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