Univariate regression involves a single independent variable used to predict or explain the relationship with a single dependent variable, making it simpler and focused on one predictor's effect. In contrast, multivariate regression uses two or more independent variables to explain or predict a single dependent variable, allowing for a more complex analysis that accounts for the combined influence of multiple factors. While univariate regression is useful for understanding direct relationships, multivariate regression provides a broader, more comprehensive view, helping to identify how several variables interact and affect the outcome simultaneously.