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I'm new to regression (vector autoregression), and recently encountered the following issue:

  1. If I use raw dependent and independent variables to do the regression, the $R^2$, DW-d test and standard error of estimate for each dependent variable are quite good. The $R^2$ is above $95\%$.

  2. However, When the dependent and independent variables are normalized to zero mean and unit variables (column normalized), these measures got worse. The $R^2$ ranges from $60\%-90\%$.

So what happened after I normalized the data?

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    $\begingroup$ I don't think it is possible for the $R^2$ to change. You didn't state the reason for normalization. I can't think of any. $\endgroup$
    – Frank Harrell
    Commented Dec 26, 2013 at 1:26

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Frank Harrell is right, it's not possible for the R2 to change, unless you've done something unusual like ... removed the intercept from your regression. See for yourself with this R-fiddle.

My suggestion? Put the intercept back in. See, for example, "Regression through the Origin and Its Pitfalls".

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