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mcdon030

September 7, 2025

Regression - Excel Linest.

upper chart for anomaly

declare lower;

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# ──────┴──────────────────────────────────────────────────────────────

# T1 T2 T3 T4 T5 T6

#DATE: 8/28/2025

#Author mcdon030

# LINEST-like Multivariable Regression in ThinkScript with Accuracy Count

# Improved version with true Multiple Linear Regression using Gaussian Elimination for exact coefficients (no approximation)

# === Inputs ===

input length = 66; # Regression period -> Optimized for ES 5 minute

input slippage = 0.005; # Allowable slippage percentage

# === Data Definitions (Independent Variables) ===

def c = close; # Dependent variable (Y)

def o = open; # Independent variable 1 (X1)

def h = high; # Independent variable 2 (X2)

def l = low; # Independent variable 3 (X3)

def v = volume; # Independent variable 4 (X4)

# add the rest for total of 7

def vwp =vwap[1]; # Independent variable 5 (X5) previous bar

def tr =trueRange(h,c,l); # Independent variable 5 (X5) previous bar

def bn = BarNumber();

def nan = Double.NaN;

def lbar = HighestAll(if IsNaN(close) then 0 else bn);

# === Ensure Calculations Start After Sufficient Bars ===

def startCalc = bn > length + 1;

# === Sum Calculations ===

# Note: Sums are over past closed bars: Y (close) from 1 to length ago, X (OHLV) from 2 to length+1 ago

# This fits close_t ~ OHLV_{t-1} on historical data, then predicts close_{t+1} ~ OHLV_t (current)

# Number of samples: n = length

def SumC =CompoundValue(1, if startCalc then fold i1 = 1 to length + 1 with sC do sC + GetValue(c, i1) else nan,0); # Sum Y

# Independent variables' sums (SumX lagged)

def SumO =CompoundValue(1, if startCalc then fold i2 = 1 to length + 1 with sO do sO + GetValue(o, i2 + 1) else nan,0);

def SumH =CompoundValue(1, if startCalc then fold i3 = 1 to length + 1 with sH do sH + GetValue(h, i3 + 1) else nan,0);

def SumL =CompoundValue(1, if startCalc then fold i4 = 1 to length + 1 with sL do sL + GetValue(l, i4 + 1) else nan,0);

def SumV =CompoundValue(1, if startCalc then fold i5 = 1 to length + 1 with sV do sV + GetValue(v, i5 + 1) else nan,0);

# add the rest for total of 7

def SumVwp =CompoundValue(1, if startCalc then fold i6a = 1 to length + 1 with sVwp do sVwp + GetValue(vwp, i6a + 1) else nan,0);

# Sum of squares for independent variables (lagged)

def SumOO =CompoundValue(1, if startCalc then fold i6 = 1 to length + 1 with sOO do sOO + Sqr(GetValue(o, i6 + 1)) else nan,0);

def SumHH =CompoundValue(1, if startCalc then fold i7 = 1 to length + 1 with sHH do sHH + Sqr(GetValue(h, i7 + 1)) else nan,0);

def SumLL =CompoundValue(1, if startCalc then fold i8 = 1 to length + 1 with sLL do sLL + Sqr(GetValue(l, i8 + 1)) else nan,0);

def SumVV =CompoundValue(1, if startCalc then fold i9 = 1 to length + 1 with sVV do sVV + Sqr(GetValue(v, i9 + 1)) else nan,0);

# add the rest for total of 7

def SumVVWAP =CompoundValue(1, if startCalc then fold i20a = 1 to length + 1 with sVVWAP do sVVWAP + Sqr(GetValue(vwp, i20a + 1)) else nan,0);

# Cross-products (Y with lagged X)

def SumOC =CompoundValue(1, if startCalc then fold i10 = 1 to length + 1 with sOC do sOC + GetValue(o, i10 + 1) * GetValue(c, i10) else nan,0);

def SumHC =CompoundValue(1, if startCalc then fold i11 = 1 to length + 1 with sHC do sHC + GetValue(h, i11 + 1) * GetValue(c, i11) else nan,0);

def SumLC =CompoundValue(1, if startCalc then fold i12 = 1 to length + 1 with sLC do sLC + GetValue(l, i12 + 1) * GetValue(c, i12) else nan,0);

def SumVC =CompoundValue(1, if startCalc then fold i13 = 1 to length + 1 with sVC do sVC + GetValue(v, i13 + 1) * GetValue(c, i13) else nan,0);

def SumVWAPC =CompoundValue(1, if startCalc then fold i14a = 1 to length + 1 with sVWAPC do sVWAPC + GetValue(v, i14a + 1) * GetValue(c, i14a) else nan,0);

