I need to implement a backward stepwise regression. I read the chapter from "The Elements of Statistical Learning" however the explanation is poor here:
Backward-stepwise selection starts with the full model, and sequentially deletes the predictor that has the least impact on the fit. The candidate for dropping is the variable with the smallest Z-score This is taken from chapter 3.3.2 pg:59
I need to know what is the "full model" mentioned here? What will I delete at each level acording to the Z-score? I need to know how this algorithm works step by step.
EDIT: I try to implement the code on matlab. I don't know I'm totally wrong or not :/ Comment on this function please
function  = BackwardStepWise(X,y,N,p) % X is Nxp matrice y is Nx1 matrice X = [ones(N,1) X]; % vector for holding column numbers v= 1:p; for k=p-1:-1:1 %create matrix with the selected columns T= [ones(N,1)]; for j=1:k %add column to the matrix T = [T X(:,v(1,j)+1)]; endfor %evaluate beta beta = inv(T' * T) * T' * y; %calculate Z-scores for each column sigmahat_sq = (y-T*beta)'*(y-T*beta)/(N-p-1); TT = inv(T'*T); Zmin = 100000; Zminindex = -1; for i=1:size(beta,2) z(i) = beta(i)/sqrt(sigmahat_sq*TT(i,i)); if(z(i) < Zmin) Zmin = z(i); Zminindex = i; endif endfor %drop column which has the smallest Z score (edit v vector) v2 = ; for i=1:size(v,2) if(i == Zminindex) continue; else v2 = [v2 v(i)]; endif endfor v = v2; endfor endfunction