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Estimating Optimal Transformations for Multiple Regression and Correlation

Leo Breiman, Jerome H. Friedman
1985 Journal of the American Statistical Association  
In regression analysis the response variable Y and the predictor variables X 1 ,... ,X p are often replaced by functions O(Y) and , p (X p). We discuss a procedure for estimating those functions 8* and €{,...,cp that minimize 1 p E{[(Y) -(X e 2 _ j = l 1 VarLe(Y)j given only a sample {(Ykxkl,...,xkp), 1 <k<N} and making minimal assumptions concerning the data distribution or the form of the solution functions. For the bivariate case, p =l, e* and 4* satisfy p= p(e*,o*) = max p[e(Y), (X)] where
more » ... p[e(Y), (X)] where p is the product moment corre-40 lation coefficient and p* is the maximal correlation between X and Y. Our procedure thus also provides a method for estimating the maximal correlation between two variables.
doi:10.2307/2288473 fatcat:7dpzs3qdnvgbva6vvsc5ew3the