Least Squares Regression, Explained: A Visual Guide with Code Examples for Beginners
REGRESSION ALGORITHM
When people start learning about data analysis, they usually begin with Linear Regression. There's a good reason for this – it's one of the most useful and straightforward ways to understand how regression works. The most common approaches to linear regression are called "Least Squares Methods" – these work by finding patterns in data by minimizing the squared differences between predictions and actual values. The most basic type is Ordinary Least Squares (OLS), which finds the best way to draw a straight line through your data points.
Sometimes, though, OLS isn't enough – especially when your data has many related features that can make the results unstable. That's where Ridge regression comes in. Ridge regression does the same job as OLS but adds a special control that helps prevent the model from becoming too sensitive to any single feature.
Here, we'll glide through two key types of Least Squares regression, exploring how these algorithms smoothly slide through your data points and see their differences in theory.
Definition
Linear Regression is a statistical method that predicts numerical values using a linear equation. It models the relationship between a dependent variable and one or more independent variables by fitting a straight line (or plane, in multiple dimensions) through the data points. The model calculates coefficients for each feature, representing their impact on the outcome. To get a result, you input your data's feature values into the linear equation to compute the predicted value.
