Consider the following partial computer output for a multiple regression model.
$\begin{array}{l}\begin{array} { l l l } \text { Predictor } & \text { Coefficient } \left( \mathrm { b } _ { \mathrm { i } } \right) & \text { Standard Dev } \left( \mathrm { s } _ { \mathrm { b } } \right) \\\text { Constant } & 99.3883 & \\\mathrm { X } 1 & - 0.007207 & 0.0031 \\\mathrm { X } 2 & 0.0011336 & 0.00122 \\\mathrm { X } 3 & 0.9324 & 0.373\end{array}\\\text { Analysis of Variance }\\\begin{array} { l l l } \text { Source } & \text { df } & \text { SS } \\\text { Regression } & 3 & 31.308 \\\text { Error (residual) } & 16 & 9.378\end{array}\end{array}$
-What is the adjusted R²?

Question

Consider the following partial computer output for a multiple regression model.

\begin{array}{l}\begin{array} { l l l } \text { Predictor } & \text { Coefficient } \left( \mathrm { b } _ { \mathrm { i } } \right) & \text { Standard Dev } \left( \mathrm { s } _ { \mathrm { b } } \right) \\\text { Constant } & 99.3883 & \\\mathrm { X } 1 & - 0.007207 & 0.0031 \\\mathrm { X } 2 & 0.0011336 & 0.00122 \\\mathrm { X } 3 & 0.9324 & 0.373\end{array}\\\text { Analysis of Variance }\\\begin{array} { l l l } \text { Source } & \text { df } & \text { SS } \\\text { Regression } & 3 & 31.308 \\\text { Error (residual) } & 16 & 9.378\end{array}\end{array}

-What is the adjusted R²?

Quizplus · Accepted Answer

The adjusted R² is calculated using the formula: 1 - [(1-R²)(n-1)/(n-k-1)], where R² = SS Regression / (SS Regression + SS Error). Here, R² = 31.308 / (31.308 + 9.378) = 0.7695. With n = 20 (df total = 19) and k = 3, adjusted R² = 1 - [(1-0.7695)(19/16)] = 0.7263 or 72.63%.

Consider the Following Partial Computer Output for a Multiple Regression