Part 5 · 1 chapters · ~8 min

Regression

Correlation and covariance, least-squares linear regression, interpreting slope and intercept, R² and residuals, multiple regression, log transforms for skewed data, confounding and why observational data cannot show causation, regression to the mean, and using regression for capacity models.

Fit, check, do not over-read

code

// least squares in a few lines
function fit(xs: number[], ys: number[]) {
  const n = xs.length, mx = xs.reduce((a, b) => a + b) / n, my = ys.reduce((a, b) => a + b) / n;
  let sxy = 0, sxx = 0; for (let i = 0; i < n; i++) { sxy += (xs[i] - mx) * (ys[i] - my); sxx += (xs[i] - mx) ** 2; }
  const b = sxy / sxx, a = my - b * mx;
  const ssRes = xs.reduce((s, x, i) => s + (ys[i] - (a + b * x)) ** 2, 0), ssTot = ys.reduce((s, y) => s + (y - my) ** 2, 0);
  return { a, b, r2: 1 - ssRes / ssTot };
}
// fit(payloadKb, latencyMs) → { a: 12.1, b: 0.84, r2: 0.71 }  "each extra KB costs ~0.84 ms" (illustrative)

Regression to the mean: the worst-performing week is usually followed by a better one regardless of what you changed, because extreme values are partly noise. Any "fix" applied after a bad week looks effective. Compare against a control or a long baseline.

REGRESSION, CAREFULLY

fitting a line, and what it can and cannot tell you

swipe the figure sideways, or tap expand for full screen

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fit

Least squares fits latency = a + b × payload size. The slope b is the marginal cost: useful for capacity models.

y = a + bxmarginal cost