Is least squares regression the same as linear regression Last Updated : 12 Nov, 2024 Summarize Comments Improve Suggest changes Share Like Article Like Report Yes, Least squares regression and linear regression are closely related in machine learning, but they’re not quite the same. Linear regression is a type of predictive model that assumes a linear relationship between input features and the output variable. Least squares is a common method used to find the best-fitting line in linear regression by minimizing the sum of the squared differences between predicted and actual values. Below is a scatter plot with a line of best fit using linear regression on sample data.This plot effectively illustrates how linear regression, using least squares regression, fits a line to model the relationship in data, while additional annotations clarify the distinction between "linear regression" as a general concept and "least squares regression" as a specific method within it.Linear RegressionLinear regression is one of the simplest and most widely used algorithms in machine learning and statistics. It tries to model the relationship between one or more input variables (also called features) and a continuous output variable by fitting a straight line through the data points. The goal of linear regression is to find the best-fitting line that describes this relationship, minimizing the error between predicted and actual values.Least Squares RegressionLeast squares regression is a specific optimization method used within linear regression to find the best-fitting line by minimizing the sum of the squared differences between the observed values and the values predicted by the model. This method is often called Ordinary Least Squares (OLS) and is the most widely used approach to calculate the coefficients of a linear regression model.The least squares method works by calculating the vertical distance (or "error") between each actual data point and the predicted point on the line. It then squares these errors (to avoid negative values canceling out positive ones) and sums them up. The objective is to find the line that produces the smallest possible sum of these squared errors—hence, the "least squares" name.Key Takeaways:Linear Regression is a predictive modeling technique assuming a linear relationship between inputs and the output.Least Squares is a method within linear regression used to find the best-fitting line by minimizing the sum of squared errors.While least squares is a key component, it’s just one of many methods that can fit a linear regression model. For example, other techniques like Lasso or Ridge regression use different approaches to minimize errors. 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