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Table of Contents
Introduction to Linear Regression
Examples of Linear Regression
Difference between Simple and Multiple Linear Regression
Assumptions of linear regression
Important Model Performance Metrics
Python Code : Linear Regression
- Importing libraries
- Splitting data into training and test sets
- Running linear regression using sklearn
- Running linear regression using statsmodels
- Calculate R-Squared and Adjusted R-Squared Manually on Test data
Summary
The post gives a comprehensive overview of linear regression, a statistical technique used for predictive modeling. It explains the basic concept, differentiates between simple and multiple linear regression, and details the process of fitting a model by minimizing the sum of squared errors.
Key points covered include:
- Introduction and Examples: Linear regression estimates a dependent variable based on one or more independent variables, assuming a linear relationship. The document gives examples like predicting house prices or car mileage.
- Model Explanation and Assumptions: The linear model assumes no multicollinearity among predictors, normally distributed error terms with a mean of zero, and constant variance of errors without outliers.
- Model Performance Metrics: The importance of R-squared and Adjusted R-squared in measuring model fit is discussed, emphasizing that R-squared always increases with additional variables, which may not necessarily mean a better model unless Adjusted R-squared also increases.
- Statistical Considerations: Various tests and methods like T-tests, F-tests, VIF (Variance Inflation Factor), and the Goldfeld Quandt test for detecting multicollinearity and heteroscedasticity are explained.
- Practical Application: The document also includes steps for implementing linear regression in Python using libraries like sklearn and statsmodels, demonstrating how to load data, split it into training and test sets, fit the model, and check assumptions.
Overall, the summary highlights the utility of linear regression in various real-world applications, the necessary assumptions that ensure reliable results, and the statistical methods for validating these assumptions.