictors. Here, $ R^2 = 0.80 $, $ n = 30 $, and $ k = 3 $ (since there are three predictors: P, I, and A). Plugging these values into the formula gives an adjusted $ R^2 $ that is slightly lower than the unadjusted $ R^2 $, which aligns with option B, 0.78, considering the formula tends to lower the $ R^2 $ value to penalize for the number of predictors.

A Multiple Regression Analysis Based on a Data Set That