# Cross-products between independent variables (lagged X)

def SumOH =CompoundValue(1, if startCalc then fold i14 = 1 to length + 1 with sOH do sOH + GetValue(o, i14 + 1) * GetValue(h, i14 + 1) else nan,0);

def SumOL = CompoundValue(1,if startCalc then fold i15 = 1 to length + 1 with sOL do sOL + GetValue(o, i15 + 1) * GetValue(l, i15 + 1) else nan,0);

def SumOV =CompoundValue(1, if startCalc then fold i16 = 1 to length + 1 with sOV do sOV + GetValue(o, i16 + 1) * GetValue(v, i16 + 1) else nan,0);

def SumHL =CompoundValue(1, if startCalc then fold i17 = 1 to length + 1 with sHL do sHL + GetValue(h, i17 + 1) * GetValue(l, i17 + 1) else nan,0);

def SumHV =CompoundValue(1, if startCalc then fold i18 = 1 to length + 1 with sHV do sHV + GetValue(h, i18 + 1) * GetValue(v, i18 + 1) else nan,0);

def SumLV =CompoundValue(1, if startCalc then fold i19 = 1 to length + 1 with sLV do sLV + GetValue(l, i19 + 1) * GetValue(v, i19 + 1) else nan,0);

# add the rest for total of 7

def SumVWAPV =CompoundValue(1, if startCalc then fold i20b= 1 to length + 1 with sLVWAP do sLVWAP + GetValue(l, i20b + 1) * GetValue(v, i20b + 1) else nan,0);

# === Regression Coefficients using Gaussian Elimination for exact MLR ===

# Matrix A = X^T X (5x5), b = X^T Y (5x1)

def n_val = length; # n

def a11 = n_val;

def a12 = SumO;

def a13 = SumH;

def a14 = SumL;

def a15 = SumV;

def a21 = SumO;

def a22 = SumOO;

def a23 = SumOH;

def a24 = SumOL;

def a25 = SumOV;

def a31 = SumH;

def a32 = SumOH;

def a33 = SumHH;

def a34 = SumHL;

def a35 = SumHV;

def a41 = SumL;

def a42 = SumOL;

def a43 = SumHL;

def a44 = SumLL;

def a45 = SumLV;

def a51 = SumV;

def a52 = SumOV;

def a53 = SumHV;

def a54 = SumLV;

def a55 = SumVV;

def bb1 = SumC;

def bb2 = SumOC;

def bb3 = SumHC;

def bb4 = SumLC;

def bb5 = SumVC;

# Gaussian Elimination (forward elimination)

# Step 1: Eliminate column 1

def m21 = if startCalc and a11 != 0 then a21 / a11 else NaN;

def m31 = if startCalc and a11 != 0 then a31 / a11 else NaN;

def m41 = if startCalc and a11 != 0 then a41 / a11 else NaN;

def m51 = if startCalc and a11 != 0 then a51 / a11 else NaN;

def a22_2 = a22 - m21 * a12;

def a23_2 = a23 - m21 * a13;

def a24_2 = a24 - m21 * a14;

def a25_2 = a25 - m21 * a15;

def bb2_2 = bb2 - m21 * bb1;

def a32_2 = a32 - m31 * a12;

def a33_2 = a33 - m31 * a13;

def a34_2 = a34 - m31 * a14;

def a35_2 = a35 - m31 * a15;

def bb3_2 = bb3 - m31 * bb1;

def a42_2 = a42 - m41 * a12;

def a43_2 = a43 - m41 * a13;

def a44_2 = a44 - m41 * a14;

def a45_2 = a45 - m41 * a15;

def bb4_2 = bb4 - m41 * bb1;

def a52_2 = a52 - m51 * a12;

def a53_2 = a53 - m51 * a13;

def a54_2 = a54 - m51 * a14;

def a55_2 = a55 - m51 * a15;

def bb5_2 = bb5 - m51 * bb1;

