Regression Analysis

Study Notes

Regression Analysis

What is Regression Analysis? Regression analysis is a statistical method used to establish a relationship between two or more variables, with the goal of predicting the value of one variable based on the values of others.

Types of Regression:

Simple Regression: One independent variable is used to predict the dependent variable.
Multiple Regression: More than one independent variable is used to predict the dependent variable.

Key Concepts:

Independent Variable (X): The variable used to predict the dependent variable.
Dependent Variable (Y): The variable being predicted.
Coefficient of Determination (R²): Measures the strength of the relationship between the independent and dependent variables.
Regression Equation: The mathematical equation that describes the relationship between the variables.
Residuals: The differences between the observed and predicted values of the dependent variable.

Methods of Regression Analysis:

Ordinary Least Squares (OLS): A method used to estimate the regression coefficients.
Maximum Likelihood Estimation: A method used to estimate the regression coefficients.

Assumptions of Regression Analysis:

Linearity: The relationship between the variables should be linear.
Independence: Each observation should be independent of the others.
Homoscedasticity: The variance of the residuals should be constant.
Normality: The residuals should be normally distributed.
No or little multicollinearity: The independent variables should not be highly correlated with each other.

Common Applications:

Predicting continuous outcomes: Regression analysis is used to predict continuous outcomes, such as stock prices or temperatures.
Identifying relationships: Regression analysis is used to identify the relationships between variables, such as the relationship between education and income.
Controlling for confounding variables: Regression analysis is used to control for confounding variables, such as age or gender, when analyzing the relationship between variables.

Regression Analysis

Definition and Types

Regression analysis is a statistical method used to establish a relationship between two or more variables, with the goal of predicting the value of one variable based on the values of others.
There are two main types of regression: Simple Regression (one independent variable) and Multiple Regression (more than one independent variable).

Key Concepts

Independent Variable (X): The variable used to predict the dependent variable.
Dependent Variable (Y): The variable being predicted.
Coefficient of Determination (R²): Measures the strength of the relationship between the independent and dependent variables.
Regression Equation: The mathematical equation that describes the relationship between the variables.
Residuals: The differences between the observed and predicted values of the dependent variable.

Methods of Regression Analysis

Ordinary Least Squares (OLS): A method used to estimate the regression coefficients.
Maximum Likelihood Estimation: A method used to estimate the regression coefficients.

Assumptions of Regression Analysis

Linearity: The relationship between the variables should be linear.
Independence: Each observation should be independent of the others.
Homoscedasticity: The variance of the residuals should be constant.
Normality: The residuals should be normally distributed.
No or little multicollinearity: The independent variables should not be highly correlated with each other.

Common Applications

Predicting continuous outcomes: Regression analysis is used to predict continuous outcomes, such as stock prices or temperatures.
Identifying relationships: Regression analysis is used to identify the relationships between variables, such as the relationship between education and income.
Controlling for confounding variables: Regression analysis is used to control for confounding variables, such as age or gender, when analyzing the relationship between variables.