>> x=1:10;x=x';y=rand(size(x)); % some toy data
>> [b,~,~,~,stats]=regress(y,[ones(size(x)) x]); % not standardized
>> [bz,~,~,~,zstats]=regress(y,[ones(size(x)) zscore(x)]); % standardize x
>> [stats' zstats']
ans =
0.0100 0.0100
0.0808 0.0808
0.7834 0.7834
0.0643 0.0643
They're the same...just must remember to standardize x before evaluating the regression.
Now, add in standarization of y, too...
>> [bzy,~,~,~,zystats]=regress(zscore(y),[ones(size(x)) zscore(x)]);
>> [stats' zstats' zystats']
ans =
0.0100 0.0100 0.0100
0.0808 0.0808 0.0808
0.7834 0.7834 0.7834
0.0643 0.0643 1.1137
>>
Now the variance of the residuals is different because the scale factor for y is changed--with the rand() y used here, it's actually larger numerical since std(y)<1.
The upshot is, those statistics whose values are dependent upon the magnitude are scaled per the computation of the statistic whereas those that are either not scaled depending on which version of standardization used (x or x and y) or are invariant to the magnitude of the variables aren't.
