ON THE STEPWISE CONSTRUCTION OF A PREDICTION EQUATION.
SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS
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In the analysis of data, it is often desired to construct an equation of the form y b0 b1x1 b2x2 ... bkxk, where y is the response variable and x1, x2, ..., xk are input variables. A familiar method of constructing such an equation is known as the forward selection procedure. At some stage of the forward selection procedure when p variables are being considered for entry into the equation, the ratio Fi SSRiMSE is computed for each variable being considered. If the ratio F maxF1, F2, ..., Fp is greater than some constant F0, the variable xi associated with this maximum ratio is included in the equation. The joint distribution of F1, F2, ..., Fp is determined under the usual assumptions for the regression model including normality of the error. Through this the distribution of F is given. Different philosophies exist concerning the choice of the value for F0. In this paper the probability integral of F is computed for p 3 and comparisons are made among the critical points F0 for these different philosophies. Author
- Statistics and Probability