If the value of the coefficient of multiple determination $R ^ { 2 }$ is .80 for a quadratic regression model, and that n = 11, then the adjusted $R ^ { 2 }$ value is
A) .75
B) .80
C) .85
D) .90
E) .95

Question

Quizplus · Accepted Answer

The adjusted $R^2$ value is calculated using the formula: $$ \text{Adjusted } R^2 = 1 - (1-R^2)\frac{n-1}{n-p-1} $$ where $R^2$ is the coefficient of determination, $n$ is the number of observations, and $p$ is the number of predictors. For a quadratic regression model, $p = 2$ (since we have the terms $x$ and $x^2$). Plugging in the values: $R^2 = 0.80$, $n = 11$, and $p = 2$, we get: $$ \text{Adjusted } R^2 = 1 - (1-0.80)\frac{11-1}{11-2-1} = 1 - (0.20)\frac{10}{8} = 1 - 0.25 = 0.75. $$

If the Value of the Coefficient of Multiple Determination R2R ^ { 2 }R2

If the Value of the Coefficient of Multiple Determination $R ^ { 2 }$