###### Course Overview

## What is regression

Regression is a statistical method which helps to determine the relationship between one dependent variable and other independent variables. It explains how the dependent variable changes when one of the independent variable varies. It is also used to know which independent variable is related to the dependent variable and what is their relationship. Regression analysis is widely used in the field of prediction and forecasting. Regression analysis is an important component for modelling and analyzing data.

Regression is of two types – Linear regression and Multiple regression. Linear regression uses one independent variable to know the outcome whereas Multiple regression uses two or more independent variable to forecast the output.

In the recent years many techniques have been developed to perform regression analysis. They are Linear regression, Logistic regression, Polynomial regression, Stepwise regression, Ridge regression, Lasso Regression and Elastic net regression.

### Uses of regression analysis

- Regression analysis helps to find the significant relationship between dependent variable and independent variable
- It helps to know the amount of impact caused by multiple independent variables on a dependent variable
- It helps to compare the effects of variables measured using different scales. This comparison will help to bring out the best to be used for predictive modelling.
- Regression analysis is used in businesses for a lot of reasons like to find out the factors responsible for business profit, to forecast the future value, to know how the interest rates can affect the stock price and so on.
- Regression analysis is used as a quantitative research method which is used when the research involves modelling and analysis of several variables.

### Course Objectives

At the end of this course you will be able to

- Know in detail about regression analysis
- Explain logistic regression and its benefits
- Understand about the key components of logistic regression
- Know about the different methods of finding the probabilities
- Develop a logistic regression model using SAS
- Learn how to interpret the modeling results and present it to others
- Know how to interpret logistic regression analysis output produced by SAS

### Pre requisites

Students or anyone taking this course should have some familiarity with SAS. There are no basic skills required to take this course.

### Target Audience

This course can be taken up by

- Researchers
- Forensic statisticians
- Data Miners
- Environmental Scientists
- Epidemiologists
- Anyone who is interested in modeling data and estimate the probabilities of given outcomes.

### Logistic Regression Course Description

### Section 1: Introduction

**Introduction**

This section gives you an overview of all the chapter which are to be covered in this course. It gives an introduction about regression analysis and logistic regression in SAS. The benefits of using logistic regression is also given in this lesson.

### Section 2: Regression Analysis

**What is Regression**

Regression analysis is a form of predictive modelling technique which helps to determine the relationship between dependent and independent variable. It helps to find out the average value of the dependent variable when the independent variables are fixed. This chapter explains in detail about regression analysis and it also includes the areas of application of regression analysis, types of regression, regression models, assumptions of regression analysis and about Interpolation and Extrapolation.

### Section 3: Predicting Probabilities

**Different methods of Predicting Probabilities**

There are three methods to estimate the predicted probabilities in logistic regression. They are Marginal standardization, prediction at the modes and prediction at the means. Each method is applied to a different target population for example, Marginal standardization method is used when making an inference to the overall population.

- Marginal standardization is a method where the predicted probabilities of the output are calculated for every observed confounder value and later combined as a weighted average for each exposure level
- Prediction at the modes is a method in which conditional probabilities are calculated for each exposure level with every confounder fixed at its common value
- In the Prediction at the means method, the conditional probabilities are calculated for each exposure level with every confounder fixed with its mean value.

These three types of predicting probabilities are explained in detail under this section using examples. This chapter also compares all the three methods and finds out the differences between them.

### Section 4: Logistic Regression

**What is Logistic Regression**

Logistic regression is also known as logit regression or logit model. This is used to find the probability of event success and event failure. Logistic regression determines the relationship between categorical dependent variable and one or more independent variables using a logistic function. This chapter contains the following topics

- History of Logistic regression
- Overview of Logistic regression
- Fields of applications of logistic regression
- Logistic function, odds, odds ratio and logit
- Model fitting

**Why Logistic Regression and Not Ordinary Least Squares (OLS)**

Logistic regression is used for predicting the probability of occurrence of an event by fitting the data to a logistic curve. Ordinary Least Squares on the other hand is an important computational problem that is used in applications when there is a need to use a linear mathematical model to measurements which are derived from the experiments. OLS takes various forms like Correlation, multiple regression, ANOVA and others. Logistic regression is most widely used in the field of medical science whereas OLS is mostly used in social sciences.

In this chapter we will see the comparison of logistic regression with OLS. Two methods are used to compare the results of both – Dropout study and High School and Beyond Study. These two methods are explained in detail using an example under this chapter.

**Modelling Key Concepts**

There are many types of logistic models but this chapter will deal with the basic three types of logistic regression models – Binary, ordinal and nominal models.

Binary logistic regression is where a binary response variable is related to a set of explanatory variables which are discrete or continuous.

