R² change: what it means and how to read it
In the report: R Square 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".
How to read it
ΔR² = 0.06 means the predictors added at this step explain 6% of Y on top of the earlier ones. Read it with Sig. F Change next to it.
In a paper: ΔR² = .06, F(1, 7) = 15.39, p = .006.
In plain words
A teacher guessed exam marks from hours of study, and the guess matched 30 out of every 100 parts of the differences between pupils. She wondered whether adding hours of sleep would add anything. With sleep added, the guess matched 36 out of 100. The R Square change is 0.06: the hours of sleep went with 6 more parts out of 100, on top of study hours. Now she can say sleep adds a little. It is a small step, so she checks the chance column next to it before she writes it in her report.
How it is computed
ΔR² = R²ᵢ − R²ᵢ₋₁Example
The cell with R Square Change is selected in each report; point at a label to see its note.
- — the sample data (50 rows) the examples use
- — two steps: x1,x2, then x added
=STATS_LINEAR(Data!A1:T51, "y", "x1,x2|x", 0) - — old syntax: regression steps, one-sample test against 15
=STATS_ANALYZE(Data!A1:T51, "linear(y|x1|x2) oneSample(x1|15)")
Where you see it
STATS_LINEAR— Multiple linear regression (OLS) with hierarchical steps separated by | and interactions a*b.STATS_ANALYZE— Runs several analyses on one range and returns one report.
Related values
- Adjusted R² — R² corrected for the number of predictors: it goes down when a predictor adds less than chance would.
- Standardized coefficient β — B in standard deviations: how many standard deviations Y changes for one standard deviation more of the predictor. The intercept has none.
- Correlation coefficient r — The correlation coefficient: the strength and direction of the relation, from −1 to 1. Empty when a column has no spread or there are fewer than 2 common rows.
- Kendall’s tau-b — Kendall’s tau-b: pairs of rows ordered the same way in both columns minus pairs ordered the opposite way, over the pairs not tied, from −1 to 1. Empty when a column has no spread or there are fewer than 2 common rows.
- Partial correlation — The correlation of the two columns with the controls held constant: of what is left of both after the linear effect of the controls is removed. Empty when a control is constant or repeats another, or when there are fewer than k + 3 complete rows (k — the number of controls).
Get it in your sheet
One formula in a cell gives the whole report, R² change included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)