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I have run multiple regression models with factor scores as the DV with several predictor variables (all dichotomous patient characteristics e.g. gender, age). Whilst some predictors and the models are significant, it can only explain less than 2% of the variance at best. We have a large sample size of over 800 participants.

Could this be because... - all the predictors variables are dichotomous - the predictors are not highly correlated with the DV (e.g. ~0.1) - there is not enough variance in the DV

My main questions are why is there such little variance explained, and would it be an issue to report the significant predictors within a paper yet with the overall model only explaining about 2% of the variance?

Thank you

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  • $\begingroup$ It would certainly be an issue if the overall model F-test is not significant--which it very well might not be with such a low $R^2$ (depending on how many variables you have considered). $\endgroup$
    – whuber ♦
    Apr 14 '20 at 16:09
  • $\begingroup$ Thank you for your comment. The overall model was always significant and the predictors also often highly significant. $\endgroup$
    – Megan_G
    Apr 15 '20 at 8:43
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Without seeing data, the answer is a definite maybe. Using only binary independent variables to explain a continuous dependent variable we might expect a low R^2 because the variance of any individual independent variable is simply restricted to 0 and 1. Simultaneously, a data set could still exhibit certain patterns that a binary variable might be able to explain well, so an R^2 of 0.02 is surprising. It may be what you have guessed: the independent variables, or the form you have them in, do not translate well into a good fit for a linear model, i.e. the variance in the dependent variable is not explained well by the independent variables.

Should you still report it? ….If you are creating a predictive model, only if the model you create has a reasonably low generalization error (but with a low R^2 I'd assume that's probably not the case). If you are making a causal argument, you may IF you can make a reasonable argument that the predictors you included are causally related to the dependent variable and other assumptions (exogeneity, autocorrelation, exclusion of other variables) are addressed.

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    $\begingroup$ Thank you for your helpful response. We were hoping to report it in an exploratory, descriptive manner whilst tentatively suggesting variables that may be able to predict the factors that were generated within a factor analysis. $\endgroup$
    – Megan_G
    Apr 15 '20 at 8:40

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