Regression Equation Calculator
Results:
Regression Equation: -
R-squared: -
Correlation Coefficient: -
Understanding Regression Analysis
What is Regression Analysis?
Regression analysis is a statistical method for modeling relationships between variables, predicting outcomes, and understanding data patterns.
Key Formulas:
Linear Regression: y = mx + b
Polynomial Regression: y = anx^n + ... + a1x + a0
R-squared: R² = 1 - (SSres/SStot)
where:
- m = slope coefficient
- b = y-intercept
- an = polynomial coefficients
- SSres = sum of squared residuals
- SStot = total sum of squares
Types of Regression
- Simple Linear Regression: One predictor variable
- Multiple Linear Regression: Multiple predictors
- Polynomial Regression: Curved relationships
- Logistic Regression: Binary outcomes
- Ridge Regression: Regularized linear regression
- Lasso Regression: Feature selection
Statistical Measures
R-squared (R²)
Goodness of fit measure
Adjusted R²
Accounts for model complexity
Standard Error
Measure of precision
P-value
Statistical significance
Advanced Topics
- Residual Analysis: Error patterns
- Multicollinearity: Correlated predictors
- Heteroscedasticity: Varying variance
- Cross-validation: Model validation
- Feature Engineering: Variable creation
- Model Selection: Choosing best fit
Applications
- Economic Forecasting
- Scientific Research
- Machine Learning
- Quality Control
- Market Analysis
- Risk Assessment