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This is a question asked in my homework assignment, the full question is "Is Logistic Regression actually used for regression (predicting a continuous value)? If not, state what task it really solves and why the name includes “regression." It feels like it's leading us toward the answer "no", but the only source that clearly states no is ChatGPT, which isn't reliable.

Some sources that I have found are

Which kind of say no, but there are also questionnaires like

that give ambiguous answers on whether logistic regression can be used as regression.

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Yes. A logistic regression predicts values on a continuum, on the interval $[0,1]$ (arguably on the open interval). Work through the equation: you take a linear combination of some feature values and then apply the inverse of the log-odds.

It is common, even if neither necessary nor always recommended, to bin those continuous predictions into categories to make categorical predictions that can be assessed by measures like accuracy and $F_1$ score. However, that is a separate step on top of the logistic regression, and I recommend learning how logistic regressions can have their predictions interpreted as probability values and how those probability values can inform decision-making. A number of links on my profile about proper scoring rules provide some good information on this and link to other sources that can take you down the rabbit hole.

This is related to a question on the statistics Stack, Cross Validated.

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  • $\begingroup$ This is a detailed answer, but I feel it misses the point of the question. The question is about what logistic regression is used for, not what it does. It does perform regression, but it is used for classification. It may have problems for normative reasons, as you argue, but that is a different issue in my opinion. $\endgroup$ Commented Nov 5 at 2:38
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You will get different answers depending on whether you're asking from a purely theoretical or purely applied perspective.

Simply put: Logistic regression is mathematically a regression technique, but in practice, it is almost always thresholded and thus turned into a binary classifier.

You will rarely find cases for using logistic regression for actual regression tasks. Consider the logistic function: $$f(x) = \frac{L}{1 + e^{-k(x - x_{0})}}$$

this function's most interesting property to data scientists is that it models binary probabilities. This is an attribute that is rarely needed in regression tasks.

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  • $\begingroup$ -1 I recommend reading the other answer and its linked material. Logistic regressions absolutely predict on a continuum, and there are plenty of instances where those continuous values are considered. $\endgroup$ Commented Nov 5 at 22:50
  • $\begingroup$ Hi, I did read them. I fear you are misunderstanding me. I actually agree with you on this! I agree that using logistic regression for classification has pitfalls for the reasons you mentioned, and that there are valid instances of using logistic regression without a threshold. My point is that this is not what the question is. It is not asking what logistics regression is, but what it is used for. The answer to this is classification. If you sampled a hundred instances of real-world usage of logistic regression, how many of them would be used for classification? $\endgroup$ Commented Nov 6 at 20:08

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