What is the difference between simple and multiple regression?

Simple linear regression analyzes the relationship between one predictor variable (X) and one outcome variable (Y). Multiple linear regression analyzes the relationship between multiple predictor variables (X₁, X₂, ..., Xₙ) and one outcome variable (Y). Use simple regression when you have one independent variable, and multiple regression when you have multiple independent variables affecting your outcome.

What is R-squared and how do I interpret it?

R-squared (R²) is the coefficient of determination, representing the proportion of variance in the dependent variable that's explained by the independent variable(s). It ranges from 0 to 1. For example, R² = 0.85 means 85% of the variance in Y is explained by the model. Higher values indicate better model fit. Adjusted R² adjusts for the number of predictors and is preferred for multiple regression.

When should I use polynomial regression?

Use polynomial regression when the relationship between X and Y is curved rather than linear. Common applications include modeling growth rates, saturation effects, or U-shaped relationships. Start with degree 2 (quadratic) for simple curves. Higher degrees (3, 4, etc.) can model more complex patterns but risk overfitting. Check the residual plot to see if a linear model is adequate.

How do I check if my regression assumptions are met?

Use the diagnostic plots: (1) Residual Plot: Should show random scatter around zero with no patterns (linearity and homoscedasticity). (2) Q-Q Plot: Points should follow the diagonal line (normality). (3) Check for influential outliers. If assumptions are violated, consider transforming variables, removing outliers, or using alternative methods like robust regression.

Free Linear Regression Calculator with Charts

1) Choose model type

Selected

Simple Linear

Y vs single X (Y = β₀ + β₁X)

• One predictor variable
• Linear relationship
• OLS estimation

Configure options below →

Multiple Linear

Y vs X₁, X₂, … (continuous/categorical)

• Multiple predictors
• Categorical support
• Adjusted R²

Polynomial

Y vs X with degree k (regularized)

• Curved relationships
• Degree 2-5 supported
• Overfitting protection

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Logistic (β)

Binary Y (future / advanced)

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• Binary outcomes
• Logistic function

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Notes & Assumptions

• Method: Ordinary Least Squares (OLS) regression minimizing sum of squared errors (MSE)

• Regression assumes linear relationship between predictors and outcome

• Residuals should be normally distributed (check Q-Q plot)

• Homoscedasticity: constant variance in residuals (check residual plot)

• For multiple regression, check VIF for multicollinearity (VIF < 10)

• Outliers can heavily influence OLS results; consider robust methods if outliers are present

1) Choose model type

Selected

Simple Linear

Y vs single X (Y = β₀ + β₁X)

• One predictor variable
• Linear relationship
• OLS estimation

Configure options below →

Multiple Linear

Y vs X₁, X₂, … (continuous/categorical)

• Multiple predictors
• Categorical support
• Adjusted R²

Polynomial

Y vs X with degree k (regularized)

• Curved relationships
• Degree 2-5 supported
• Overfitting protection

Coming Soon

Logistic (β)

Binary Y (future / advanced)

• Coming soon
• Binary outcomes
• Logistic function

Plan only →

Data Input & Mapping

Enter X and Y data manually or upload CSV

X Variable

Y Variable

Options

Confidence Level

Results & Diagnostics

Configure options and fit model to see results

Configure your model and click "Fit Model" to see results

Regression Calculator

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Simple Linear

Multiple Linear

Polynomial

Logistic (β)

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Results & Diagnostics

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Notes & Assumptions

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1) Choose model type

Simple Linear

Multiple Linear

Polynomial

Logistic (β)

Data Input & Mapping

Results & Diagnostics