Multivariate Linear Regression in Matlab Programming

Introduction

Multivariate linear regression is an extension of simple linear regression, where the dependent variable yyy depends on two or more independent variables x1,x2,...,xnx_1, x_2, ..., x_nx1?,x2?,...,xn?.

The model is expressed as:

y=β0+β1x1+β2x2+?+βnxn+?y = beta_0 + beta_1 x_1 + beta_2 x_2 + dots + beta_n x_n + epsilony=β0+β1?x1+β2x2?+?+βn?xn?+?

MATLAB provides functions like fitlm and matrix operations to perform multivariate regression efficiently.

Step 1: Prepare Data

Suppose we have the following dataset:

Here, X has two features, and y is the target variable.

Step 2: Using Matrix Approach (Least Squares)

Add a column of ones for the intercept:

• beta(1) → Intercept (β0\beta_0β0?)

• beta(2:end) → Coefficients for features (β1,β2,...beta_1, beta_2, ...β1?,β2?,...)

Step 3: Using MATLAB’s fitlm Function

fitlm provides a higher-level interface with statistics:

• View coefficients, R-squared, p-values, and confidence intervals

• predict function can be used for new data:

Step 4: Visualizing Regression (2 Features Example)

For two features, you can create a 3D plot:

Step 5: Evaluating the Model

• R-squared: Measures the goodness of fit

• Residual analysis: Check errors for randomness

• p-values: Test statistical significance of coefficients

fitlm provides these directly:

Step 6: Applications of Multivariate Linear Regression

• Predicting house prices based on size, location, and features

• Sales forecasting using multiple market factors

• Engineering and scientific data modeling

• Machine learning feature-based prediction

Conclusion

Multivariate linear regression in MATLAB allows you to model complex relationships involving multiple independent variables. Using matrix operations or fitlm, you can efficiently compute coefficients, make predictions, and analyze model performance.

Mastering this technique is essential for data analysis, predictive modeling, and engineering applications where multiple factors influence outcomes.