What Is SSR SST SSE?
SST is the total sum of squares, how far the y values are from their mean. SSE is the error sum of squares, how far they are from the fitted line. SSR is the regression sum of squares, how far the fitted values are from the mean.
For a least squares line with an intercept, SST = SSR + SSE exactly. R² is then SSR divided by SST, the share of the variation the line explains.
Paste x and y and the calculator fits the line for you, or enter your own observed and predicted values.
How to Use the SSR SST SSE Calculator
- Choose whether to fit a line or supply predictions.
- Enter the values.
- Read the three sums of squares and R².
SSR SST SSE Formula
Decomposition
R squared
SSR SST SSE Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| SST | Total sum of squares | Σ(y − ȳ)² |
| SSR | Regression sum of squares | Σ(ŷ − ȳ)² |
| SSE | Error sum of squares | Σ(y − ŷ)² |
| R² | Coefficient of determination | SSR / SST |
SSR SST SSE Worked Example
With the example values loaded in the calculator above, the steps are:
- Predictions are fitted by least squares: ŷ = 0.17143 + 1.9786x. ȳ = 9.075.
- SST = Σ(y − ȳ)² = 165.195.
- SSE = Σ(y − ŷ)² = 0.775714.
- SSR = Σ(ŷ − ȳ)² = 164.419.
- R² = 1 − SSE ÷ SST = 0.995304.
Result: SST (total sum of squares) = 165.195; SSR (regression sum of squares) = 164.419; SSE (error sum of squares) = 0.775714.
What each one means
SST measures how far the y values are from their mean. SSE measures how far they are from the fitted line. SSR measures how far the fitted values are from the mean.
A good model has a small SSE and a large SSR, so R² is near 1.
A note on abbreviations
Some books call SSR the "sum of squares of residuals" and SSE the "explained sum of squares". Here SSR is the regression (explained) part and SSE is the error part, which is the more common convention in regression software.
Where SSR SST SSE Is Used
Regression coursework
Fill in an ANOVA table for a regression.
Judging model fit
See how much variation a model explains.
Checking predictions
Compute SSE and R² for predictions from any model.
Common SSR SST SSE Mistakes to Avoid
- Check which convention your course uses for SSR and SSE.
- R² always rises when you add predictors, so compare models with adjusted R².
SSR SST SSE Terms and Definitions
- SST
- Total sum of squares around the mean of y.
- SSE
- Sum of squared errors, the unexplained part.
SSR SST SSE FAQs
What is the relationship between SST, SSR and SSE?
SST = SSR + SSE for a least squares line with an intercept.
How do you get R² from these?
R² = SSR ÷ SST, or 1 − SSE ÷ SST.
What does a large SSE mean?
The model leaves a lot of variation unexplained.
Can SSR be larger than SST?
Not for a least squares line. It can happen with predictions that did not come from a fit.