Standard error of the estimate: what it means and how to read it

In the report: Std. Error of the Estimate — The typical size of a residual: how far the observed Y is from the predicted one, in the units of Y.

How to read it

How precise the predictions are: with 2.5, a prediction is typically off by about 2.5 points of Y.

In plain words

A teacher guessed scores from study hours. For a student who studied 5 hours she got a guessed score of 70, but she did not know how far off that could be. She counted the standard error of the estimate and it came out 2.5. Now she can say a guess is usually off by about 2.5 points. So a student with a guessed 70 will most likely score somewhere around 67.5 to 72.5. If the number had been 10, she would say the guesses are too loose to be of much use.

How it is computed

√(SSE / (n − p − 1)) — the square root of MS Residual

Example

The cell with Std. Error of the Estimate 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.

Sample size — The rows used: only rows where Y and every predictor of every step are filled (listwise), the same rows for all steps.
Variance inflation factor — How much the variance of B grows because the predictor is correlated with the other predictors. Empty when lambda is above 0.
Covariance — How the two columns vary together, in the product of their units: positive — they rise together, negative — one rises as the other falls.
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.

Get it in your sheet

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

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