Linear Regression Slope Indicator: Formula, Settings and How to Read It

Linear Regression Slope ships with the Senzoukria desktop app, in the Momentum group of the indicator catalogue. It is drawn in its own panel below the chart.

What Linear Regression Slope measures

The regression is computed in a centred form, with the time axis measured from the middle of the window rather than from its first bar. That choice is numerical, not cosmetic: on five-figure futures closes the textbook formulation subtracts two large and nearly equal sums, which discards roughly half the significant digits. The default window is 20 bars, the same statistical window used by the Bollinger bands and the z-score in this catalogue. Because the sum of squared time deviations is strictly positive for any window of two or more bars, a perfectly flat window yields a slope of exactly 0 - a real value, not a masked division by zero. Before the window is full, no value is plotted.

The formula, as implemented

This is not a description of how the indicator is usually defined elsewhere — it is what the shipped code computes, documented next to the implementation:

Entier ≥ `min` depuis les params (garde-fou UI). */ function intParam( params: Record<string, unknown>, key: string, fallback: number, min = 1, ): number { return Math.max(min, Math.floor(numParam(params, key, fallback))); } function toPoints( bars: readonly FootprintBar[], values: ReadonlyArray<number | null>, ): SeriesPoint[] { return bars.map((b, i) => ({ time: b.bucketTsNs, value: values[i] ?? null })); } /** Rendements alignés sur les barres : ret[i] = close[i] − close[i−1] ; ret[0] = null (pas de barre précédente). Cf. en-tête pour le choix différence vs log-return. */ function closeReturns(bars: readonly FootprintBar[]): Array<number | null> { return bars.map((b, i) => (i === 0 ? null : b.close - bars[i - 1].close)); } /** Les N derniers rendements se terminant à la barre `i`. `null` tant que la fenêtre n'est pas pleine — il faut i ≥ N puisque ret[0] n'existe pas. */ function returnWindow( rets: ReadonlyArray<number | null>, i: number, n: number, ): number[] | null { if (i < n) return null; const win: number[] = []; for (let j = i - n + 1; j <= i; j++) { const r = rets[j]; if (r === null) return null; win.push(r); } return win; } /** Les N derniers closes se terminant à la barre `i` (i ≥ N−1). */ function closeWindow( bars: readonly FootprintBar[], i: number, n: number, ): number[] { const win: number[] = new Array<number>(n); for (let j = 0; j < n; j++) win[j] = bars[i - n + 1 + j].close; return win; } /** Moyenne et Σ(x − moyenne)² — TWO-PASS (cf. en-tête). Tableau vide → ss = 0 et moyenne 0 : les appelants ne passent jamais de fenêtre vide, la garde `ss > 0` en aval couvre le cas. */ function meanSS(xs: readonly number[]): { mean: number; ss: number } { if (xs.length === 0) return { mean: 0, ss: 0 }; let sum = 0; for (const x of xs) sum += x; const mean = sum / xs.length; let ss = 0; for (const x of xs) { const d = x - mean; ss += d * d; } return { mean, ss }; } /** Corrélation de Pearson TWO-PASS entre deux séries de même longueur : r = Σ(x−x̄)(y−ȳ) / ( √Σ(x−x̄)² · √Σ(y−ȳ)² ) Deux racines SÉPARÉES au dénominateur (jamais √(Sxx·Syy)) : le produit de deux sommes de carrés déborderait sur des volumes cumulés. Sxx ou Syy nul (une des deux séries plate) → null : la corrélation est indéfinie, pas « 0 ». Borné dur [−1, 1] — l'arrondi f64 peut dépasser de 1 ulp sur une corrélation parfaite. */ function pearson(xs: readonly number[], ys: readonly number[]): number | null { const a = meanSS(xs); const b = meanSS(ys); if (!(a.ss > 0) || !(b.ss > 0)) return null; let sxy = 0; for (let i = 0; i < xs.length; i++) { sxy += (xs[i] - a.mean) * (ys[i] - b.mean); } return clamp(sxy / (Math.sqrt(a.ss) * Math.sqrt(b.ss)), -1, 1); } function clamp(v: number, lo: number, hi: number): number { return Math.min(hi, Math.max(lo, v)); } type Fit = { /** Pente b de y = a + b·t, en unités de PRIX PAR BARRE. */ slope: number; /** Valeur du fit au point COURANT : a + b·(n−1). */ value: number; /** Coefficient de détermination ∈ [0,1] ; null si la fenêtre est plate. */ r2: number | null; }; /** Moindres carrés y = a + b·t sur t = 0 (la plus ANCIENNE) … n−1 (la courante), formulation CENTRÉE : t̄ = (n−1)/2 ; Sxx = Σ(t−t̄)² = n(n²−1)/12 ; Sxy = Σ(t−t̄)(y−ȳ) b = Sxy/Sxx ; a = ȳ − b·t̄ ; fit(n−1) = ȳ + b·(n−1)/2 R² = Sxy² / (Sxx·Syy) (Syy = Σ(y−ȳ)²) Centrée et non « normale » (Σt·y) : sur des closes de futures à 5 chiffres, Σt·y et Σt·Σy sont deux grands nombres presque égaux — leur différence perd la moitié des chiffres significatifs. Sxx > 0 dès n ≥ 2, donc la pente n'a JAMAIS de division par zéro (une fenêtre plate rend une pente 0 EXACTE, pas un 0/0). Syy = 0 → R² null (variance nulle, cf. en-tête). n < 2 → null (pas de droite à ajuster). / function regressFit(ys: readonly number[]): Fit | null { const n = ys.length; if (n < 2) return null; const tBar = (n - 1) / 2; const { mean: yBar, ss: syy } = meanSS(ys); let sxx = 0; let sxy = 0; for (let t = 0; t < n; t++) { const dt = t - tBar; sxx += dt * dt; sxy += dt * (ys[t] - yBar); } const slope = sxy / sxx; // sxx = n(n²−1)/12 > 0 dès n ≥ 2 return { slope, value: yBar + slope * (n - 1 - tBar), r2: syy > 0 ? clamp((sxy * sxy) / (sxx * syy), 0, 1) : null, }; } /** Moment centré d'ordre p, convention POPULATION (÷N). */ function centralMoment( xs: readonly number[], mean: number, p: number, ): number { let acc = 0; for (const x of xs) acc += (x - mean) ** p; return acc / xs.length; } /** Dimension fractale de HIGUCHI (1988) sur une fenêtre de n valeurs : pour k = 1…kmax et m = 1…k (sous-séries décimées de pas k, départ m) : L_m(k) = [ Σ_{i=1..⌊(n−m)/k⌋} |x(m+ik) − x(m+(i−1)k)| · (n−1) / (⌊(n−m)/k⌋ · k) ] / k L(k) = moyenne des L_m(k) sur m L(k) ∝ k^(−D) ⇒ D = − pente de ln L(k) vs ln k (moindres carrés). Higuchi PLUTÔT que Katz ou box-counting : c'est l'estimateur de référence sur une série temporelle échantillonnée régulièrement (les barres le sont), il ne dépend d'aucune échelle d'amplitude (Katz mélange une distance de prix et un nombre de pas — donc dépend de l'instrument) et il se calcule en O(n·kmax) sans structure auxiliaire. D ∈ [1, 2] en théorie (1 = courbe lisse, 2 = bruit qui remplit le plan) ; l'estimateur n'est PAS borné artificiellement — on rend ce que la pente dit. kmax est clampé à ⌊n/2⌋ (au-delà, les sous-séries n'ont plus qu'un segment et L(k) n'a plus de sens) et à 2 minimum (une pente exige 2 points). Un L(k) nul (fenêtre plate, ou zigzag exactement en phase avec le pas k) rend le log-log indéfini → null : on ne trace pas une pente amputée. / function higuchiFd(x: readonly number[], kmaxParam: number): number | null { const n = x.length; const kmax = Math.min(Math.max(2, Math.floor(kmaxParam)), Math.floor(n / 2)); if (n < 4 || kmax < 2) return null; const lnK: number[] = []; const lnL: number[] = []; for (let k = 1; k <= kmax; k++) { let acc = 0; let used = 0; for (let m = 1; m <= k; m++) { const count = Math.floor((n - m) / k); if (count < 1) continue; let sum = 0; for (let i = 1; i <= count; i++) { sum += Math.abs(x[m + i * k - 1] - x[m + (i - 1) * k - 1]); } acc += (sum * (n - 1)) / (count * k * k); used += 1; } if (used === 0) return null; const lk = acc / used; if (!(lk > 0)) return null; // ln indéfini → pas de valeur inventée lnK.push(Math.log(k)); lnL.push(Math.log(lk)); } if (lnK.length < 2) return null; const a = meanSS(lnK); if (!(a.ss > 0)) return null; const yBar = meanSS(lnL).mean; let sxy = 0; for (let i = 0; i < lnK.length; i++) sxy += (lnK[i] - a.mean) * (lnL[i] - yBar); return -(sxy / a.ss); } // ── Défs — régression linéaire (le trio partage fenêtre et formule) ───────── /** Pente de la régression linéaire des N derniers closes (moindres carrés, formulation centrée — cf. `regressFit`), en PRIX PAR BARRE : > 0 = la droite monte. Défaut N=20 (la fenêtre statistique standard du catalogue, celle des Bollinger et du z-score). Warm-up (< N barres) → null ; fenêtre plate → 0 EXACT (Sxx > 0, ce n'est pas un 0/0).

