what is the fastest way to do many univariate regression? same Y against different x, one x at a time

try to use for loop

i have Y, a column vector, 133x1 and a data matrix, X, 133x6; the first column are ones, starting from second column x1, x2,x3, x4, and x5

i was thinking to use for loop e.g. a=1:5 Z=[X(:,1) X(:,1+a)] % so each time, it takes the column of ones and one x variable and form a new matrix of 133x2

then to run another loop to regress Y against each of those new matrix

anyone has another idea how to do?

Answer 1

[Alfonso Nieto-Castanon]

Not terribly different in practice, but if you want you could compute all of those regressions simultaneously using a sparse block diagonal data matrix, e.g.:

 [N,M] = size(X);
 Xblk = sparse(repmat(1:N*(M-1),2,1)', repmat([1:2:2*(M-1) 2:2:2*(M-1)],N,1), X(:,[ones(1,M-1) 2:M]));
 B = Xblk \ repmat(Y,M-1,1);

B will contain first the two coefficients of the first regression, followed by the two coefficients of the second regression, etc.

Answer 2

[bing cai]

don't really get it...

But, do you know how to do it using for loop?