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Understanding Regression Analysis Techniques
Sep 26, 2024
Regression Analysis Lecture Notes
Introduction
Instructor
: Hannah
Topic
: Regression Analysis
Goals
:
Understand regression analysis
Differentiate between simple and multiple linear regression
Interpret results and understand assumptions
Use of dummy variables
Basics of logistic regression
Calculate regression online
What is Regression Analysis?
Purpose
: Infer/predict a variable based on others
Example
: Influences on salary (education, working hours, age)
Dependent Variable
: Criterion (e.g., salary)
Independent Variables
: Predictors (e.g., education level)
Goals
:
Measure influence of variables
Predict a variable
Types of Regression
Simple Linear Regression
One Independent Variable
Example
: Impact of working hours on hourly wage
Multiple Linear Regression
Several Independent Variables
Example
: Influence of working hours and age on hourly wage
Logistic Regression
Categorical Dependent Variable
Example
: Probability of burnout (Yes/No)
Key Concepts
Linear Regression
: Dependent variable is metric
Logistic Regression
: Dependent variable is categorical
Dummy Variables
: Used for categorical variables with more than two characteristics
Simple Linear Regression
Goal
: Predict dependent variable based on one independent variable
Method
: Least squares to determine the best fit line
Example
: Hospital stay prediction based on age
Calculation
:
Slope (b) and intercept (a)
Error (epsilon) represents the difference between estimated and true values
Multiple Linear Regression
Allows Multiple Variables
: Controls influence of multiple factors
Equation
: Coefficients (b) indicate change in dependent variable per unit change in independent variable
Use Cases
: Empirical social research, market research
Interpretation of Results
Model Summary
: Correlation coefficient (R), coefficient of determination (R^2)
F-test
: Tests null hypothesis that all slopes are zero
Significance Levels
: P-values for coefficients
Assumptions for Linear Regression
Linearity
: Relationship between variables should be linear
Normal Distribution of Error
: Error term epsilon should be normally distributed
No Multicollinearity
: Independent variables should not be highly correlated
Homoscedasticity
: Constant variance of residuals
Dummy Variables
Use
: For categorical predictors with more than two characteristics
Method
: Create binary variables for each category
Example
: Vehicle type (sedan, sports car, family van)
Logistic Regression
Dependent Variable
: Categorical (e.g., disease risk)
Uses
: Predict outcome probabilities
Equation
: Logistic function to ensure probabilities between 0 and 1
Calculation
: Maximum likelihood method
Online Regression Calculation
Tool
: DataTab
Process
: Input data, select variables, and interpret results
Conclusion
Regression analysis is a powerful tool for prediction and understanding variable influences.
Different types of regression are suited for different kinds of data.
Statistical software facilitates complex calculations easily.
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