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Why do residuals cancel at the mean?
Interactive example
- Sum of residuals
- 0
- Squared error (SSE)
- 26.75
At the sample mean, signed residuals sum to zero, while SSE remains positive unless every value is identical.
See the values
| Observation | Value | Residual |
|---|---|---|
| 1 | 2 | -3.75 |
| 2 | 5 | -0.75 |
| 3 | 7 | 1.25 |
| 4 | 9 | 3.25 |
What to notice
Separate signed residual cancellation from squared error.
Conditions
The four displayed values are treated as a fixed sample.
What this example cannot show
This does not estimate a population parameter or construct an interval.
Sources and context
These sources provide topic context. The values and interaction are authored by AXIOVUM; no institutional endorsement is implied.