Introduction to Linear Regression

Study Notes

Introduction to Linear Regression

Linear regression is a supervised machine learning algorithm used to model the relationship between a dependent variable and one or more independent variables.
It assumes a linear relationship, meaning the dependent variable changes proportionally with the independent variable(s).
The goal is to find the best-fitting linear equation that describes the relationship.
It's widely used for prediction and forecasting.

Types of Linear Regression

Simple Linear Regression: Involves one independent variable and one dependent variable.
- The relationship is represented by a straight line.
- Equation: y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope, and b is the y-intercept.
Multiple Linear Regression: Involves two or more independent variables and one dependent variable.
- The relationship is represented by a hyperplane.
- Equation is more complex, including multiple coefficients for each independent variable.

Key Concepts

Dependent Variable (Target Variable): The variable we want to predict or understand.
Independent Variable(s) (Predictor Variables): The variables used to predict the dependent variable.
Coefficients: Values assigned to each independent variable in the linear equation. They represent the change in the dependent variable for a unit change in the corresponding independent variable.
Intercept: The value of the dependent variable when all independent variables are zero.
Error Term: The difference between the predicted value and the actual value.
Residuals: The differences between the observed values and the predicted values in the data set.
Goodness of Fit: Measures how well the regression line fits the data. Common metrics include R-squared, adjusted R-squared, and Mean Squared Errors (MSE); higher values generally indicate a better fit.

Model Building

Data Preparation: Cleaning, preprocessing, and transforming data (e.g., handling missing values, scaling features).
Feature Selection: Choosing relevant independent variables that contribute to the prediction.
- Feature importance can be assessed using various metrics and methods.
Model Training: Estimating the coefficients by minimizing the sum of squared errors using techniques like Ordinary Least Squares (OLS).
- OLS finds the line of best fit by minimizing the squared distances between the observed values and the predicted values.

Evaluating Model Performance

Accuracy Metrics: Assessing how well the model predicts on unseen data.
- R-squared helps determine the proportion of variance explained by the model.
- Adjusted R-squared corrects R-squared for the number of independent variables.
Residual Analysis: Inspecting the residuals to ensure that the model assumptions are met.
Cross-Validation: Evaluating the model's performance on different subsets of the data, providing a more robust estimate of its generalization ability.

Applications

Predicting sales: Using historical sales data and factors like advertising spend to forecast future sales.
Assessing risk: Using financial data to predict the likelihood of default or other financial risks.
Medical diagnosis: Using patient data to predict the probability of disease.
Pricing models: Predicting the price for products or services.
Trend analysis: Using historical trends and factors to predict future trends.

Assumptions of Linear Regression

Linearity: The relationship between the dependent and independent variables is linear.
Independence of Errors: The errors for the data points are independent of each other.
Homoscedasticity: The errors have constant variance across all values of independent variables.
Normality of Errors: The errors are normally distributed.
No Multicollinearity: Independent variables are not highly correlated with each other.

Description

This quiz covers the fundamentals of linear regression, a key supervised machine learning algorithm. Participants will learn about simple and multiple linear regression techniques, including their equations and applications in modeling relationships. Ideal for beginners looking to understand predictive modeling.