That seems too simple.

- Thread starter noetsi
- Start date

That seems too simple.

regards

Well, there are a few ways to think about this - for any given particular design. For example, the classical easy case would be Y=Performance and regressed on X=Anxiety. This case has been demonstrated - time and again - that X^2 (Anxiety^2) should be included into the regression model.

Another way to think about this is in an ANOVA/Regression context: That is, R^2 in an ANOVA context provides the Correlation Ratio (think of, say 4 groups, with 3 dummy vectors), whereas the R^2 from the regression context, with one X, provides the linear relationship between the dependent variable (Y) and X (X is quantitative). The difference between the Correlation Ratio and the R^2 from a linear regression analysis is referred to as the "Deviation from Linearity". That s aid, typically a hierarchical approach is taken to approach the problem i.e., linear, quadratic, cubic, quartic.....but seldom does research go beyond a quadratic fit.

The same can be said in the context of what is called "Trend Analysis."

And, interaction terms are also relevant in the context of an IV (X) which can be considered as a "Moderating Variable."

Summary: It's all about the context and what prior research has demonstrated for any given research topic.

Another way to think about this is in an ANOVA/Regression context: That is, R^2 in an ANOVA context provides the Correlation Ratio (think of, say 4 groups, with 3 dummy vectors), whereas the R^2 from the regression context, with one X, provides the linear relationship between the dependent variable (Y) and X (X is quantitative). The difference between the Correlation Ratio and the R^2 from a linear regression analysis is referred to as the "Deviation from Linearity". That s aid, typically a hierarchical approach is taken to approach the problem i.e., linear, quadratic, cubic, quartic.....but seldom does research go beyond a quadratic fit.

The same can be said in the context of what is called "Trend Analysis."

And, interaction terms are also relevant in the context of an IV (X) which can be considered as a "Moderating Variable."

Summary: It's all about the context and what prior research has demonstrated for any given research topic.

Last edited:

regards

That seems too simple.

I thought one of the good things about straight up OLS regression is that one can plot the residuals and look for patterns there?

I mean it's not an exact formal test but it's definitely something nice to look at.

I mean it's not an exact formal test but it's definitely something nice to look at.

You can, but my data commonly has 10,000 points or more so even plotting partial regression plots to test non-linearity (as recommended) commonly results in large blobs of data. Its not easy to see any pattern in that, which is why I was looking for a formal test.

http://blogs.sas.com/content/iml/2011/03/04/how-to-use-transparency-to-overcome-overplotting.html

Have you tried sorting the residuals then sampling every ith point (say every 100th point)? I know it sounds crude, but it would get rid of the "blob" effect and allow you to see a pattern.

Also, someone mentioned code for a heat map in another post. This might help you see a pattern even through the blob.

http://www.talkstats.com/showthread.php/65358-Interpreting-residuals?highlight=heat+map