Multiple Linear Regression Calculator

Model outcomes using several predictors with confidence. Get coefficients, residual checks, and fit statistics fast. Build sharper insights from structured data with reliable outputs.

Regression input form

Paste a header row and numeric observations. The first column must be the response variable.

Format: first row can be headers. Each new line is one observation. Use commas between values.

Example data table

Sales AdSpend Price WebVisits
1203012400
1353511450
1283313420
1504210520
160459580
1554410540
170488620
175508650
165469590
180557700
190587760
185578730

Formula used

Model equation:
ŷ = β₀ + β₁X₁ + β₂X₂ + ... + βₚXₚ
Coefficient estimate:
β = (XᵀX)⁻¹Xᵀy
Goodness of fit:
R² = 1 - SSE / SST,    Adjusted R² = 1 - [(1 - R²)(n - 1) / (n - k)]
Error metrics:
SSE = Σ(y - ŷ)²,    MSE = SSE / (n - k),    RMSE = √MSE
Significance testing:
t = β / SE(β),    F = (SSR / df_model) / (SSE / df_residual)

This page estimates regression coefficients through ordinary least squares. It also computes confidence intervals, p-values, variance inflation factors, residual diagnostics, and fit statistics for practical model review.

How to use this calculator

  1. Enter how many predictors your model includes.
  2. List predictor names separated with commas, or use the dataset header row.
  3. Paste your dataset into the textarea with the response variable first.
  4. Choose a confidence level and decimal precision.
  5. Click Run regression to estimate coefficients and diagnostics.
  6. Review the equation, coefficient table, VIF values, graphs, and residual table.
  7. Download the results as CSV or PDF for reporting or later analysis.

Frequently asked questions

1) What does multiple linear regression measure?

It estimates how one outcome changes when several predictors move together. The model isolates each predictor’s average linear effect while holding the others constant.

2) What is the intercept?

The intercept is the predicted outcome when every predictor equals zero. It can be meaningful in some datasets and only a mathematical anchor in others.

3) How should I read p-values?

A small p-value suggests the coefficient is unlikely to be zero under the model assumptions. It does not prove importance by itself and should be read with context.

4) What does R² tell me?

R² shows the share of outcome variation explained by the fitted model. Higher values indicate stronger fit, but they do not guarantee accurate forecasting or causal meaning.

5) Why is adjusted R² useful?

Adjusted R² penalizes unnecessary predictors. It helps compare models with different sizes and can reveal when extra variables add complexity without improving fit.

6) What does VIF mean?

Variance inflation factor measures how much predictor overlap inflates coefficient uncertainty. Large VIF values often signal multicollinearity and less stable estimates.

7) What should I look for in residuals?

Residuals should look patternless around zero. Curves, funnels, or clusters may suggest missing variables, nonlinearity, outliers, or unequal variance across predictions.

8) Can I use this page for forecasting?

Yes, but forecasting quality depends on data quality, stable relationships, and reasonable assumptions. Always validate the model on fresh observations before relying on it.

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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.