Sum of squares: what it means and how to read it
In the report: SS — The sum of squares of each part of the variance.
How to read it
The ingredient of R² (Regression SS / Total SS) and of F; rarely reported on its own.
In plain words
A teacher saw marks from 40 to 100 in her class and wanted to know how much of that spread goes together with hours of study. She asked the add-on for SS. It gave her two numbers: 600 for all the differences in marks, and 150 for the differences still left after hours of study were taken into account. Now she can say that 450 out of 600 go together with hours of study, which is three quarters. SS is rarely written in a report on its own. It is a building block that other numbers are made from.
How it is computed
Total: SST = Σ (y − ȳ)²; Residual: SSE = Σ (y − ŷ)²; Regression: SST − SSEExample
The cell with SS 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.
Related values
- Mean square — The sum of squares divided by its degrees of freedom.
- Sum of squares between groups — The spread of the group means around the grand mean, weighted by group size.
- Sum of squares within groups — The spread of values around their own group mean, summed over all groups.
- Mean square between groups — The between-group sum of squares per degree of freedom.
- Mean square within groups — The within-group sum of squares per degree of freedom: the pooled variance of the groups.
Get it in your sheet
One formula in a cell gives the whole report, Sum of squares included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)