Why isn't Logistic Regression called Logistic Classification? Since Logistic Regression is a statistical classification model dealing with categorical dependent variables, why isn't it called Logistic Classification? Shouldn't the "Regression" name be reserved to models dealing with continuous dependent variables?
 A: 
Blockquote
The U.S. Weather Service has always phrased rain forecasts as probabilities. I do not want a classification of “it will rain today.” There is a slight loss/disutility of carrying an umbrella, and I want to be the one to make the tradeoff.
Blockquote

Dr. Frank Harrell, https://www.fharrell.com/post/classification/
Classification is when you make a concrete determination of what category something is a part of. Binary classification involves two categories, and by the law of the excluded middle, that means binary classification is for determining whether something “is” or “is not” part of a single category. There either are children playing in the park today (1), or there are not (0).
Although the variable you are targeting in logistic regression is a classification, logistic regression does not actually individually classify things for you: it just gives you probabilities (or log odds ratios in the logit form). The only way logistic regression can actually classify stuff is if you apply a rule to the probability output. For example, you may round probabilities greater than or equal to 50% to 1, and probabilities less than 50% to 0, and that’s your classification.
if you want to read more please check this link for more detail
https://ryxcommar.com/2020/06/27/why-do-so-many-practicing-data-scientists-not-understand-logistic-regression/
A: Abstractly, regression is the problem of calculating a conditional expectation $E[Y|X=x]$. The form taken by this expectation is different depending on the assumptions of how the data were generated:


*

*Assuming (Y|X=x) to be normally distributed yields with classical linear regression.

*Assuming a Poisson distribution yields Poisson regression.

*Assuming a Bernoulli distribution yields logistic regression.


The term "regression" has also been used more generally than this, including approaches like quantile regression, which estimates a given quantile of $(Y|X=x)$.
A: Logistic regression is emphatically not a classification algorithm on its own. It is only a classification algorithm in combination with a decision rule that makes dichotomous the predicted probabilities of the outcome. Logistic regression is a regression model because it estimates the probability of class membership as a (transformation of a) multilinear function of the features.
Frank Harrell has posted a number of answers on this website enumerating the pitfalls of regarding logistic regression as a classification algorithm. Among them:

*

*Classification is a decision. To make an optimal decision, you need to asses a utility function, which implies that you need to account for the uncertainty in the outcome, i.e. a probability.

*The costs of misclassification are not uniform across all units.

*Don't use cutoffs.

*Use proper scoring rules.

*The problem is actually risk estimation, not classification.
If I recall correctly, he once pointed me to his book on regression strategies for more elaboration on these (and more!) points, but I can't seem to find that particular post.
A: Apart from already provided good answers, another view is that Logistic regression predicts probabilities (which is continuous value) that have got range from 0 to 1. 