# Step 2: Eliminate column 2

def m32 = if startCalc and a22_2 != 0 then a32_2 / a22_2 else NaN;

def m42 = if startCalc and a22_2 != 0 then a42_2 / a22_2 else NaN;

def m52 = if startCalc and a22_2 != 0 then a52_2 / a22_2 else NaN;

def a33_3 = a33_2 - m32 * a23_2;

def a34_3 = a34_2 - m32 * a24_2;

def a35_3 = a35_2 - m32 * a25_2;

def bb3_3 = bb3_2 - m32 * bb2_2;

def a43_3 = a43_2 - m42 * a23_2;

def a44_3 = a44_2 - m42 * a24_2;

def a45_3 = a45_2 - m42 * a25_2;

def bb4_3 = bb4_2 - m42 * bb2_2;

def a53_3 = a53_2 - m52 * a23_2;

def a54_3 = a54_2 - m52 * a24_2;

def a55_3 = a55_2 - m52 * a25_2;

def bb5_3 = bb5_2 - m52 * bb2_2;

# Step 3: Eliminate column 3

def m43 = if startCalc and a33_3 != 0 then a43_3 / a33_3 else NaN;

def m53 = if startCalc and a33_3 != 0 then a53_3 / a33_3 else NaN;

def a44_4 = a44_3 - m43 * a34_3;

def a45_4 = a45_3 - m43 * a35_3;

def bb4_4 = bb4_3 - m43 * bb3_3;

def a54_4 = a54_3 - m53 * a34_3;

def a55_4 = a55_3 - m53 * a35_3;

def bb5_4 = bb5_3 - m53 * bb3_3;

# Step 4: Eliminate column 4

def m54 = if startCalc and a44_4 != 0 then a54_4 / a44_4 else NaN;

def a55_5 = a55_4 - m54 * a45_4;

def bb5_5 = bb5_4 - m54 * bb4_4;

# Back Substitution

def BetaV = if startCalc and a55_5 != 0 then bb5_5 / a55_5 else NaN; # Beta for V

def bb4_final = bb4_4 - a45_4 * BetaV;

def BetaL = if startCalc and a44_4 != 0 then bb4_final / a44_4 else NaN; # Beta for L

def bb3_final = bb3_3 - a34_3 * BetaL - a35_3 * BetaV;

def BetaH = if startCalc and a33_3 != 0 then bb3_final / a33_3 else NaN; # Beta for H

def bb2_final = bb2_2 - a23_2 * BetaH - a24_2 * BetaL - a25_2 * BetaV;

def BetaO = if startCalc and a22_2 != 0 then bb2_final / a22_2 else NaN; # Beta for O

def bb1_final = bb1 - a12 * BetaO - a13 * BetaH - a14 * BetaL - a15 * BetaV;

def Intercept = if startCalc and a11 != 0 then bb1_final / a11 else NaN; # Intercept

# === Prediction for Next Close ===

def prediction = if startCalc then Intercept + BetaO * o + BetaH * h + BetaL * l + BetaV * v else NaN;

# === Standard Deviation Bands ===

def UpperBand = prediction * (1 + slippage);

def LowerBand = prediction * (1 - slippage);

# === Accuracy Testing ===

def actualNextClose = GetValue(c, -1);

def actualNextClose2 = GetValue(c, -2);

def actualNextClose3 = GetValue(c, -3);

def actualNextClose5 = GetValue(c, -5);

def predictionError = AbsValue(prediction - actualNextClose) / actualNextClose;

def predictionError2 = AbsValue(prediction - actualNextClose2) / actualNextClose2;

def predictionError3 = AbsValue(prediction - actualNextClose3) / actualNextClose3;

def predictionError5 = AbsValue(prediction - actualNextClose5) / actualNextClose5;

def isAccurate = if predictionError <= slippage then 1 else nan;

def isAccurate2 = if predictionError2 <= slippage then 1 else nan;

def isAccurate3 = if predictionError3 <= slippage then 1 else nan;

def isAccurate5 = if predictionError5 <= slippage then 1 else nan;

# === Accuracy Count ===

def AccurateCount = CompoundValue(1, if !IsNaN(isAccurate) then AccurateCount[1] + 1 else AccurateCount[1], 0);

def AccurateCount2 = CompoundValue(1, if !IsNaN(isAccurate2) then AccurateCount2[1] + 1 else AccurateCount2[1], 0);

def AccurateCount3 = CompoundValue(1, if !IsNaN(isAccurate3) then AccurateCount3[1] + 1 else AccurateCount3[1], 0);

def AccurateCount5 = CompoundValue(1, if !IsNaN(isAccurate5) then AccurateCount5[1] + 1 else AccurateCount5[1], 0);

def percentAccurate = AccurateCount / (bn - length - 1);

def percentAccurate2 = AccurateCount2 / (bn - length - 1);

def percentAccurate3 = AccurateCount3 / (bn - length - 1);

def percentAccurate5 = AccurateCount5 / (bn - length - 1);

