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State the original displayed-number construction
Use benchmark percentage numbers −2/−1/0/1/2 and asset percentage numbers 4/1/0/1/4. In this hypothetical record, each asset percentage number is the square of the benchmark percentage number. This is a supplied data construction, not a financial return law.
Calculate the straight-line summary
Benchmark mean is zero and asset mean 2%. The centered cross-product is zero by symmetry, so the fitted slope is zero and intercept 2%. R² is zero for this linear fit.
Inspect the remaining shape
| Benchmark (%) | Asset (%) | Residual (percentage points) |
|---|---|---|
| −2 | 4 | 2 |
| −1 | 1 | −1 |
| 0 | 0 | −2 |
| 1 | 1 | −1 |
| 2 | 4 | 2 |
Keep absence of a linear fit separate
The residuals reveal a curved pattern even though the linear score is zero. Zero slope or correlation does not generally establish independence or absence of every relationship. This construction also does not prove a causal effect.