If you have the Statistics and Machine Learning Toolbox, it sounds like you want this:
>> x = randn(20,3);
>> y = x*[1 0;0 1;1 1];
>> corr(x,y)
ans =
0.9221 -0.1434
-0.2979 0.8438
0.6825 0.5606
I'm not sure what you mean by mean squared error. The following adds some noise to get z, then computes coefficients for predicting y from z, then computes the sum of squared differences between y and the predicted values for each column. Does this point you in the right direction?
>> z = x+randn(size(x))/100;
>> b
b =
0.9983 -0.0009
-0.0000 0.9964
1.0016 1.0049
>> sum((y-yhat).^2)
ans =
0.0025 0.0054
