Regression Analysis

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:

1. Simple Regression: One independent variable is used to predict the dependent variable.
2. 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:

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

Assumptions of Regression Analysis:

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

Common Applications:

1. Predicting continuous outcomes: Regression analysis is used to predict continuous outcomes, such as stock prices or temperatures.
2. Identifying relationships: Regression analysis is used to identify the relationships between variables, such as the relationship between education and income.
3. 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.