Regression Coefficient Calculator

Estimate simple and multiple regression coefficients, inspect significance, residuals, multicollinearity, confidence intervals, predictions, standardized effects, regularization, and export complete machine learning results with ease.

Regression Results

Coefficient Statistics

Term Coefficient Standardized Std. Error t Statistic p Value Confidence Interval VIF Interpretation

Observation Diagnostics

# Actual Predicted Residual Squared Residual Standardized Residual Leverage Cook's Distance

Prediction

Charts

Exportable Report


        

Calculator Inputs

0 behaves like Ridge. 1 behaves like Lasso.
Use the first row as headers. The last selected column is the target. Text predictors are automatically dummy encoded.

Formula Used

Ordinary least squares estimates coefficients by minimizing squared residuals. The matrix equation produces all coefficients together. Regularized models add shrinkage to reduce unstable estimates.

β̂ = (XᵀWX)⁻¹XᵀWy
ŷ = β₀ + β₁x₁ + β₂x₂ + ··· + βₚxₚ
R² = 1 − SSE / SST
Adjusted R² = 1 − (1 − R²)(n − 1)/(n − p − 1)
Ridge: minimize SSE + λΣβⱼ²
Elastic Net: minimize SSE + λ[αΣ|βⱼ| + (1 − α)Σβⱼ²/2]

How to Use

  1. Paste a table with headers into the dataset box.
  2. Enter the target column name exactly as written.
  3. Select OLS, Ridge, Lasso, or Elastic Net.
  4. Enable polynomial, interaction, or standardization options when needed.
  5. Click Calculate Coefficients and review diagnostics.
  6. Enter new predictor values to create a prediction.
  7. Copy or export the complete result report.

Example Data

HoursExperienceDepartmentSales
21North18
52South31
84North48
126South71

Frequently Asked Questions

What is a regression coefficient?

It estimates how much the predicted target changes. Other predictors remain fixed during interpretation. Units depend on each original variable.

What does a positive coefficient mean?

A positive value indicates an increasing fitted relationship. Larger predictor values produce larger predictions. Causation is not automatically established.

Why include an intercept?

The intercept estimates the target when predictors equal zero. It often improves model calibration. Remove it only with strong justification.

What are standardized coefficients?

They express effects in standard deviation units. This supports rough predictor comparisons. Correlated predictors still complicate importance claims.

What does a large VIF indicate?

A large VIF suggests multicollinearity among predictors. Coefficient uncertainty may become inflated. Consider combining or regularizing related features.

When should Ridge regression be used?

Ridge helps when predictors are strongly correlated. It shrinks coefficients without forcing zeros. Scaling predictors is usually recommended first.

How does Lasso differ from Ridge?

Lasso can shrink some coefficients exactly to zero. Ridge generally retains every predictor. Their behavior depends heavily on scaling.

What is Cook's distance?

Cook's distance summarizes an observation's model influence. Large values deserve careful investigation. They do not automatically justify deletion.

Can categorical predictors be used?

Yes, text columns are dummy encoded automatically. One level becomes the baseline. Coefficients compare remaining levels against it.

Related Calculators

Linear Regression CalculatorPolynomial Regression CalculatorRidge Regression CalculatorLasso Regression CalculatorElastic Net Regression CalculatorLogistic Regression CalculatorRegression Prediction CalculatorResidual Error CalculatorMean Squared Error CalculatorMean Absolute Error Calculator

Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.