In a recent post I raised the point about the spurious degree of precision that is often encountered with reported regression results. So, here's a challenge for you - how many decimal places (or maybe significant digits) are appropriate when reporting OLS regression results?
Of course, the answer will depend on the data that are used, and the precision to which they are available in the first place, so let's be specific. Consider the following sample of n = 10 observations:
These data are in a text file on the Data page that goes with this blog.
Suppose that I estimate the following simple regression model by OLS:
yi = α + β xi + εi ; i = 1, 2, 3, ...., 10.
Here is the output that's obtained when the model is estimated using EViews:
Here are the results when you use the (free!) gretl package:
(The EViews and gretl files are available this blog's Code page.)
I have a slight preference for the gretl output - can you see why?
Given the precision of the original data, what level of numerical precision (number of decimal places) do you think is really appropriate here when reporting:
- The estimated regression coefficients?
- The standard errors?
- The coefficient of determination (R2)?
I'll look forward to your comments!
© 2011, David E. Giles