Continuous output: logistic vs linear regression

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Main Question or Discussion Point

so say I suspect that there is a positive trend in the data from the scatter plot. Say the output y is continuous.

A linear regression would give me a possitive estimate of the slope. For a one unit increase in x, I would get a so and so increase in y.

I can also split the data for the y variable between high and low, dichotomizing it. And calculate the estimated increase in log odds for a one unit increase in x.

Is there even a point in doing so?

It seems like the question can be answered using linear regression.

I don't see the point in using logistic regression unless the output is necessarily binary (gender, political affiliation etc)

Even if we are interested in a output of,say,having high income vs low income, you can just have income as a continuous spectrum and use ols to get the answer.

Is there something I'm missing?
 

Answers and Replies

  • #2
andrewkirk
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Yes, logistic regression was designed for cases with a binary result, like death or loan default. The only circumstance in which I can imagine it might be worth considering a logistic regression for a continuous result variable is where the variable's distribution is strongly bimodal, with nearly all values clustering around one or the other of two widely separated points, and very low probability densities in between. Even then I'm not sure what value it would add, but it might add something.
 
  • #3
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Yes, logistic regression was designed for cases with a binary result, like death or loan default. The only circumstance in which I can imagine it might be worth considering a logistic regression for a continuous result variable is where the variable's distribution is strongly bimodal, with nearly all values clustering around one or the other of two widely separated points, and very low probability densities in between. Even then I'm not sure what value it would add, but it might add something.
That makes sense. Because we can meaningfully cut the data and categorize it between high and low values. If the data were not bimodal, then we can't make a meaningful cut and any logistic analysis that follow would only give the log odds of passing that cut, which isn't even valid in the first place.
 
  • #4
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If your data has outliers, or if it violates any assumptions of the OLS regression, and provided you are looking for a binary answer, it could be a good idea to transform the response variable to a binary one and do a logistic regression instead. It would be interesting to compare both though!
 
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  • #5
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so say I suspect that there is a positive trend in the data from the scatter plot. Say the output y is continuous.

A linear regression would give me a possitive estimate of the slope. For a one unit increase in x, I would get a so and so increase in y.

I can also split the data for the y variable between high and low, dichotomizing it. And calculate the estimated increase in log odds for a one unit increase in x.

Is there even a point in doing so?

It seems like the question can be answered using linear regression.

I don't see the point in using logistic regression unless the output is necessarily binary (gender, political affiliation etc)

Even if we are interested in a output of,say,having high income vs low income, you can just have income as a continuous spectrum and use ols to get the answer.

Is there something I'm missing?
It depends. If you want to spot a trend, check regression. The output will tell you whether there is a "reasonable" linear regression ( if the confidence interval of the slope does not include 0 ); you also check the value of the coefficient r, so that is "high-enough". As Andrew said, logistic regression is most often used in classification: you set up a cutoff point , e.g., you have a yes beyond your chosen cutoff point and a no otherwise.
 

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