R²: what it means and how to read it

In the report: R Square — The share of the variance of Y explained by the predictors.

How to read it

R² = 0.25 means the predictors account for a quarter of the differences in Y. A common guide (Cohen): 0.02 small, 0.13 medium, 0.26 large.

In a hierarchical model the rise of R² from one step to the next is what the added predictors explain on top of the earlier ones; the ANOVA table of each step gives it as R Square Change with its F Change test.

In a paper: R² = .25, F(2, 47) = 7.83, p = .001.

In plain words

A teacher wanted to know how much of the differences in scores go together with study hours and sleep hours. She counted R Square and it came out 0.25. Now she can say the two columns account for 25 out of every 100 parts of the differences in scores, a quarter, and the other 75 parts go with something else. When she adds columns in steps, she watches how many parts out of 100 each new step adds: if study hours alone gave 20 parts and adding sleep hours brings it to 25, then sleep adds 5 parts on top of what study hours already gave.

How it is computed

R² = 1 − SSE / SST = SS Regression / SS Total

Example

The cell with R Square is selected in each report; point at a label to see its note.

— the sample data (50 rows) the examples use
— =STATS_LINEAR(Data!A1:T51, "y", "x1,x2", 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.

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".
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.

Get it in your sheet

One formula in a cell gives the whole report, R² included. ALS Stats is a free add-on for Google Sheets™.

Install ALS Stats from Google Workspace Marketplace (opens in a new tab)