Multiple Regression Analysis

Statistics • Multiple Regression

Written by STEM Calculators Team Published December 27, 2025 Updated February 24, 2026

Paste a data table (CSV/TSV), choose the response y and predictors x₁, …, x_p, then fit a multiple regression model. The graphs update first; detailed calculation steps appear only after a successful calculation.

1) Data input

Paste table / CSV

Upload CSV

Delimiter

No data loaded

Tip: The first row should be column names. Missing/invalid rows will be removed automatically when fitting.

2) Column picker

Response (y)

Find predictor

Detect columns to choose predictors.

3) Model & inference options

Include intercept

Standardized coefficients

Confidence level

Prediction interval

Residual drop-lines (Obs vs Pred)

3D view (if exactly 2 predictors)

If β* is enabled, the calculator reports standardized effects using β*_j = b_j · (s_xj / s_y).

4) Prediction at a point

Choose input mode

Row

5) Partial view (teaches adjusted effect)

Pick a predictor x_k

The partial plot shows residualized y vs residualized x_k (both adjusted for the other predictors).

Ready

Visuals

Observed vs Predicted

Scatter of (y, ŷ) with a 45° reference line. Residual drop-lines can be animated.

Partial view for x_k

Plot of residual(y | others) vs residual(x_k | others) with the fitted partial line.

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Multiple Regression Analysis

Use this calculator to fit a multiple linear regression model, interpret the coefficients, test overall model fit, and compute confidence/prediction intervals for a chosen set of predictor values.

1) Enter your data

Paste your data into Paste table / CSV, or use Upload CSV.
Make sure the first row contains column names (header row).
Choose a delimiter (or leave it on Auto-detect).
Click Detect columns to populate the response and predictor selectors.

Rows with missing or non-numeric entries in the selected columns are automatically removed when fitting the model.

2) Choose response and predictors

Select your response variable in Response (y).
Select predictors in the checklist. You can filter them using Find predictor.
Use Select all numeric to quickly pick all numeric predictors (except y).

If you accidentally select the response column as a predictor, it will be ignored automatically.

3) Set model and inference options

Include intercept: keep this on in most applications.
Standardized coefficients (β*): enables a standardized effect-size column for comparing predictors.
Confidence level: used for coefficient confidence intervals and for the prediction intervals section.
Residual drop-lines: toggles animated residual lines on the Observed vs Predicted plot.
3D view: if you select exactly two predictors, you can turn on a 3D projection with a fitted plane.

4) Predictions at a point

Choose Pick a row from data to predict using an existing row of predictor values.
Or choose Enter x-values manually to type predictor values yourself.
Click Use predictor means to auto-fill the manual inputs with the average predictor values.
Select whether to show a CI (mean response), a PI (new observation), or both.

5) Read the graphs (shown before the steps)

Observed vs Predicted: points near the 45° line indicate good agreement; the drop-lines show residual size.
Partial view for x_k: choose a predictor in the partial selector to see its adjusted relationship after removing the effect of the other predictors.
3D view (optional): appears only when exactly two predictors are selected and 3D view is enabled.

6) Fit the model and export results

Click Fit model to compute the regression and show results.
Use the buttons under Model results to copy a summary, copy results CSV, download results CSV, or copy the cleaned dataset.
The Calculation steps section appears only after a successful fit.

Quick sample data format

Your dataset should look like this:

y,x1,x2,x3
14.2,1.0,4.1,7.2
15.1,1.3,3.9,7.8
16.0,1.5,3.7,8.3

Frequently Asked Questions

How should I format my data for the Multiple Regression Analysis calculator?

Use a table where the first row contains column names and each following row is an observation. Paste it as CSV/TSV or upload a CSV, then run column detection and select one response (y) plus one or more numeric predictors.

What does "Include intercept" mean in multiple regression?

Including an intercept estimates a constant term so the model can fit a baseline value when predictors are zero. Turning it off forces the regression through the origin, which is only appropriate when theory or measurement design justifies it.

What is the difference between a confidence interval and a prediction interval?

A confidence interval estimates the mean response at the chosen predictor values, while a prediction interval estimates the range for a new individual observation. Prediction intervals are typically wider because they include both model uncertainty and individual variability.

How are standardized coefficients (beta star) computed and why use them?

Standardized coefficients rescale effects to comparable units, using beta star for a predictor as b_j multiplied by (s_xj / s_y). They help compare the relative strength of predictors measured on different scales.

Why does the 3D view only appear sometimes?

The 3D plot is shown only when exactly two predictors are selected, because a plane can be visualized in three dimensions with two x-axes and one y-axis. With more than two predictors, the fitted relationship cannot be displayed as a single 3D surface.