Multiple correlation R: what it means and how to read it

In the report: 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.

How to read it

From 0 to 1. It is rarely reported: R Square, its square, is easier to read.

In plain words

A teacher guessed scores from study hours and sleep hours. She wanted one number for how closely the guessed scores match the real ones. She counted the multiple correlation R and it came out 0.5. R runs from 0, where the guesses have nothing to do with the real scores, to 1, where every guess hits exactly, so she can say the guesses follow the real scores fairly well but often miss. She rarely writes R in a report, since R Square next to it is easier to read: here it says the two columns go with about 25 parts out of 100 of the differences in scores.

How it is computed

R = √R²

Example

The cell with R 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 — 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".
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.

Get it in your sheet

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

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