# === R-squared Calculation (In-Sample on Training Data) ===

def meanClose = if startCalc then SumC / length else NaN;

def SSR = if startCalc then fold i20 = 1 to length + 1 with ssra do ssra + Sqr(GetValue(c, i20) - (Intercept + BetaO * GetValue(o, i20 + 1) + BetaH * GetValue(h, i20 + 1) + BetaL * GetValue(l, i20 + 1) + BetaV * GetValue(v, i20 + 1))) else NaN;

def SST = if startCalc then fold i21 = 1 to length + 1 with ssta do ssta + Sqr(GetValue(c, i21) - meanClose) else NaN;

def Rsquared = if startCalc and SST != 0 then 1 - (SSR / SST) else NaN;

# - Trade Signals

def signal1 = if prediction < LowerBand[1] then 1 else if prediction > UpperBand[1] then -1 else 0;

def signal = if prediction > close * (1 + slippage) then 1 else if prediction < close * (1 - slippage) then -1 else 0;

# === Visualization ===

plot PredictedClose = if startCalc then prediction else NaN;

PredictedClose.AssignValueColor(if prediction < LowerBand[1] then Color.RED else if prediction > UpperBand[1] then Color.GREEN else Color.CYAN);

plot previousPrediction =prediction[1];

previousPrediction.AssignValueColor(if signal[1]==1 then Color.green else if signal[1]==-1 then Color.red else Color.yellow);

addCloud(previousPrediction ,PredictedClose ,color.red,color.green);

plot Accurate = if isAccurate then prediction else NaN;

Accurate.SetDefaultColor(GetColor(3));

Accurate.SetLineWeight(2);

plot UpperBandPlot =double.nan;# UpperBand[1];

UpperBandPlot.SetDefaultColor(GetColor(5));

plot LowerBandPlot =double.nan;# LowerBand[1];

LowerBandPlot.SetDefaultColor(GetColor(6));

# Clouds for deviations

def top = if prediction > UpperBand[1] then UpperBand[1] else NaN;

def topp = if prediction > UpperBand[1] then prediction else NaN;

def bot = if prediction < LowerBand[1] then LowerBand[1] else NaN;

def botp = if prediction < LowerBand[1] then prediction else NaN;

AddCloud(topp, top, Color.GREEN, Color.GREEN); # Green for above upper

AddCloud(bot, botp, Color.RED, Color.RED); # Red for below lower

# Add Labels for Regression Coefficients

AddLabel(startCalc, "Intercept: " + Round(Intercept, 4), Color.GRAY);

AddLabel(startCalc, "BetaO (Open): " + Round(BetaO, 4), Color.GRAY);

AddLabel(startCalc, "BetaH (High): " + Round(BetaH, 4), Color.GRAY);

AddLabel(startCalc, "BetaL (Low): " + Round(BetaL, 4), Color.GRAY);

AddLabel(startCalc, "BetaV (Volume): " + Round(BetaV, 4), Color.GRAY);

# Add Labels for Prediction Accuracy

AddLabel(startCalc, "R-Squared: " + AsPercent(Rsquared), if Rsquared > 0.6 then Color.GREEN else Color.RED);

#AddLabel(startCalc, "Prediction Accuracy: " + (if isAccurate then "Accurate" else "Not Accurate"),

# if isAccurate then Color.GREEN else Color.RED);

# Add Accuracy Count Labels (fixed typos and descriptions)

AddLabel(startCalc, "Total Accurate Bars (1 Bar): " + AccurateCount, Color.CYAN);

AddLabel(startCalc, "1 Bar % Accurate: " + AsPercent(percentAccurate), Color.CYAN);

AddLabel(startCalc, "2 Bar % Accurate: " + AsPercent(percentAccurate2), Color.CYAN);

AddLabel(startCalc, "3 Bar % Accurate: " + AsPercent(percentAccurate3), Color.CYAN);

AddLabel(startCalc, "5 Bar % Accurate: " + AsPercent(percentAccurate5), Color.CYAN);

