Multivariate Regression

TL;DR

Use when a single independent variable may influence multiple dependent variables.
Estimates the strength of the relationship between the independent variable and each dependent variable, and the overall effect.
Helps identify which factors significantly impact outcomes and supports decisions about allocating resources.

Definition

Multivariate regression is a type of regression analysis that involves more than one dependent variable and one independent variable. This type of regression is used to determine the relationship between multiple dependent variables and a single independent variable.

Explanation

Multivariate regression analyzes how a single independent variable relates to several dependent variables simultaneously. The analysis determines the strength of the relationship between the independent variable and each dependent variable, and it can quantify the overall effect on an outcome of interest. By modeling multiple dependent variables at once, multivariate regression provides a more comprehensive picture of interrelated outcomes and can reveal which factors have the strongest impacts. These insights can inform decisions such as how to allocate resources or where to focus efforts to achieve a desired result.

Examples

Student admissions example

Analyzing the relationship between a student’s GPA, test scores, and extracurricular activities on their chances of being accepted into a prestigious university. In this example, the independent variable is the student’s GPA, and the dependent variables are the test scores and extracurricular activities. The regression analysis would determine the strength of the relationship between the independent variable and each of the dependent variables, as well as the overall effect on the chances of being accepted into the university.

Company profitability example

Analyzing the relationship between a company’s sales, advertising expenditures, and product quality on their overall profitability. In this example, the independent variable is the company’s sales, and the dependent variables are the advertising expenditures and product quality. The regression analysis would determine the strength of the relationship between the independent variable and each of the dependent variables, as well as the overall effect on the company’s profitability.

Use cases

Situations where multiple dependent variables may be influenced by a single independent variable and a simultaneous, comprehensive analysis is desired.
Decision-making contexts where identifying which factors have significant impact informs resource allocation.

Notes or pitfalls

One key advantage is identifying specific factors that have a significant impact on the dependent variables (for example, revealing that extracurricular activities may have a stronger effect than test scores on university acceptance chances).
Another advantage is analyzing multiple dependent variables at once to provide a more complete view of how different factors affect an outcome (for example, showing that sales may positively affect profitability while advertising expenditures may have a negative effect).

Regression analysis
Independent variable
Dependent variable