Multivariate / multiple Regression
03/01/2024 | By: FDS
Multivariate regression is an extension of simple linear regression that involves using multiple independent variables to model the relationship with a dependent variable. This allows for the exploration of more complex relationships in data.
Features of Multivariate Regression:
- Multiple Independent Variables: In contrast to simple linear regression, which uses only one independent variable, multivariate regression can consider multiple independent variables.
- Multidimensional Equation: The equation for multivariate regression takes the form: \[ Y = \beta_0 + \beta_1X_1 + \beta_2X_2 + \ldots + \beta_pX_p + \varepsilon \]
- Examine Interactions: Multivariate regression allows for the examination of interactions between independent variables to see if their combination has a significant impact on the dependent variable.
Applications of Multivariate Regression:
- Econometrics: Modeling economic relationships with multiple influencing factors.
- Medical Research: Analyzing health data considering various factors.
- Marketing Analysis: Predicting sales figures considering multiple marketing variables.
- Social Sciences: Investigating complex social phenomena with various influencing factors.
Example:
Suppose we want to examine the influence of advertising expenses (\(X_1\)), location (\(X_2\)), and product prices (\(X_3\)) on the revenue (\(Y\)) of a company. Multivariate regression could help us model the combined effect of these factors.