[R] in R when I get negative adjusted R^2 using "lm", what might be the problem?

[Peter Dalgaard]

Tom Backer Johnsen wrote:
> Greg Snow wrote:
>> No problem, adjusted R-squared can be negative.  If there truly is no
>> relationship, then the adjusted R-squared should average to 0, so
>> sometimes it must be negative.  All of your R-squared and adjusted
>> R-squared values suggest that there is not much of a relationship
>> (less without the transform).
> 
> Nevertheless, there remains the logical problem of a negative squared
> value.

Not really, it is an adjusted squared value, not a squared adjusted
one... Other programs have used "% variance accounted for", which is
effectively the same thing modulo a factor of 100%, and that too can be
negative if the variance actually increases.

> 
> In any case, given the relatively large difference between the R-square
> and the adjusted value, he probably has a relative large number of
> independent variables compared to the number of rows in the data set.
> And the dependent variable is probably quite skewed as well.

Yes. An unfortunately placed large outlier could have this sort of
effect. (Was the orignal question homework? If so, the intention was
probably to have the student look into residuals and influence plots. If
not, it still seem like that would be a good idea.)

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