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Logistic Regression gives the probability associated with each category or each individual outcome. The probability function is joined with the linear equation using probability distribution. In Logistic Regression we use binomial distribution where we work on two category problems.

**Example 1** – Suppose we are interested in the factors that influence whether a political candidate wins an election or not. The outcome (response) variable is binary (0/1); win or lose. The predictor variables of interest are the amount of money spent on the campaign, the amount of time spent campaigning negatively and whether or not the candidate is an incumbent. These are the explanatory or independent variable.

**Example 2** – A researcher is interested in how variables, such as GRE (Graduate Record Exam scores), GPA (grade point average) and prestige of the undergraduate institution, affect admission into graduate school. The response variable, admit/don’t admit, is a binary variable.

Here logistic regression always applies in a situation where we want to find out the probability associated with any two outcomes.

**Logit Regression** – Logit is a function through which the binary distribution is associated with the linear equation.

In statistics, logistic regression or logit regression is a type of regression analysis used for predicting the outcome of a categorical dependent variable. The probabilities describing the possible outcomes of a single trial are modeled, as a function of the explanatory (predictor) variable, using a logistic function. Frequently (and subsequently in this article) “logistic regression” is used to refer specifically to the problem in which the dependent variable is binary – that is, the number of available categories is two.

Question : In a scenario when the dependent variable is category variable, then can we use linear regression?

The answer is no since the probability value may go beyond 0 or 1 which is not possible.

The explanation of logistic regression is supported with the formula below.

Here β0 = A & β1 = B associated with y = a+bx. In case of logistic regression, π(x) is a probability of x and the probability always comes through the exponential function of a+bx. The denominator is always greater than numerator that is why it gives probability range of 0 to 1.

Here β0 = A & β1= B . In logistic regression, ln = log function.

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What maths behind of calculating b0 and b1 in logistics regression.

thanks