Regression analysis of my research data showed a significant (p=0.0003) linear relationship between tested parameters. But, the R-square value of the model was 59.78. How can I interpret this result? Can I use the predicted model to further discuss of data?
Hi, Darshani, Is the R2 you provide the adjusted value -meaning, after taking into account the number of parameters in the model? And, by 59.78, do you mean, 59.78%, or 0.5978? If we assume the answer to these questions is yes, then yes, I'd say that this R2 value indicates that you've explained almost 60% of the variation in your dependent variable. Not bad at all. The correlation, r, is the square root of R2 , and is, in this case, 77.3%
Hi Darshani,
The R2 of 60% is not bad. But, it would be more appropriate to conduct regression diagnostic studies to understand whether the variables considered in the model are explaining your dependent variable significantly based on your data. A plot of regression residuals vs. fitted values would come handy to chek it.
Hello Darshani,
An R-squared of approximately 0.6 might be a tremendous amount of explained variation, or an unusually low amount of explained variation, depending upon the variables used as predictors (IVs) and the outcome variable (DV). Context matters for interpretation.
Jacob Cohen, in his 1988 text, Statistical power analysis for the behavioral sciences (2nd ed.), offered guidelines for social/behavioral sciences in interpreting magnitude of R-squared when an understanding of context was unavailable:
R-squared = .02 (yes, 2% of variance). "Small" effect size.
R-squared = .13. "Medium" effect size.
R-squared = .26. "Large" effect size.
However, in your field, these values may be unrealistic.
Good luck with your work!
Just to clarify: Mary wrote "The correlation, r, is the square root of R2 , and is, in this case, 77.3%". Strictly this is multiple correlation coefficient R (the correlation between observed data and model predictions) not r. R = r only if there is a single predictor. With multiple predictors (the case here) r is undefined.
Yes, what is a "good" r-squared to a psychologist may not be a "good" r-squared to an analytical chemist!
Dear all, thank you very much for your valuable comments.
Best regards,
Dear Mary,
Here, R2 = 59.78%, Adjusted R2 = 57.1%.
Thanks!
One belated reply -- yes your field does matter, and the level of the data matters more. In sociology and psychology, researchers who rely on micro-level data (basically, persons) may be very happy even with R-sq below 10% (adjusted or not). On the other hand, economists using macro-level data (e.g., nations) in predictive models often get R-sq of 99%+. I'm sorry but I do not know the ranges in agricultural studies.
As some of the comments above indicates it depends on the purpose of the study. For example if it is for series cases in medical drugs we may need less error and more accuracy however in some case we may tolerate some amount of inaccuracy. Anyhow R^2 shows that how much the dependent variable is explained or cause due to the independent/explanatory variables. Generally, it indicates the variability caused by independent variables. It also shows how much the model has fit well. In contrast to that the high value of R^2 doesn't mean always the model is good fit because when we add more independent variables in the model it may obviously increase. So, it is good to check diagnostics checking of the model to verify the goodness of the model.
Regression analysis of my research data showed a significant (p=0.0003) linear relationship between tested parameters. But, the R-square value of the model was 59.78. How can I interpret this result? Can I use the predicted model to further discuss of data?
Case1.
Correlation measures the degree of linear relationship between two variables. If your regression model is linear (that is, of the model Y=a+bx), and a good and standard statistical package such as SPSS (Statistic Package for Social Sciences) used, the result (r=0.773175; R2 =59.78; p=0.0003; p
Dear Dauglas, Yemane and Felix, Thank you very much for your contribution.
Best regards,
In a recently conducted regression analysis between student perception and scores, I have a low adjusted r-square of 10.4% only (although the factors are significant predictors of the DV). Can this be attributed to the unpredictability of human perceptions??
Samrat,
For your data set, it may be the case that: (a) the measure(s) you used do not yield scores with as high a reliability and/or validity as might be desired; (b) that you have an unusual sample; or (c) that there genuinely isn't an extraordinarily strong relationship between the kinds of perception and performance indicators you used.
There is literature to support the latter point, especially confirming that peoples' self-appraisal is often poorly calibrated to their performance potential. See, for example, this web site: http://www.porterblepeople.com/2015/03/why-we-are-all-competent-idiots-the-dunning-kruger-effect/
Finally, don't forget that "low" and "high" values of r-square do depend on the specific variables and population under investigation.
Good luck with your work!
Thank you so much David. I actually conducted a factor analysis (perception questionnaire) from which I derived 5 factors to correlate with the student scores (DV). The factor that explained the most variance is not showing any correlation but two of the other factors that explained only about 4% variance each showed significant relationship (even after a regression analysis) with the DV. However, the adj.R squared value was low. was not sure how to report these findings.
Namaskar
I am working on panel data. As per my regression analysis the R-square value of the model was R-squared 0.369134 Adjusted R-squared 0.302597. Kindly suggest ways to solve the issue.