What is multivariate regression analysis and how is it used in data analysis?

Multivariate regression analysis is a statistical technique examining the relationship between a single dependent variable and multiple independent variables. It estimates how changes in predictors collectively influence the outcome variable. This method assumes a linear relationship between variables and requires quantitative data, though categorical predictors can be incorporated using dummy coding. Key principles include minimizing residual variance through ordinary least squares estimation. Critical considerations are multicollinearity between independent variables, which inflates standard errors, and the necessity of meeting assumptions like homoscedasticity and normality of residuals. Variable selection and interpretation are crucial for meaningful models. It is extensively used for prediction and explanation in fields like economics, epidemiology, and social sciences. Implementation involves defining the research question, collecting relevant data, preparing data (handling missing values, encoding), fitting the regression model, evaluating significance (p-values, R-squared) and diagnostics, validating model assumptions, interpreting coefficients (magnitude, direction, significance), and deploying the model for forecasting or causal inference analysis.