The R squared value indicates the goodness of fit of the model; that is, it can help explain the variability of the data close to the mean, but in social studies there are many outliers and data can be difficult to obtain. I've read that a low R squared value is not necessarily bad. My question is why? And should I interpret it?
Generally, R2 values can only be compared with the R2s that other researchers have found for the topic you are studying. In analyses based on surveys, R2 seldom go over 50%, and 30% may be very good in some study areas and very bad in others. Outliers is a general problem that is separate from R2 (although it can reduce R2) and the question for the analyst is to determine what to do with them - that is, keep them in the sample or not :-)
This really depends on your research question. Statistics mean nothing except in the context of the research question or hypothesis that you are trying to address. If your question is whether some variable has any predictive power (i.e., if a model with that variable predicts the data better than a model without) then absolute R2 doesn't matter at all, all that matters is the change in R2 between the models you're comparing. Just think about the goals of your research and what is needed to accomplish them. If absolute R2 is irrelevant to your hypothesis, then ignore it.
Thank you both for these answers; they help tremendously. My study examined English education background variables (including a numeric assessment of English proficiency) and its influence on income in tourism employees. I ran several simple and multiple regressions using income as the dependent and other variables as the independents. My sample was not incredibly large, but small either (292 respondents). I got R squared values of 11, 13, and 16%. I haven’t been able to find many similar studies. At any rate, these R2 values are positive. Now I have a much better angle on how to interpret these values.
R2 is always positive. R2 represents the percentage of variance in the dependent variable that the model accounts for; the model can't account for a negative percentage of variance. (Plus, R2 is literally "R squared". The square of any [real, nonzero] number is always positive.)
Yes, once it is squared it becomes positive (the reason for squaring too). Perhaps I miswrote...what I really mean is that the values are not low, such 2 or 3%, clearly not near zero. My prediction is that higher English proficiency as well as longer years of English education result in higher incomes. My R2 values then could indicate quite significant findings.
R2 isn't really relevant to your prediction, then. Your prediction would be tested by testing the coefficient for proficiency; if it's positive and significant, then your prediction is supported. Another way to test this is with model comparison: you construct a model including proficiency as a predictor, and another maximally similar model without proficiency in it, and then see if the first model fits the data significantly better than the second (as indicated by a significant increase in R2). Either way, either of these tests could still be significant in a model with R2 of only 2 or 3%, as long as that's still significantly higher than the model you're comparing it to. So, R2 doesn't matter at all for a test of statistical significance. (It might matter for measuring practical importance [although in your case I think the regression coefficient atters more] but that is a separate question, and one that isn't really directly measured by statistical tests.)
Also note that R2 itself could never answer your research question of whether "higher English proficiency as well as longer years of English education result in higher incomes." Hypothetically speaking, you could have data where higher English proficiency and more English education result in lower incomes, but this effect is very robust and there are few other sources of variance in income; such a model might have an R2 like 90% or something, but would be completely inconsistent with your prediction. So, again, R2 is not really relevant.
Ok, thank you for the explanation. I think what I would be comparing my outcome to is very important then. I just started to do regression with my data and have been looking for other studies to compare to it. I've examined the data with descriptive statistics and whatnot and wanted to try regression, butI'm beginning to feel that regression is not the best statistical test to use in this situation.
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