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Keep the original paired record
| Period | Benchmark (%) | Asset (%) |
|---|---|---|
| 1 | -2 | -3 |
| 2 | -1 | -0.5 |
| 3 | 0 | 1 |
| 4 | 1 | 2.5 |
| 5 | 2 | 6 |
Compute the centered sums
Benchmark mean is 0% and asset mean 1.2%. Benchmark deviations are −2/−1/0/1/2; asset deviations are −4.2/−1.7/−0.2/1.3/4.8 percentage points. Their cross-products sum to 21 and benchmark squares to 10.
Recover fitted values and deviations
| Period | Fitted (%) | Residual (percentage points) |
|---|---|---|
| 1 | -3 | 0 |
| 2 | -0.9 | 0.4 |
| 3 | 1.2 | -0.2 |
| 4 | 3.3 | -0.8 |
| 5 | 5.4 | 0.6 |
Reconcile both fitting identities
Residuals 0/0.4/−0.2/−0.8/0.6 sum to zero, and their benchmark-weighted sum is also zero. Squared residuals sum to 1.2. Those identities verify the supplied least-squares calculation, not statistical assumptions about future errors.