# add possible trade direcition

AddChartBubble(signal !=0,PredictedClose, "sig",if signal[1]==1 then Color.green else if signal[1]==-1 then Color.red else Color.CYAN);

AddChartBubble(bn == lbar, PredictedClose, "Predicted Close: " + Round(prediction, 2) + "\nBias: " + (if prediction > close * (1 + slippage) then "Bullish" else if prediction < close * (1 - slippage) then "Bearish" else "Neutral"), if prediction > close * (1 + slippage) then Color.GREEN else if prediction < close * (1 - slippage) then Color.RED else Color.GRAY);

AddLabel(1, "Predicted Close: " + Round(prediction, 2) + " \nBias: " + (if prediction > close * (1 + slippage) then "Bullish" else if prediction < close * (1 - slippage) then "Bearish" else "Neutral") , if prediction > close * (1 + slippage) then Color.GREEN else if prediction < close * (1 - slippage) then Color.RED else Color.GRAY);

declare upper;

# ─────────────────────────────────────────────

# │ MarketFragments.com | DNA & Market │

# │ info@marketfragments.com │

# │ www.marketfragments.com │

# | marketfragments going live by 9/15/2025

# ─────────────────────────────────────────────

# Time →

# │

# █ █ █│ █

# █ █ █ │ █ █

# █ █ █ │ █ █ █ ╭─╮

# █ █ █ │ █ █ █ █ ╭─╯ ╰─╮

# █ █ █ │ █ █ █ █ █ █ ╭─╯ ╰─╮

# █ █ █ │ █ █ █ █ █ █ █ █ ╭─╯ ╰─╮

# █ █ █ │ █ █ █ █ █ █ █ █ █ █╭─╯ ╰─╮

# █ █ █ │ █ █ █ █ █ █ █ █ ╰─╮ ╭─╯

# █ █ █ │ █ █ █ █ █ █ ╰─╮ ╭─╯

# █ █ █ │ █ █ █ █ ╰─╮ ╭─╯

# █ █ █ │ █ █ ╰─╮ ╭─╯

# █ █ █ │ █ ╰─────╯

# T1 T2 T3 T4 T5 T6

#DATE: 8/28/2025

#Author mcdon030

# LINEST-like Multivariable Regression in ThinkScript with Accuracy Count

# Improved version with true Multiple Linear Regression using Gaussian Elimination for exact coefficients (no approximation)

# Note: upper chart area is for anamoly detection

# === Inputs ===

input length = 66; # Regression period -> Optimized for ES 5 minute

input slippage = 0.005; # Allowable slippage percentage

# === Data Definitions (Independent Variables) ===

def c = close; # Dependent variable (Y)

def o = open; # Independent variable 1 (X1)

def h = high; # Independent variable 2 (X2)

def l = low; # Independent variable 3 (X3)

def v = volume; # Independent variable 4 (X4)

def vwp =vwap; # Independent variable 5 (X5)

def bn = BarNumber();

def nan = Double.NaN;

def lbar = HighestAll(if IsNaN(close) then 0 else bn);

# === Ensure Calculations Start After Sufficient Bars ===

def startCalc = bn > length + 1;

# === Sum Calculations ===

# Note: Sums are over past closed bars: Y (close) from 1 to length ago, X (OHLV) from 2 to length+1 ago

# This fits close_t ~ OHLV_{t-1} on historical data, then predicts close_{t+1} ~ OHLV_t (current)

# Number of samples: n = length

def SumC =CompoundValue(1, if startCalc then fold i1 = 1 to length + 1 with sC do sC + GetValue(c, i1) else nan,0); # Sum Y

# Independent variables' sums (SumX lagged)

def SumO =CompoundValue(1, if startCalc then fold i2 = 1 to length + 1 with sO do sO + GetValue(o, i2 + 1) else nan,0);

def SumH =CompoundValue(1, if startCalc then fold i3 = 1 to length + 1 with sH do sH + GetValue(h, i3 + 1) else nan,0);

def SumL =CompoundValue(1, if startCalc then fold i4 = 1 to length + 1 with sL do sL + GetValue(l, i4 + 1) else nan,0);

def SumV =CompoundValue(1, if startCalc then fold i5 = 1 to length + 1 with sV do sV + GetValue(v, i5 + 1) else nan,0);

