Take the partial derivative of the cost function, ∑ (yi – ŷi)^2 with respect to b: Take the partial derivative of the cost function, sum of squared residuals, ∑(yi – ŷi)^2 with respect to m: The following represents the calculus method for minimizing the sum of squares residuals to find the unknown parameters for the model y = mx + b Minimizing the sum of squares residuals using the calculus method This method is also known as the least-squares method for regression or linear regression. The sum of squared residuals is also termed the sum of squared error (SSE). In other words, the OLS method finds the best-fit line for the data by minimizing the sum of squared errors or residuals between the actual and predicted values. The OLS method can be used to estimate the unknown parameters ( m and b) by minimizing the sum of squared residuals. The coefficients m and b can also be called the coefficients of determination. Where ŷ is the predicted value, b is the intercept, and m is the slope of the line. Note the method discussed in this blog can as well be applied to multivariate linear regression model. A simple linear regression model used for determining the value of the response variable, ŷ, can be represented as the following equation. Where yi is the actual value, ŷi is the predicted value. In mathematical terms, this can be written as: The residual can be defined as the difference between the actual value and the predicted value.

The method relies on minimizing the sum of squared residuals between the actual and predicted values. The ordinary least squares (OLS) method can be defined as a linear regression technique that is used to estimate the unknown parameters in a model. What is the ordinary least squares (OLS) method? Minimizing the sum of squares residuals using the calculus method.What is the ordinary least squares (OLS) method?.

Machine learning least squares