Question

is there any scenarios when can a low R2 value be acceptable?

Answer 1

R² is very important statistic .R-squared is a statistical measure of how close the data are to the fitted regression line. It is also known as the coefficient of determination, or the coefficient of multiple determination for multiple regression.

A big R² is always said to be good it doesn't mean a small one is always bad.Generally it is said that no regression model with an R² smaller than .7 should even be interpreted but there may be a context in which that rule makes sense, but as a general rule, no.Just because effect size is small doesn’t mean it’s bad, unworthy of being interpreted, or useless. It’s just small. Even small effect sizes can have scientific or clinical significance. It depends on your field.

Let the model R² be .04, although the model can be significant.It’s easy to dismiss the model as being useless because you’re only explaining 4% of the variation? Why bother?But if you think about all of the things that might affect someone’s health, do you really expect religious attendance to be a major contributor?

Even though you are not a health researcher but you can think about such few variables that you would expect to be much better predictors of health. For example age, disease history, stress levels, family history of disease, job conditions.And putting all of them into the model would indeed give better predicted values.

The point was to see if there was a small, but reliable relationship and there was.

Do small effect sizes require larger samples to find significance? Sure. But this data set had over 10000 people. Will not be a problem.

Some researchers turned to using effect sizes because evaluating effects using p-values alone can be misleading. But effect sizes can be misleading too if you don’t think about what they mean within the research context.

Sometimes being able to easily improve an outcome by 4% is clinically or scientifically important. Sometimes it’s not even close enough.   Sometimes it depends on how much time, effort, or money would be required to get a 4% improvement.

As much as we’d all love to have straight answers to what’s big enough, that’s not the job of any statistic. You’ve got to think about it and interpret accordingly depend upon the different scenario.

You can think it alternatively as well that the interpretation of the R-squared will depend upon whether the output is significant or not. You can see the significance of this in the ANOVA output. In most instance is the ANOVA test that the R- and R-squared are significant, even if they are low in value, still you can use them in your research. The interpretation of the coefficients should be be solely based on the value itself.

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