# add the rest for total of 7

def SumVwp =CompoundValue(1, if startCalc then fold i6a = 1 to length + 1 with sVwp do sVwp + GetValue(vwp, i6a + 1) else nan,0);

# Sum of squares for independent variables (lagged)

def SumOO =CompoundValue(1, if startCalc then fold i6 = 1 to length + 1 with sOO do sOO + Sqr(GetValue(o, i6 + 1)) else nan,0);

def SumHH =CompoundValue(1, if startCalc then fold i7 = 1 to length + 1 with sHH do sHH + Sqr(GetValue(h, i7 + 1)) else nan,0);

def SumLL =CompoundValue(1, if startCalc then fold i8 = 1 to length + 1 with sLL do sLL + Sqr(GetValue(l, i8 + 1)) else nan,0);

def SumVV =CompoundValue(1, if startCalc then fold i9 = 1 to length + 1 with sVV do sVV + Sqr(GetValue(v, i9 + 1)) else nan,0);

# add the rest for total of 7

def SumVVWAP =CompoundValue(1, if startCalc then fold i20a = 1 to length + 1 with sVVWAP do sVVWAP + Sqr(GetValue(vwp, i20a + 1)) else nan,0);

# Cross-products (Y with lagged X)

def SumOC =CompoundValue(1, if startCalc then fold i10 = 1 to length + 1 with sOC do sOC + GetValue(o, i10 + 1) * GetValue(c, i10) else nan,0);

def SumHC =CompoundValue(1, if startCalc then fold i11 = 1 to length + 1 with sHC do sHC + GetValue(h, i11 + 1) * GetValue(c, i11) else nan,0);

def SumLC =CompoundValue(1, if startCalc then fold i12 = 1 to length + 1 with sLC do sLC + GetValue(l, i12 + 1) * GetValue(c, i12) else nan,0);

def SumVC =CompoundValue(1, if startCalc then fold i13 = 1 to length + 1 with sVC do sVC + GetValue(v, i13 + 1) * GetValue(c, i13) else nan,0);

def SumVWAPC =CompoundValue(1, if startCalc then fold i14a = 1 to length + 1 with sVWAPC do sVWAPC + GetValue(v, i14a + 1) * GetValue(c, i14a) else nan,0);

# Cross-products between independent variables (lagged X)

def SumOH =CompoundValue(1, if startCalc then fold i14 = 1 to length + 1 with sOH do sOH + GetValue(o, i14 + 1) * GetValue(h, i14 + 1) else nan,0);

def SumOL = CompoundValue(1,if startCalc then fold i15 = 1 to length + 1 with sOL do sOL + GetValue(o, i15 + 1) * GetValue(l, i15 + 1) else nan,0);

def SumOV =CompoundValue(1, if startCalc then fold i16 = 1 to length + 1 with sOV do sOV + GetValue(o, i16 + 1) * GetValue(v, i16 + 1) else nan,0);

def SumHL =CompoundValue(1, if startCalc then fold i17 = 1 to length + 1 with sHL do sHL + GetValue(h, i17 + 1) * GetValue(l, i17 + 1) else nan,0);

def SumHV =CompoundValue(1, if startCalc then fold i18 = 1 to length + 1 with sHV do sHV + GetValue(h, i18 + 1) * GetValue(v, i18 + 1) else nan,0);

def SumLV =CompoundValue(1, if startCalc then fold i19 = 1 to length + 1 with sLV do sLV + GetValue(l, i19 + 1) * GetValue(v, i19 + 1) else nan,0);

# === Regression Coefficients using Gaussian Elimination for exact MLR ===

# Matrix A = X^T X (5x5), b = X^T Y (5x1)

def n_val = length; # n

def a11 = n_val;

def a12 = SumO;

def a13 = SumH;

def a14 = SumL;

def a15 = SumV;

def a21 = SumO;

def a22 = SumOO;

def a23 = SumOH;

def a24 = SumOL;

def a25 = SumOV;

def a31 = SumH;

def a32 = SumOH;

def a33 = SumHH;

def a34 = SumHL;

def a35 = SumHV;

def a41 = SumL;

def a42 = SumOL;

def a43 = SumHL;

def a44 = SumLL;

def a45 = SumLV;

def a51 = SumV;

def a52 = SumOV;

def a53 = SumHV;

def a54 = SumLV;

def a55 = SumVV;

def bb1 = SumC;

def bb2 = SumOC;

def bb3 = SumHC;

def bb4 = SumLC;

def bb5 = SumVC;

