Least Square Regression in MATLAB Programming

Introduction

Least Squares Regression is a fundamental technique in statistics and data analysis used to find the best-fitting line or curve for a set of data points. In MATLAB, it is widely used for predictive modeling, data fitting, and trend analysis.

The goal is to minimize the sum of squared differences between the observed data and the model prediction:

S=∑i=1n(yi−yi^)2S = sum_{i=1}^{n} (y_i - hat{y_i})^2S=i=1∑n?(yi?−yi?^?)2

where yiy_iyi? are the observed values, and yi^hat{y_i}yi?^? are the predicted values from the regression model.

Step 1: Define Data in MATLAB

Suppose you have the following dataset:

These vectors represent independent variable $x$ and dependent variable $y$.

Step 2: Perform Least Squares Regression

For linear regression, the model is:

$$y=a\ast x+b$$

You can compute the coefficients using the backslash operator or polyfit() in MATLAB.

Method 1: Using polyfit()

Method 2: Using Matrix Approach

Step 3: Predict and Visualize

Predict the fitted values:

Plot the data and the fitted regression line:

Step 4: Evaluate Regression Accuracy

Compute R-squared to measure the goodness of fit:

A higher R-squared (close to 1) indicates a better fit.

Step 5: Nonlinear Regression (Optional)

MATLAB also supports nonlinear regression using fit() or nlinfit():

This allows fitting more complex models beyond straight lines.

Conclusion

Least Squares Regression in MATLAB provides a simple yet powerful way to fit data, make predictions, and analyze trends. With functions like polyfit, matrix operations, and fit, you can handle both linear and nonlinear regression efficiently. This method is widely used in engineering, finance, and scientific research.