Multinomial logistic regression explains how a multinomial response depends on a set of explanatory variables. The polytomous response can be either or ordinal or nominal. There are few models which suits ordinal response like cumulative logit model, adjacent categories model and continuation ratios model. The other models can be used for both ordinal or nominal response.

**This section covers the following topics**

- Key concepts of Binary logistic regression
- Binary logistic regression with a single categorical predictor
- Binary logistic regression for Three way and k way tables
- Baseline category logit model
- Adjacent category logit model
- Proportional odds cumulative logit model

**Logistic Regression Key Concepts**

This chapter contains the key concepts of logistic regression.

**Odds**– Odds are the ratio of the probability of an event to occur versus the probability of an event that will not occur.**Odds Ratio**– It is a comparative measure of two odds relative to a different events.**Logit –**The logit function is the log of the odds function

**Binning Approach and Other Approaches**

Binning is a way to group a number of more or less continuous values into smaller number of bins. For example if you have data about a group of employees you might arrange them into smaller number as per their salary intervals. Even categorical values can also be converted into bins. Binning can also be used in multivariate statistics where binning is done in several dimensions at once. Few topics which are covered in this chapter are

- What is binning
- Why is binning required
- Binning continuous variables
- Binning categorical variables
- How binning is used in logistic regression

### Section 5: SAS Methodology

**SAS Methodology Part 1**

SAS is a general purpose software used to perform a wide variety of statistical analysis. The main procedures for categorical data analysis are FREQ, GENMOD, LOGISTIC, NLMXIED, GLIMMIX and CATMOD. Apart from this many procedures in SAS are used to perform logistic regression. For most of the applications PROC LOGISTIC is the preferred option. PROC LOGISTIC is used to analyze binary response as well as ordinal response data. PROC LOGISTIC gives ML fitting of binary response models, cumulative link models for ordinal responses and baseline category logit models for nominal responses.

PROC SURVEYLOGISTIC fits binary and multi category regression models to survey data by incorporating the sample design into the analysis and uses the method of pseudo ML. This section contains the following topics

- Binary response
- Ordinal response
- Infinite parameters – Complete separation, Quasicomplete separation, Overlap
- Ordering of the binary response levels
- Other logistic regression applications – Conditional logistic regression, Bardley Terry model for paired comparison, Multinomial Logit Choice model

**SAS Methodology Part 2**

In this chapter examples of logistic regression using SAS and the SAS code for logistic regression is given in detail for your easy understanding.

**Model Fit**

Model fit statistics computes various fit criteria based on a model with intercepts only and a model with intercepts and explanatory variables. There are three criteria’s in model fitting -2 log likelihood, Akaike’s information criterion and Schwarz (Bayesian information) criterion. Each of these criterions are explained in detail under this chapter with examples.

### FAQ’s General Questions

**What does this course offer ?**

This course offers theoretical and practical training for researchers, statisticians and other professionals with particular emphasis on logistic regression model. This is a course where freshers can become an expert at using SAS to analyze binary response data using logistic regression. There are many practical examples and case studies given in this course which will help you to learn better. After taking this course you will become a more confident user of SAS to compute logistic regression.

**What is the most practical thing which I can learn from this course ?**

After completing this course you will be able to build a statistical model on logistic regression using SAS. You will get all the necessary skills to understand and develop your own models. You will be able to understand the process better.

**What are the other sources from where I can learn more about logistic regression in SAS ?**

The materials of this course will be provided to you and it will contain all the sections of the course in detail. But you may also supplement your learning experience in this field by purchasing few textbooks. You can contact the course instructor to know the details of the books. Our customer support centre is available 24*7 and you can send all your queries to them. They will guide you in contacting your instructor.

### Testimonials

**Hiraj**

This is a very good introductory course about logistic regression with reasonable pricing. This course is more informative as well as rewarding. The course does not take much time to make me understand the concepts of logistic regression. This is a best course for statisticians and researchers who wanted to use SAS for computing logistic regression. This also serves as a best course for beginners because it covers all the topic from basic introduction to what is regression to all the detailed concepts of logistic regression. Overall a worthy course at a worthy price.

**Stanley**

I have completed this course successfully two weeks back. I took up this course to help me in my research and it served the purpose. This course was of great help to me in completing my research. The course starts with a brief introduction about regression and slowly flows into explaining what is logistic regression and how it can be used in SAS. The content and flow of the course was excellent and interrelated. It explained even the complex concepts in an easy to understand manner through some examples. Examples were also real life and it can be used by us in our research. The quality of the content was good and updated. This is overall a great course for beginners as well as for professionals who wanted to learn about logistic regression in SAS.

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