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 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 R²?

Quizplus · Accepted Answer

The R² refers to the R-squared (R^2) value of the regression model, which is calculated as the ratio of the regression sum of squares (SS) to the total sum of squares (TSS). TSS is the sum of the regression SS and the error (residual) SS. Here, R^2 = Regression SS / (Regression SS + Error SS) = 31.308 / (31.308 + 9.378) = 31.308 / 40.686 = 0.7695 or 76.95%.

Consider the Following Partial Computer Output for a Multiple Regression