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by jrd79
1547 days ago
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You are avoiding the question of whether it is appropriate to present the results of a linear regression on data that is so poorly explained by a linear relationship. Random looking balls of data points don't have slopes. It is invalid to perform a linear fit on data that does not derive in large part from a linear generative process. And presenting a fit from a model that is facially absurd to apply is bad data science. Whether or not an informed reader would discount the absurd model fit is not material to whether it is appropriate to present such a fit. They could have binned the data and plotted percentile bands. They could have used a non-parametric density estimator. There are lots of things they could have done to summarize the data and make some sense of the ball of points. But linear regression with slope error bars is not an appropriate choice. That it is easy to compute linear fits, and that it helped them make their point is not justification. |
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That is exactly what they are saying. This is from TFA:
> The graphics above demonstrate that variation in rates of homelessness cannot be explained by variation in rates of individual factors such as poverty and mental illness.
They are, in my words, saying "Look at this plot, the x-axis has no bearing on the y-axis. To give you a sense of how bad it is, we fit a line to it and it is exactly 0 useful." I don't know why you are focusing so hard on the plots without reading their words. You are in agreement with TFA. Now, for the plot with R^2 of 0.55, that clearly has some positive relationship to it.
As for your last paragraph, I disagree 100%. They are trying to find an explanatory variable, not "summarize the data". By showing all the points, it is evident there is no relationship. As you have continuously pointed this out, the plot achieved its goal. In my opinion, the line is a nice touch for statisticians to know that no illusions from scaling of the axes are playing tricks.