How to read it

• The sign tells you which way the fitted line points over the window; it does not tell you whether price is currently near that line.
• Compare the magnitude against the instrument's tick size: a slope of a quarter of a tick per bar is a different statement than a slope of two ticks per bar.
• The slope crossing zero means the best-fit line through the window has flattened and reversed, which happens after price itself has turned, since the older bars still weigh on the fit.
• Pair it with R-Squared over the same period: the slope gives the direction and steepness, R-Squared says whether a straight line describes that window at all.
• The oldest and newest bars in the window carry the most weight in a least-squares slope, so a single outlier at either edge moves the line more than one in the middle does.

Parameters and defaults

Period defaults to 20 and accepts 2 to 500. A short window produces a slope that changes sign frequently and reacts within a few bars; a long window produces a steadier reading whose sign survives ordinary pullbacks, at the cost of reacting later to a genuine turn.

What it does not show

The slope reports the steepness of a fit, never its quality: a window of pure noise still has a slope, and it can be large. The unit is price per bar, so readings are not comparable between instruments, between bar intervals, or across a futures contract roll where the price level itself jumps. It uses closes only, so ranges, gaps and intrabar structure are invisible. Volume and the aggressor side are absent as well - a steep slope on two contracts per bar and a steep slope on heavy participation produce the same number.

Using it in Senzoukria

Add it from the Indicators panel of any footprint chart or candle chart. It runs on futures data from Rithmic or Databento and on crypto pairs from Binance and Bybit, on the same engine — the calculation does not change with the venue, only the data feeding it does. Market data subscriptions are billed by the provider, separately from the app.

Related indicators

• RSI — Momentum
• MACD — Momentum
• Stochastic — Momentum
• Stoch RSI — Momentum
• CCI — Momentum
• ROC — Momentum

See the full indicator library, or start with the order flow guide if you are new to reading aggression, delta and absorption.