My data is violating the linearity assumption of multiple regression. What should I do to resolve this issue?

[Muhammad Danial Khan]

I am checking the effect of a group of variables on another using the Multiple regression model in Stata. Attached is a document where i have checked for linearity assumption using scatter plots and augmented component plus residual plot. My data is violating the linearity assumption of multiple regression. What should I do to resolve this issue?

[Clyde Schechter]

Please read the FAQ, to increase your chances of getting a timely, helpful response. Attaching Microsoft Office documents is discouraged on this forum. Some of the frequent responders don't use Office. Others, like me, who do, will not download an Office document from a stranger, because they can contain malware (which, by the way, has recently been a particular problem for Word documents.) The best way to show Stata output is to copy/paste it directly from your log file onto this forum between code delimiters. (You will learn about code delimiters when you read the FAQ.) If you want to show graphs, you should -export- them from Stata as .png files and attach those.

Generically, when there is non-linearity, the solution is to look for a transformation of one or more variables that will linearize the relationship. Just what transformation and which variables to transform depends entirely on the situation, which is why you need to show your results in order to comment specifically.

[Muhammad Danial Khan]

Thank you Sir. I am uploading the png files. Please take a look at my data.

[Muhammad Danial Khan]

Acpr plots

[Clyde Schechter]

Well, the -rvpplot-s are not very convincing one way or another: you have a small number of data points, and it isn't clear in those plots whether you have a problem or not.

But the acpr plots for equity to assets, debt to equity and tier 1 capital are pretty clearly non-linear, and somewhat less convincing is ln(assets to liabilities).

However, before we jump to conclusions, it is possible for the outcome variable to have a linear relationship to a combination of variables, even though it doesn't have a good linear relationship to any one of them. And I didn't see in your outputs an overall -rvfplot-. If the error structure looks OK there, I wouldn't really worry about it. If, however, that one is not supportive of linearity, then I think you need to look at transforming some of these variables. For the three that I've mentioned above as persuasive, if I were approaching this in a vacuum, I would probably try including a quadratic term in each of those variables. That said, I do not work in finance, and it may be that there are well known standard approaches to use for these particular variables. If so, you should go with those. A review of the finance literature may be helpful, or you might ask a colleague in your discipline for advice. Or perhaps one of the many people who work in finance and follow this forum will chime in.

[Richard Williams]

Are there really only 10 cases in these regressions??? That is what it looks like to me, but maybe each dot represents a 100 cases. If only 10 though, that is going to limit how much you can do.

Some general advice on dealing with nonlinear relations can be found at

http://fmwww.bc.edu/repec/bocode/t/transint.html

http://www3.nd.edu/~rwilliam/stats2/l61.pdf

I agree with Clyde that my first impulse would be to include a squared term. But presumably you are not the first person in the world to deal with issues like this so see what the literature says.