MATLAB Implementation of Multiple Linear Regression with Coefficient Testing

Multiple linear regression is a widely used method in statistics and data analysis that explores the relationship between multiple independent variables and a dependent variable. This approach not only includes specific coefficient testing procedures and comprehensive input/output handling, but also allows investigation of interactions between independent variables and their collective impact on the dependent variable through relationship adjustments. In MATLAB implementation, this typically involves using the `regress` function or `fitlm` for model fitting, where the input matrix X contains multiple predictor variables and vector y represents the response variable. Key implementation aspects include calculating regression coefficients using the least squares method (β = (X'X)^-1 X'y), performing hypothesis testing on coefficients with t-statistics, and generating ANOVA tables for model significance assessment. The code often includes residual analysis, confidence interval calculation, and prediction intervals for new observations. Therefore, multiple linear regression serves as an extremely valuable tool that enables comprehensive data understanding and facilitates more accurate predictions and analyses through proper statistical validation and model diagnostics.