11.37 Because the coefficient of determination R2 never decreases when a new independent variable is added to the model, it is tempting to include many variables in a model to force R2 to be near 1. However, doing so reduces the degrees of freedom available for estimating , which adversely affects our ability to make reliable inferences. As an example, suppose you want to use 18 economic indicators to predict next year’s GNP.You fit the model where Y  GNP and , are indicators.

Only 20 years of data (n  20) are used to fit the model, and you obtain R2  0.95. Test to x1, x2, Á , x18 Y = b0 + b1x1 + b2x2 + Á + b17x17 + b18x18 + e see whether this impressive-looking R2 value is large enough for you to infer that this model is useful, that is, that at least one term in the model is important for predicting GNP. Use  
0.05.