1. What is Multiple Linear Regression?

Multiple Linear Regression is a statistical technique that models the relationship between a dependent variable (y) and multiple independent variables (X₁, X₂, etc.) by fitting a linear equation to observed data. The coefficients are typically determined using the least squares method.

2. How Does the Calculator Work?

The calculator uses the Multiple Linear Regression equation:

Where:

• \( y \) — Dependent variable (predicted value)
• \( B_0 \) — Intercept (constant term)
• \( B_1, B_2, \dots, B_k \) — Regression coefficients
• \( X_1, X_2, \dots, X_k \) — Independent variables

Explanation: The equation calculates the predicted value by multiplying each independent variable by its corresponding coefficient and summing these products with the intercept.

3. Importance of Multiple Linear Regression

Details: Multiple Linear Regression is widely used in statistics, machine learning, and scientific research for prediction, forecasting, and understanding relationships between variables.

4. Using the Calculator

Tips: Enter the intercept value, comma-separated coefficients, and comma-separated independent variable values. The number of coefficients must match the number of independent variables.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between simple and multiple linear regression?
A: Simple regression uses one independent variable, while multiple regression uses two or more independent variables.

Q2: How are the coefficients determined in practice?
A: Coefficients are typically calculated using statistical software that implements the least squares method to minimize the sum of squared residuals.

Q3: What assumptions does multiple linear regression make?
A: Key assumptions include linearity, independence, homoscedasticity, and normal distribution of residuals.

Q4: What is R-squared in regression?
A: R-squared measures the proportion of variance in the dependent variable that's predictable from the independent variables.

Q5: Can this calculator handle categorical variables?
A: No, this calculator only handles numerical variables. Categorical variables need to be converted to dummy variables first.