Coefficient B: what it means and how to read it
In the report: B — The coefficient of the predictor.
How to read it
How the outcome changes when the predictor grows by one unit, the other predictors held fixed.
In plain words
A teacher kept telling his class to prepare for exams, but could not say how many hours was worth it. So after the last exam he asked every student how long they had studied and put it next to their marks. He found the link between hours and marks, a regression, and got B = 5: students who studied one hour more got, on average, 5 points more. Now he can tell the class what an extra hour of study usually goes with. A minus sign would show the other direction: more hours going with lower marks.
Example
The cell with B 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) - — two steps; pass is coded 0 and 1
=STATS_LOGISTIC(Data!A1:T51, "pass", "x1,x2|x", 0, 50, 1e-8) - —
=STATS_BOOTSTRAP(Data!A1:T51, "y", "x1,x2", 2000, "pairs", 0.95)
Where you see it
STATS_LINEAR— Multiple linear regression (OLS) with hierarchical steps separated by | and interactions a*b.STATS_LOGISTIC— Binary logistic regression with optional ridge regularization (lambda >= 0).STATS_BOOTSTRAP— Bootstrap confidence intervals for regression via resampling.STATS_ANALYZE— Runs several analyses on one range and returns one report.
Related values
- Standard error of B — How much B would vary from sample to sample.
- Standard 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.
- 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.
Get it in your sheet
One formula in a cell gives the whole report, Coefficient B included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)