# Gaussian Elimination (forward elimination)

# Step 1: Eliminate column 1

def m21 = if startCalc and a11 != 0 then a21 / a11 else nan;

def m31 = if startCalc and a11 != 0 then a31 / a11 else nan;

def m41 = if startCalc and a11 != 0 then a41 / a11 else nan;

def m51 = if startCalc and a11 != 0 then a51 / a11 else nan;

def a22_2 = a22 - m21 * a12;

def a23_2 = a23 - m21 * a13;

def a24_2 = a24 - m21 * a14;

def a25_2 = a25 - m21 * a15;

def bb2_2 = bb2 - m21 * bb1;

def a32_2 = a32 - m31 * a12;

def a33_2 = a33 - m31 * a13;

def a34_2 = a34 - m31 * a14;

def a35_2 = a35 - m31 * a15;

def bb3_2 = bb3 - m31 * bb1;

def a42_2 = a42 - m41 * a12;

def a43_2 = a43 - m41 * a13;

def a44_2 = a44 - m41 * a14;

def a45_2 = a45 - m41 * a15;

def bb4_2 = bb4 - m41 * bb1;

def a52_2 = a52 - m51 * a12;

def a53_2 = a53 - m51 * a13;

def a54_2 = a54 - m51 * a14;

def a55_2 = a55 - m51 * a15;

def bb5_2 = bb5 - m51 * bb1;

# Step 2: Eliminate column 2

def m32 = if startCalc and a22_2 != 0 then a32_2 / a22_2 else nan;

def m42 = if startCalc and a22_2 != 0 then a42_2 / a22_2 else nan;

def m52 = if startCalc and a22_2 != 0 then a52_2 / a22_2 else nan;

def a33_3 = a33_2 - m32 * a23_2;

def a34_3 = a34_2 - m32 * a24_2;

def a35_3 = a35_2 - m32 * a25_2;

def bb3_3 = bb3_2 - m32 * bb2_2;

def a43_3 = a43_2 - m42 * a23_2;

def a44_3 = a44_2 - m42 * a24_2;

def a45_3 = a45_2 - m42 * a25_2;

def bb4_3 = bb4_2 - m42 * bb2_2;

def a53_3 = a53_2 - m52 * a23_2;

def a54_3 = a54_2 - m52 * a24_2;

def a55_3 = a55_2 - m52 * a25_2;

def bb5_3 = bb5_2 - m52 * bb2_2;

# Step 3: Eliminate column 3

def m43 = if startCalc and a33_3 != 0 then a43_3 / a33_3 else nan;

def m53 = if startCalc and a33_3 != 0 then a53_3 / a33_3 else nan;

def a44_4 = a44_3 - m43 * a34_3;

def a45_4 = a45_3 - m43 * a35_3;

def bb4_4 = bb4_3 - m43 * bb3_3;

def a54_4 = a54_3 - m53 * a34_3;

def a55_4 = a55_3 - m53 * a35_3;

def bb5_4 = bb5_3 - m53 * bb3_3;

# Step 4: Eliminate column 4

def m54 = if startCalc and a44_4 != 0 then a54_4 / a44_4 else nan;

def a55_5 = a55_4 - m54 * a45_4;

def bb5_5 = bb5_4 - m54 * bb4_4;

# Back Substitution

def BetaV = if startCalc and a55_5 != 0 then bb5_5 / a55_5 else nan; # Beta for V

def bb4_final = bb4_4 - a45_4 * BetaV;

def BetaL = if startCalc and a44_4 != 0 then bb4_final / a44_4 else nan; # Beta for L

def bb3_final = bb3_3 - a34_3 * BetaL - a35_3 * BetaV;

def BetaH = if startCalc and a33_3 != 0 then bb3_final / a33_3 else nan; # Beta for H

def bb2_final = bb2_2 - a23_2 * BetaH - a24_2 * BetaL - a25_2 * BetaV;

def BetaO = if startCalc and a22_2 != 0 then bb2_final / a22_2 else nan; # Beta for O

def bb1_final = bb1 - a12 * BetaO - a13 * BetaH - a14 * BetaL - a15 * BetaV;

def Intercept = if startCalc and a11 != 0 then bb1_final / a11 else nan; # Intercept

# === Prediction for Next Close ===

def prediction = if startCalc then Intercept + BetaO * o + BetaH * h + BetaL * l + BetaV * v else nan;