Covariance: what it means and how to read it

In the report: covariance — How the two columns vary together, in the product of their units: positive — they rise together, negative — one rises as the other falls.

How to read it

Its size depends on the units of the columns, so it is hard to read on its own; r is the same relation on a scale from −1 to 1.

In plain words

A coach wrote down the hours of practice and the goals scored for 8 players and wanted to know whether the two go together. He counted the covariance and it came out 12. It is positive, so players who practised more hours also scored more goals. A negative number would mean the opposite: more practice going with fewer goals. But 12 depends on the units. If the same practice were counted in minutes, it would come out 720 and look much bigger. So for a number that is easy to read he looks at the correlation, which always lies between minus 1 and 1.

How it is computed

Σ (x − x̄)(y − ȳ) / (n − 1); with pop = TRUE in Settings, divided by n

Example

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

— the sample data (50 rows) the examples use
— old syntax, 3 reports =STATS_ANALYZE(Data!A1:T51, "pearson(x1,x2)alpha(/^q/)anova(x1,x2)")

Where you see it

STATS_PEARSON — Pearson correlation (r).
STATS_ANALYZE — Runs several analyses on one range and returns one report.

Regression slope — The least-squares slope of this column on the column xCol, on the rows where both are numbers; empty with fewer than 2 rows or without spread of X.
Resampling method — pairs — whole rows are drawn with replacement; residual — the fitted values plus residuals drawn with replacement.
Slope — The least-squares coefficient B of the last predictor of the step, the other predictors of the model held fixed — computed on the data as they are.
Ridge penalty — The ridge penalty: 0 — ordinary logistic regression; above 0 the slopes are shrunk toward 0.
−2 Log Likelihood (deviance) — How far the predicted probabilities are from the observed 0s and 1s: −2 times the log-likelihood. Lower is better.

Get it in your sheet

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

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