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Re: st: Testing to compare goodness of fit

From   Nick Cox <>
Subject   Re: st: Testing to compare goodness of fit
Date   Tue, 4 Oct 2011 21:51:07 +0100

Relying on R-sq alone is not a good idea.

Goodness of fit can be compared by

1. Plotting the two sets of predictions in time.
1a. Plotting the two sets of residuals in time.

2. Looking for autocorrelation in residuals.

3. Scatter plots of observed vs predicted in each case.
3a. Residual vs predicted plots.

One maxim is never to use a R-sq without inspecting the corresponding
scatter plot. Another is that a good model is associated with
pattern-free residuals.

If the models look equally good, there is likely to be some scientific
reason to discriminate between them.


On Tue, Oct 4, 2011 at 9:35 PM,  <> wrote:

I have two univariate time series models, both explaining variable Y,
one with variable X and one with variable Z as the explanatory
variable (plus a constant). Now, both models yield an R-squared that
is rather close to each other. Can I really say that model X is better
than model Z just by comparing these R-squareds (since with 5
observation more or less, things might look different)? Or can I test
whether these r-squareds are statistically different from each other?
Any other idea to evaluate goodness of fit in that case, except for
comparing RMSE? Or is in this case comparing (f-testing) the
coefficients of X and Z helpful?
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