Nagelkerke pseudo R²: what it means and how to read it
In the report: Nagelkerke R Square — Cox & Snell R² rescaled so that a perfect model reaches 1.
How to read it
The pseudo R² reported most often: 0 — the model adds nothing, 1 — a perfect fit. It is built from the likelihood, not from variance: do not read 0.30 as "30% of the variance explained".
In a paper: "Nagelkerke R² = .30".
In plain words
A teacher guessed who passes from study hours and wanted one number for how good the guesses are. She counted Nagelkerke R Square and it came out 0.30. On this ruler, 0 would mean study hours add nothing to the guess, and 1 would mean every guess is right. Now she can say the guesses are better than guessing blind, but a fair way from perfect. She must not say that study hours account for 30 parts out of 100 of the differences, since this number is built another way. In her report she writes it under its full name, Nagelkerke R Square, so readers know which number it is.
How it is computed
Cox & Snell R² / (1 − exp(2 · LL₀ / n))Example
The cell with Nagelkerke R Square is selected in each report; point at a label to see its note.
- — the sample data (50 rows) the examples use
- — two steps; pass is coded 0 and 1
=STATS_LOGISTIC(Data!A1:T51, "pass", "x1,x2|x", 0, 50, 1e-8)
Where you see it
STATS_LOGISTIC— Binary logistic regression with optional ridge regularization (lambda >= 0).
Related values
- Classification accuracy — The share of rows classified correctly when a predicted probability of 0.5 or more is read as 1.
- Odds ratio — The odds ratio: how many times the odds of Y = 1 multiply for one unit more of the predictor. In the Intercept column it is the odds of Y = 1 when every predictor is 0, not a ratio. Empty when lambda is above 0.
- Multiple correlation R — The square root of R Square. For ordinary least squares it equals the correlation between the observed and the predicted Y; with lambda above 0 it does not.
- R² — The share of the variance of Y explained by the predictors.
- R² change — What this step adds to the share of explained variance: its R² minus the R² of the step before (at the first step, its own R²). Shown when the model has two or more steps, as SPSS "Change Statistics".
Get it in your sheet
One formula in a cell gives the whole report, Nagelkerke pseudo R² included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)