I have run a regressions relating metal revenue to a metal index in each of 25 different factories. In 24 of the factorias $R^2$ is greater than .75. In one factory the $R^2$ is .061.
Why is that $R^2$ is so low in one factory?
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You can think of the R-squared as a property of the factory. You should have a conceptual understanding of why there should be a relationship between your two variables in each factory and what leads to stronger or weaker relationships. You have encountered an outlier observation (i.e., the factory with low $R^2$). It's up to you to analyse the data and think about what might have caused the outlier. As @whuber notes a useful strategy is to plot the scatterplots of your two variables in each organisation, and particularly in the outlier organisation. There may be a mistyped datapoint in the outlier. Alternatively, something unique may have been occurring in the factory to prevent the relationship from holding (e.g., the factory broke down or their was industrial action, etc.). |
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The $R^2$ is small which just means that the regression is not a very good fit. You can have a poorly fitting regression and still have the regression coefficient statistically significantly different from 0. This could happen if you had a lot of data so that the variance of the regression coefficient is small and hence the coefficient itself can be statistically significantly different from 0 even though it is small. Nevertheless you could still have large residuals meaning that the regression model only explains a small percentage of the total variance, 6.1% in your case. |
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