# Logistic Regression using One Predictor

**NOTE:** Except in cases of complex calculations, we use brackets [ ] to indicate “functions of” and parentheses ( ) to indicate “multiplication.”

**SE[Beta_1-hat]** = the standard error of the estimated slope Beta_1-hat. There is no multiplication!

**Beta_1-hat(AGE)** = the multiplication of estimated slope Beta_1-hat and the variable AGE.

## Introduction and Links to Materials

In Unit 4 we will review two-variable methods for binary outcomes along with the measures of association: excess risk, relative risk, and odds ratio. Then we will provide an introduction to logistic regression using one predictor in each of the cases we discussed for linear regression but we will cover them in a different order: one binary predictor, one multi-level predictor, and one continuous predictor. Then in Unit 5 we will look at including multiple predictors including interactions as we did for multiple linear regression.

The right side of our models will look almost identical to that for linear regression and many of the techniques and ideas translate easily from linear to logistic regression. However, the added mathematical details introduced with logistic regression often require extra attention. We need to remember rules relating to LOGARITHMS and EXPONENTIAL functions.

Please carefully review the videos we provide and go through those examples yourself carefully to help prepare you for assignments. We will also provide full SAS code and output for this unit which will be useful for the software assignments as well as for future reference for those of you planning to conduct regression analysis in your own research.

Useful **SAS Procedures**

- PROC FREQ
- PROC LOGISTIC
- CLASS statement in PROC LOGISTIC
- Other procedures as needed for exploratory data analysis

Consider the following materials from **Penn State STAT 501** as support for our lecture materials for this content.

Review Penn State materials with a** focus on the definitions, concepts, and interpretations. The do a MINIMAL job of discussing logistic regression but you may find their information helpful. **

## PROC LOGISTIC

We will be using PROC LOGISTIC for simple and multiple logistic regression so let’s look at some PROC LOGISTIC documentation including examples.

**SAS Documentation: Coming soon…**

- Getting Started: LOGISTIC Procedure
- SYNTAX
- PROC LOGISTIC statement
- CLASS statement
- ODDS-RATIO statement
- UNITS statement
- Example 73.2 Logistic Modeling with Categorical Predictors
- Example 73.6 Logistic Regression Diagnostics
- Example 73.7 ROC Curve, Customized Odds Ratios, Goodness-of-Fit Statistics, R-Square, and Confidence Limits

## PHC 6053 Videos (49:56)

## Introduction to Logistic Regression (10:30)

View Lecture Slides with Transcript

## Logistic Regression for One Binary Predictor (9:17)

View Lecture Slides with Transcript

## Logistic Regression with One Multi-Level Categorical Predictor

View Lecture Slides with Transcript

## Part A (8:14)

- Slides 1-16

## Part B (9:17)

- Slides 17-end