Introduction
Linear regression is one of the most fundamental statistical techniques for modeling relationships between variables. This comprehensive guide covers everything from basic concepts to advanced diagnostics.
Understanding Linear Regression
At its core, linear regression models the relationship between a dependent variable (Y) and one or more independent variables (X) using a linear equation.
Simple Linear Regression
The equation for simple linear regression is: Y = β₀ + β₁X + ε
- β₀ is the intercept
- β₁ is the slope coefficient
- ε is the error term
Key Assumptions
Linear regression relies on several important assumptions:
- Linearity: The relationship between X and Y is linear
- Independence: Observations are independent
- Homoscedasticity: Constant variance of residuals
- Normality: Residuals are normally distributed
- No multicollinearity: Independent variables are not highly correlated
Model Diagnostics
Always check your model's assumptions using diagnostic plots:
- Residual plots for linearity and homoscedasticity
- Q-Q plots for normality
- VIF for multicollinearity
- Cook's distance for influential points
Using MCP Analytics for Linear Regression
MCP Analytics makes it easy to perform linear regression analysis with automatic diagnostics and visualizations. Simply provide your dataset and specify your target and feature variables.