How to Calculate the Intercept in MATLAB's Regress Function

The regress function in MATLAB is used to perform linear regression on a dataset, which involves finding the best-fitting line that minimizes the sum of squared residuals between the data points and the line. However, when using this function, it may not be immediately clear how to extract the intercept value from the output. In this article, we will explore how to calculate the intercept in MATLAB's regress function.

First, let us consider the form of a linear regression equation: y = mx + b, where m is the slope and b is the intercept. The goal of linear regression is to find the values of m and b that minimize the sum of squared residuals between the data points and the line. To do this, we can use the MATLAB regress function, which returns a matrix containing the coefficients for the best-fitting line.

One way to extract the intercept value from the output of the regress function is by using the vander command in MATLAB. This command generates the Vandermonde matrix, which is used to compute the regression coefficients. By solving for x, we can find the pseudo-inverse of the matrix, which contains the intercept value.

Another approach is to decompose the problem into a system of linear equations and solve it using basic Calculus and linear algebra techniques. Specifically, we can re-arrange the equations to isolate m and b on one side and the rest on the other side, and then solve for these values by finding the minimum of the cost function.

The key insight here is that the cost function is convex, which means there is an optimal minimum value that can be determined. By taking the derivative of the cost function with respect to each parameter and setting it equal to zero, we can find the values of m and b that minimize the sum of squared residuals between the data points and the line.

In summary, calculating the intercept in MATLAB's regress function requires understanding how to use the vander command or solving a system of linear equations. By following these steps, you can extract the intercept value from the output of the regress function and gain insight into the best-fitting line for your dataset.

Note that this article does not require any prior knowledge of MATLAB or linear regression theory, but it does assume some basic understanding of Calculus and linear algebra.

Matlab regress function intercept