# Functional Forms of Independent Variables

If our objective is to ascertain the relationship (specifically, sign and significance of Beta coefficient) between independent variables and dependent variable in an OLS regression (cross sectional or time series or panel regressions), should we actually care about an appropriate functional form of the independent variables? I have observed that in order to establish such relationship and to explain variation in the dependent variable, research papers keep on suggesting fresh set of variables as potential determinants of dependent variable without discussing the issue of functional form. For example, in majority of corporate finance research, some financial variables (explanatory variables) are picked up from the financial statements to explain variation in another financial variable (dependent variable) without even making a mention of the issue of functional form.

However, I have read in Gujarati (2009) that one must transform an independent variable by looking at its graphical relationship with dependent variable and then include it in the model. Further, I also have not come across a research paper which reports the results of RAMSEY RESET to suggest the appropriateness of the functional forms used by them in the model.

Thanks!

• Could you please explain what you mean by "functional form of the independent variables"? – whuber Dec 24 '18 at 16:17
• By functional form, I mean the mathematical transformation which is generally used to redefine a variable. For eg. taking log of a variable (log transformation), taking square of a variable (quadratic transformation), taking inverse of a variable (reciprocal transformation) etc. – Prateek Bedi Dec 24 '18 at 17:45
• You are therefore asking "should we actually care about [the mathematical transformation which is generally used to redefine a variable]?" This seems tautological, because one re-expresses a variable for some particular reason, not just for fun! For some information about this, please see the hits at stats.stackexchange.com/…. That leaves your question about the RESET test: are you trying to ask whether this test might be used to find appropriate ways to re-express variables? – whuber Dec 24 '18 at 17:53
• Let me re-frame the question. As mentioned here: stats.stackexchange.com/questions/298/…, one of the reasons for log transformation is to linearize a variable. Now since we are trying to fit a linear relationship between DV and IV in a regression and we observe that the graph does not suggest the same, we transform the IV in order to achieve a linear relation graphically. My question is why don't we always verify and attempt to achieve this graphical linear relationship between DV and IV? – Prateek Bedi Dec 24 '18 at 18:29
• Some methods I have described on this site are careful modeling (stats.stackexchange.com/a/64039/919 and stats.stackexchange.com/a/34186/919), Tukey's three-point method, and spread vs. level plots. There are many more methods, ranging from a "fractional polynomial" method for logistic regression described by Hosmer & Lemeshow all the way to machine-learning models like SVMs. – whuber Dec 26 '18 at 19:54