This document provides an overview of logistic regression, including: - Logistic regression predicts the probability of an event occurring based on independent variables. - It is used when the dependent variable is binary (coded as 0 or 1) and includes examples like voting outcomes or disease diagnosis. - The objective is to find the best fitting model describing the relationship between binary dependent variables and independent variables.

1. Why use logistic regression?
• There are many important research topics for which the dependent
variable is "limited."
• For example: voting, morbidity or mortality, and participation data
is not continuous or distributed normally.
• Binary logistic regression is a type of regression analysis where the
dependent variable is a dummy variable: coded 0 (did not vote) or
1(did vote)

2. Introduction
• Logistic regression estimates the probability of a certain event
occurring.
• It is used in a situation where a researcher is interested to predict the
occurrence of any happenings.
Objective of Logistic Regression
• The objective of logistic regression is to find the best fitting model
to describe the relationship between the dichotomous (binary)
characteristics of interest and a set of independent variables.
Examples of Binary Outcomes
• Should a bank give a person loan or not.
• What determines admittance into a school.
• Which consumers are more likely to buy a new product.

3. Uses of Logistic Regression
• Prediction of group membership
• It is also provides knowledge of the relationship and strength among
the variables.
• Casual relationship between one or more independent variables and
one binary dependent variables.
• Used to forecast the outcome event.
• Used to predict changes in probabilities.

4. Assumptions
• The relationship between the dependent and independent variable
may be linear or non-linear.
• The outcome variable must be coded as 0 and 1.
• The independent variable do not need to be metric.
• Independent variable linearly related to the log odds.
• It requires quit large sample size.

5. Key terms in Logistic Regression
• Dependent variable
– It is binary in nature.
• Independent variable
– Select the different variables that you expect to influence the
dependent variable. May be two or more.
• Hosmer-lemeshow test
– It is commonly used measure of goodness of fit.
• Odd ratio
– It is the ratio of the probability of success to the probability of
failure.

6. • Logit
– The logit is function which is equal to the log odds of a variable.
If p is a probability that Y=1(occurrence of an event), then p/(1-
p) is corresponding odds. The logit of probability p is given by
𝐿𝑜𝑔𝑖𝑡(𝑝) = log(
𝑝
1−𝑝
)
Predicting the Probability p
𝑍 = 𝑏𝑂 + 𝑏1𝑥1 + 𝑏2𝑥2 + ⋯ ⋯ + 𝑏𝑛𝑥𝑛
𝑏0 is the intercept and 𝑏1 , 𝑏2 are the slopes against independent
variables 𝑥1 , 𝑥2 which need to estimated.

7. Multiple Logistic Regression
• It applies when there is a single dichotomous outcome and more than one
independent variable.
• In multiple logistic regression, the predictor variables may be of
any data level (categorical, ordinal, or continuous).
• A major use of this technique is to examine a series of predictor
variables to determine those that best predict a certain outcome.

8. Multinomial logistic regression
• It is sometimes considered an extension of binomial logistic regression to allow
for a dependent variable with more than two categories.
• As with other types of regression, multinomial logistic regression can have
nominal and/or continuous independent variables and can have interactions
between independent variables to predict the dependent variable.
• Example:-
Which Flavor of ice cream will a person choose?
Dependent Variable:
• Vanilla
• Chocolate
• Butterscotch
• Black Current

9. Independent Variables:
• Gender
• Age
• Occasion
• Happiness
• Etc.