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

  1. Linearity: Relationship between variables should be linear
  2. Normal Distribution of Error: Error term epsilon should be normally distributed
  3. No Multicollinearity: Independent variables should not be highly correlated
  4. 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.