low R-squared values and p-values above 0.1

[jrhoworth]

I am using regression to look at the relationship between different measures of well-being and income, with 100 obvs and 14 independent variables.

For all of my regression models, the R-squared values are very low, with the highest one being 22.16%.

Then for all of the independent variables the p-values are very high, with some of them being up to 0.9.

Does this suggest that there is no relationship that is statistically significant between well-being and income? Can i still use this dataset or does this suggest it isn't very good?

[Richard Williams]

First off, that R^2 value does not strike me as being inherently low. Second, with 100 cases, it is going to be hard to get significant results for a few independent variables, let alone 14. If you add extraneous variables to a model, the standard errors go up, making it harder and harder to identify any variables whose effects may be important. Try to figure out what the really important variables are from a theoretical standpoint and then trim down your model accordingly. Or, consider whether some of your items could be combined into scales.

[jrhoworth]

Would reducing the number of predictors increase the risk of bias in the estimators? I've reduced the independent variables to 2 and the p-value is still very large.

[Richard Williams]

This handout briefly discusses the trade-off between leaving relevant variables out (possibly causing omitted variable bias) and putting extraneous variables in (possibly leading to inflated standard errors). You don't want estimates to be biased but at the same time you can't afford to toss in bunches of dubious variables just to be safe, especially when your sample size is small.

http://www3.nd.edu/~rwilliam/xsoc63993/l41.pdf

If you can't get significant effects even with only one or two variables, it may be that the sample is too small or the effects really are zero.