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# Re: st: Statistically significant difference in R Squared

 From Richard Williams To statalist@hsphsun2.harvard.edu, "statalist@hsphsun2.harvard.edu" Subject Re: st: Statistically significant difference in R Squared Date Fri, 24 Aug 2012 10:16:45 -0400

```At 08:15 AM 8/24/2012, Christopher Baum wrote:
```
```<>
On Aug 24, 2012, at 2:33 AM, Ani wrote:

> I am running a time-series regression model over a 10 year period. I would
```
> be interested in splitting the sample into two five year periods and finding
```> out whether the model has a statistically significantly higher R^2 during
```
> the second period as compared to the first. Is there a test for this, and if
```> so is it possible to implement in Stata?

```
I don't think this is a very well posed question. In the example below, -robvar- applied to the residuals of a single model shows that the forecast performance of the model deteriorates after 1987q3. Running separate subperiod regressions confirms this: the model produces more accurate forecasts in the earlier period. Yet the R^2 is higher in the later subperiod! I would be more interested in the model's accuracy, in terms of forecast confidence intervals, than I would in R^2.
```
use http://fmwww.bc.edu/cfb/data/usmacro1,clear
reg d.cpi d.oilprice d.wage, robust
predict double res if e(sample)
g break = (tin(1987q3,))
robvar res, by(break)
reg d.cpi d.oilprice d.wage if !break, robust
reg d.cpi d.oilprice d.wage if break, robust
```
```
```
I would add that R^2 can be affected by many things. A larger R^2 could be due to a bigger structural coefficient in one group, but it could also be due to things like differences in the exogenous variances. A simple discussion of this can be found at
```
http://www.nd.edu/~rwilliam/xsoc63993/l72.pdf

-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
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