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 for models dealing with continuous dependent variables?
See Bernoulli's probability distribution
P (Y=y)= py (1-p)1-y = (p/1-p)y (1-p) = eyln(p/1-p)+(1-p) y=0, 1
So the Bernoulli distribution can easily be converted to an exponential distribution.
We call ln(p/1-p) the natural parameter of exponential distribution.
Now in a logistic regression model, this natural parameter is placed in the Dependent Variable position, ie
ln(p/1-p) = y = b0 +b1X1 + b2X2 + .... + bkXk y=0, 1
Pay attention to y=0, 1
Dependent variable is not a categorical dependent variable, it can only accept two values of zero and one.
Logistic regression is originally a regression technique. By including a decision rule, it is transformed into a classifier. It is more successful in classification problems but it is also used in regression problems.
I agree with Serkan Balli's point
Logistic regression is the appropriate regression analysis to conduct when the dependent variable is dichotomous (binary). Like all regression analyses, the logistic regression is a predictive analysis. Logistic regression is used to describe data and to explain the relationship between one dependent binary variable and one or more nominal, ordinal, interval or ratio-level independent variables.
On the other hand, the logistic classification model (or logit model) is a binary classification model in which the conditional probability of one of the two possible realizations of the output variable is assumed to be equal to a linear combination of the input variables, transformed by the logistic function.
The way I see it, logistic regression is a classifier that uses regression techniques. The output of the logit function used in logistic regression is indeed continuous (probability of log odds). However, you can impose a threshold to these probabilities and thus predict categories. Thus, you successfully used a regression technique to predict classes.
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