R square and adjusted r square

[Shikha Sachdeva]

Hello all 

What are the ways of improving r square and adjusted r square when its extremely low (below 0.10)? And how important is it when out of 3 IDVs i have got 2 significant p values in one regression model and the study is cross sectional and comes under orrganisational behaviour and development, but the r square is extremely low. 

Regards

Shikha

[Neeraj Kaushik]

Dear Shikha

Low r2 indicate any of the two possibilities:

1. Poor Review of Literature. 

There might be some very important IDVs which are not considered. You might consider reviewing once again about the predictors of your DV.

2. OLS Regression talks about the linear relation. If there is the curvilinear or non-linear relation between the vars(s), this procedure will not be able to capture that. Use scatter plot to determine the relationship between DV and IDV and then if reqd, use Curve-estimation option in Regression.

Best wishes

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[Dr. Rudra Rameshwar]

Dear Shikha,

You need to understand that R-square is a measure of explanatory power, not fit.

You can generate lots of data with low R-square, because we don't expect models (especially in social or behavioral sciences) to include all the relevant predictors to explain an outcome variable. You can cite works by Neter, Wasserman, et al. or many other authors about R-square.

You should note that R-square, even when small, can be significantly different from 0, indicating that your regression model has statistically significant explanatory power. However, you should always report the value of R-square as an effect size, because people might question the practical significance of the value.

As I said, in some fields, R-square is typically higher, because it is easier to specify complete, well-specified models. But in the social sciences, where it is hard to specify such modes, low R-square values are often expected. You can read about the difference between statistical significance and effect sizes if you want to know more.

This question goes to the multiple uses of regression. If one's purpose is to build very efficient predictive models, then maximizing R2 or adj. R2 is key. 

In the social sciences and management area, where most often we're interested in testing hypotheses about certain variables while adjusting for the effects of others, the significance levels of key variables are much more important (although that's perhaps a discussion for another forum).

If in your model you determine that you are or are not able to reject H0s of interest, the amount of variance explained by your total model is more or less irrelevant. Hope that helps and good luck with your analysis.

For more details, don't forget to refer given link and below reference in addition to above explanation - Link: https://www.stata.com/support/faqs/statistics/two-stage-least-squares/

Reference: Bedeian, A. G. & Mossholder, K. W. 1994. Simple question, not so simple answer: Interpreting interaction terms in moderated multiple regression. Journal of Management, 20(1): 159-165.

Best wishes,

Rudra

On Sat, Sep 23, 2017 at 9:58 PM, Shikha Sachdeva <5seps...@gmail.com> wrote:

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[Neeraj Kaushik]

Excellent explanation Sir.

I wish to hear more often from you.

Regards

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