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A regression equation is computed to predict the weight of a bear (inlb) using the predictor variables 鈥渨eight鈥�, 鈥渓ength,鈥� and 鈥渃hest size.鈥�

The p-value and the adjusted\({R^2}\)value are 0.000 and 0.925, respectively.

Further, another predictor variable 鈥渘eck size鈥� is added to the equation, and the p-value and the adjusted \({R^2}\) are 0.000 and 0.933, respectively.

To identify the best regression equation, consider the equation with the highest value of adjusted\({R^2}\).

Here, the regression equation with two independent variables, 鈥渓ength鈥� and 鈥渃hest size鈥�, has the adjusted \({R^2}\) value of 0.925. Moreover, the p-value for this regression is equal to 0.000, indicating that the regression is significant.

Further, another predictor variable 鈥渘eck size鈥� is added to the previous equation.

Now, the regression equation with three independent variables of 鈥渓ength鈥�, 鈥渃hest size鈥� and 鈥渘eck size鈥� has a new adjusted \({R^2}\) value at 0.933.The new p-value is 0.000, which implies that the new regression is still significant.

Here,

\(\begin{array}{c}{\rm{New}}\;{\rm{Adjusted}}\;{R^2} > {\rm{Adjusted}}\;{R^2}\\0.933 > 0.925\end{array}\)

Since the new regression equation with the variable 鈥渘eck size鈥� has a larger value of adjusted\({R^2}\)and the regression is significant, the new regression equation is the best. It explains more variation in the response variable as compared to the equation with only two predictors.