Coefficient of Multiple Determination

Statistics • Multiple Regression

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

Compute and interpret the coefficient of multiple determination: R² and (optionally) adjusted R², and see how they change as predictors are added.

1) Data input

Paste table / CSV

Upload CSV

Delimiter

No data loaded

Tip: include a header row. Rows with missing/non-numeric values in selected columns will be dropped.

2) Choose response and predictors

Response (y)

Show adjusted R²

Find predictor

Compare two models

Model A predictors

Detect columns to choose predictors.

Ready

Variance decomposition

R² = —

Explained vs unexplained variance

Stacked bar: SSR (explained) vs SSE (unexplained). Updates when predictors change.

R² vs number of predictors

Nested models built by adding Model A predictors in the checklist order.

Incremental gains (waterfall)

ΔR² from adding each predictor (Model A order).

Rate this calculator

0.0 /5 (0 ratings)

Be the first to rate.

Your rating

Name (optional) Review (optional)

You can update your rating any time.

Coefficient of Multiple Determination (R²)

This calculator shows how much of the variability in your response variable is explained by the selected predictors. It reports R², (optionally) adjusted R², and how these values change as predictors are added.

1) Add your dataset

Paste your data into Paste table / CSV, or click Upload CSV.
Choose a delimiter (or keep Auto-detect).
Click Detect columns to load column names and enable selection controls.

A header row is required. Non-numeric columns are shown but cannot be selected as predictors.

2) Choose response and build the model(s)

Select the response column in Response (y).
Check predictors in Model A predictors (required).
Optional: turn on Compare two models to select a separate set of predictors for Model B.
Use Show adjusted R² to include or hide adjusted R².

If comparison is on, the calculator also reports ΔR² (and ΔR²_adj when enabled).

3) Run and read the graphs

Click Calculate R².
The graphs appear first, then the numerical summary and calculation steps.
The stacked bar shows the variance split: Explained (SSR) vs Unexplained (SSE).
The line chart shows R² (and optionally R²_adj) as the number of predictors increases.
The waterfall shows each predictor’s incremental contribution ΔR² in the chosen order.

4) Export and reuse results

Use Copy results CSV to paste results into notes/spreadsheets.
Use Download CSV to save a small file containing R², adjusted R², and sums of squares.
Use Copy data to quickly duplicate your input table elsewhere.

Quick sample data format

Your dataset should look like this (header row required):

y,x1,x2,x3
12.0,1.0,4.2,7.1
12.8,1.2,4.0,7.4
13.4,1.3,3.9,7.6

Frequently Asked Questions

What is the coefficient of multiple determination (R^2) in multiple regression?

R^2 measures the proportion of variability in the response variable y explained by the selected predictors in the model. Values closer to 1 indicate more of the variance in y is explained by the predictors.

How is R^2 computed from sums of squares?

R^2 is computed using the variance decomposition with total variability SST and explained variability SSR. A common form is R^2 = SSR / SST, which is equivalent to 1 - SSE / SST.

What is the difference between R^2 and adjusted R^2?

Adjusted R^2 penalizes adding predictors that do not meaningfully improve the model, accounting for sample size and the number of predictors. It can decrease when you add weak predictors, while R^2 typically does not.

Why does R^2 usually increase when I add more predictors?

Adding predictors gives the model more flexibility to fit the observed data, which tends to reduce SSE and increase R^2. This is why adjusted R^2 is useful for balancing fit against model complexity.

How do I compare two regression models with this calculator?

Turn on Compare two models, then choose predictors for Model A and Model B. The calculator reports each model's R^2 (and adjusted R^2 if enabled) and shows the difference between the two models.