1. What Is Multivariate Regression?

Multivariate regression is a statistical technique that models the relationship between a dependent variable (Y) and multiple independent variables (X₁, X₂, ..., Xₙ). It extends simple linear regression to account for multiple predictors simultaneously.

2. How Does The Calculator Work?

The calculator uses the multivariate regression equation:

Where:

• \( Y \) — Dependent variable (predicted value)
• \( \beta_0 \) — Intercept (constant term)
• \( \beta_1, \beta_2, \ldots, \beta_n \) — Regression coefficients
• \( X_1, X_2, \ldots, X_n \) — Independent variable values

Explanation: Each coefficient (β) represents the change in Y for a one-unit change in the corresponding X variable, holding all other variables constant.

3. Applications Of Multivariate Regression

Details: Multivariate regression is widely used in economics, social sciences, healthcare, and business analytics to understand complex relationships between variables, make predictions, and control for confounding factors.

4. Using The Calculator

Tips: Enter the intercept value, comma-separated coefficients, and comma-separated variable values. Ensure the number of coefficients matches the number of variables for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between multivariate and multiple regression?
A: While often used interchangeably, multivariate regression typically refers to models with multiple dependent variables, while multiple regression has one dependent variable with multiple predictors.

Q2: How are regression coefficients interpreted?
A: Each coefficient represents the expected change in the dependent variable for a one-unit change in the predictor, assuming all other variables remain constant.

Q3: What assumptions does multivariate regression make?
A: Key assumptions include linearity, independence of errors, homoscedasticity, normality of residuals, and absence of multicollinearity.

Q4: When should I use multivariate regression?
A: Use it when you want to understand how multiple factors simultaneously influence an outcome or when you need to control for confounding variables.

Q5: What are limitations of this approach?
A: It assumes linear relationships, can be sensitive to outliers, and may suffer from overfitting if too many variables are included relative to sample size.