Logistic Regression
Abstract
In statistics, the logistic model (or logit model) is a statistical model that models the probability of an event taking place by having the log-odds for the event be a linear combination of one or more independent variables.
Introduction
Logistic regression is a statistical analysis method to predict a binary outcome, such as yes or no, based on prior observations of a data set. A logistic regression model predicts a dependent data variable by analyzing the relationship between one or more existing independent variables. For example, a logistic regression could be used to predict whether a political candidate will win or lose an election or whether a high school student will be admitted or not to a particular college. These binary outcomes allow straightforward decisions between two alternatives.
The most common logistic regression models a binary outcome; something that can take two values such as true/false, yes/no, and so on. Multinomial logistic regression can model scenarios where there are more than two possible discrete outcomes.
Types of logistic regression:
Binary logistic regression: In this approach, the response or dependent variable is dichotomous in nature—i.e. it has only two possible outcomes (e.g. 0 or 1).
Multinomial logistic regression: In this type of logistic regression model, the dependent variable has three or more possible outcomes; however, these values have no specified order.
Ordinal logistic regression: This type of logistic regression model is leveraged when the response variable has three or more possible outcome, but in this case, these values do have a defined order.
Uses:
Fraud detection: Logistic regression models can help teams identify data anomalies, which are predictive of fraud.
Disease prediction: In medicine, this analytics approach can be used to predict the likelihood of disease or illness for a given population.
Churn prediction: Specific behaviors may be indicative of churn in different functions of an organization
Formula
where P is the probability of a 1 (the proportion of 1s, the mean of Y), e is the base of the natural logarithm (about 2.718) and a and b are the parameters of the model.
Real life applications
Credit scoring
ID Finance is a financial company that makes predictive models for credit scoring. They need their models to be easily interpretable. They can be asked by a regulator about a certain decision at any moment. Logistic regression is widely used in credit scoring and it shows remarkable results.
Gaming
Speed is one of the advantages of logistic regression, and it is extremely useful in the gaming industry. Speed is very important in a game. Very popular today are the games where you can use in-game purchases to improve the gaming qualities of your character, or for fancy appearance and communication with other players. In-game purchases are a good place to introduce a recommendation system.
Text editing
It is worth mentioning that logistic regression is a popular choice in many natural language processing tasks. First, the text preprocessing is performed, then features are extracted, and finally, logistic regression is used to make some claim about a text fragment. Toxic speech detection, topic classification for questions to support, and email sorting are examples where logistic regression shows good results. Other popular algorithms for making a decision in these fields are support vector machines and random forest.
Problems and solutions
Q1. 
Solution:
Conclusion
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Therefore logistic regression produces a logistic curve, which is limited to values between 0 and 1. Logistic regression is similar to a linear regression, but the curve is constructed using the natural logarithm of the "odds" of the target variable, rather than the probability. Moreover, the predictors do not have to be normally distributed or have equal variance in each group.
References
[1]. https://en.wikipedia.org/wiki/Logistic_regression
[2]. http://faculty.cas.usf.edu/mbrannick/regression/Logistic.html
[3]. https://www.techtarget.com/searchbusinessanalytics/definition/logistic-regression