```
/ This source code is subject to the terms of the Mozilla Public License 2.0 at https://mozilla.org/MPL/2.0/
// © RicardoSantos
//@version=4
study(title="Function Polynomial Regression", overlay=true)
f_array_polyreg(_X, _Y)=>
//{
//| Returns a polynomial regression channel using (X,Y) vector points.
//| Resources:
//| language D: https://rosettacode.org/wiki/Polynomial_regression
int _sizeY = array.size(id=_Y)
int _sizeX = array.size(id=_X)
//
float _meanX = array.sum(id=_X) / _sizeX
float _meanY = array.sum(id=_Y) / _sizeX
float _meanXY = 0.0
float _meanY2 = 0.0
float _meanX2 = 0.0
float _meanX3 = 0.0
float _meanX4 = 0.0
float _meanX2Y = 0.0
if _sizeY == _sizeX
for _i = 0 to _sizeY - 1
float _Xi = array.get(id=_X, index=_i)
float _Yi = array.get(id=_Y, index=_i)
_meanXY := _meanXY + (_Xi * _Yi)
_meanY2 := _meanY2 + pow(_Yi, 2)
_meanX2 := _meanX2 + pow(_Xi, 2)
_meanX3 := _meanX3 + pow(_Xi, 3)
_meanX4 := _meanX4 + pow(_Xi, 4)
_meanX2Y := _meanX2Y + pow(_Xi, 2) * _Yi
_meanXY := _meanXY / _sizeX
_meanY2 := _meanY2 / _sizeX
_meanX2 := _meanX2 / _sizeX
_meanX3 := _meanX3 / _sizeX
_meanX4 := _meanX4 / _sizeX
_meanX2Y := _meanX2Y / _sizeX
//-----------|covs
float _sXX = _meanX2 - _meanX * _meanX
float _sXY = _meanXY - _meanX * _meanY
float _sXX2 = _meanX3 - _meanX * _meanX2
float _sX2X2 = _meanX4 - _meanX2 * _meanX2
float _sX2Y = _meanX2Y - _meanX2 * _meanY
//-----------|
float _b = (_sXY * _sX2X2 - _sX2Y * _sXX2) / (_sXX * _sX2X2 - _sXX2 * _sXX2)
float _c = (_sX2Y * _sXX - _sXY * _sXX2) / (_sXX * _sX2X2 - _sXX2 * _sXX2)
float _a = _meanY - _b * _meanX - _c * _meanX2
//-----------|
float[] _predictions = array.new_float(size=0, initial_value=0.0)
float _max_dev = 0.0
float _min_dev = 0.0
float _stdev = 0.0
for _i = 0 to _sizeX - 1
float _Xi = array.get(id=_X, index=_i)
float _vector = _a + _b * _Xi + _c * _Xi * _Xi
array.push(id=_predictions, value=_vector)
//
float _Yi = array.get(id=_Y, index=_i)
float _diff = _Yi - _vector
if _diff > _max_dev
_max_dev := _diff
if _diff < _min_dev
_min_dev := _diff
_stdev := _stdev + abs(_diff)
//| Output:
//| _predictions: Array with adjusted _Y values.
//| _max_dev: Max deviation from the mean.
//| _min_dev: Min deviation from the mean.
//| _stdev/_sizeX: Average deviation from the mean.
//}
[_predictions, _max_dev, _min_dev, _stdev/_sizeX]
int length = input(10)
var float[] prices = array.new_float(size=length, initial_value=open)
var int[] indices = array.new_int(size=length, initial_value=0)
if pivothigh(2, 2)
e = array.pop(id=prices)
i = array.pop(id=indices)
array.insert(id=prices, index=0, value=high[2])
array.insert(id=indices, index=0, value=bar_index[2])
if pivotlow(2, 2)
e = array.pop(id=prices)
i = array.pop(id=indices)
array.insert(id=prices, index=0, value=low[2])
array.insert(id=indices, index=0, value=bar_index[2])
[P, Pmax, Pmin, Pstdev] = f_array_polyreg(indices, prices)
//|----------------------------------------------------------------------------||
//|----------------------------------------------------------------------------||
//|----------------------------------------------------------------------------||
//|----------------------------------------------------------------------------||
//|----------------------------------------------------------------------------||
//|----------------------------------------------------------------------------||
color _pr_mid_col = input(color.blue)
color _pr_std_col = input(color.aqua)
color _pr_max_col = input(color.purple)
f_init_mid()=>line.new(x1=bar_index, y1=0.0, x2=bar_index, y2=0.0, color=_pr_mid_col, style=line.style_solid, width=2)
f_init_std()=>line.new(x1=bar_index, y1=0.0, x2=bar_index, y2=0.0, color=_pr_std_col, style=line.style_dashed, width=1)
f_init_max()=>line.new(x1=bar_index, y1=0.0, x2=bar_index, y2=0.0, color=_pr_max_col, style=line.style_dotted, width=1)
var line pr_mid00 = f_init_mid(), var line pr_min00 = f_init_max(), var line pr_max00 = f_init_max()
var line pr_mid01 = f_init_mid(), var line pr_min01 = f_init_max(), var line pr_max01 = f_init_max()
var line pr_mid02 = f_init_mid(), var line pr_min02 = f_init_max(), var line pr_max02 = f_init_max()
var line pr_mid03 = f_init_mid(), var line pr_min03 = f_init_max(), var line pr_max03 = f_init_max()
var line pr_mid04 = f_init_mid(), var line pr_min04 = f_init_max(), var line pr_max04 = f_init_max()
var line pr_mid05 = f_init_mid(), var line pr_min05 = f_init_max(), var line pr_max05 = f_init_max()
var line pr_mid06 = f_init_mid(), var line pr_min06 = f_init_max(), var line pr_max06 = f_init_max()
var line pr_mid07 = f_init_mid(), var line pr_min07 = f_init_max(), var line pr_max07 = f_init_max()
var line pr_mid08 = f_init_mid(), var line pr_min08 = f_init_max(), var line pr_max08 = f_init_max()
var line pr_mid09 = f_init_mid(), var line pr_min09 = f_init_max(), var line pr_max09 = f_init_max()
var line pr_lower00 = f_init_std(), var line pr_upper00 = f_init_std()
var line pr_lower01 = f_init_std(), var line pr_upper01 = f_init_std()
var line pr_lower02 = f_init_std(), var line pr_upper02 = f_init_std()
var line pr_lower03 = f_init_std(), var line pr_upper03 = f_init_std()
var line pr_lower04 = f_init_std(), var line pr_upper04 = f_init_std()
var line pr_lower05 = f_init_std(), var line pr_upper05 = f_init_std()
var line pr_lower06 = f_init_std(), var line pr_upper06 = f_init_std()
var line pr_lower07 = f_init_std(), var line pr_upper07 = f_init_std()
var line pr_lower08 = f_init_std(), var line pr_upper08 = f_init_std()
var line pr_lower09 = f_init_std(), var line pr_upper09 = f_init_std()
f_pr_mid_line_selector(_i)=>(_i==0?pr_mid00:(_i==1?pr_mid01:(_i==2?pr_mid02:(_i==3?pr_mid03:(_i==4?pr_mid04:(_i==5?pr_mid05:(_i==6?pr_mid06:(_i==7?pr_mid07:(_i==8?pr_mid08:(_i==9?pr_mid09:pr_mid00))))))))))
f_pr_max_line_selector(_i)=>(_i==0?pr_max00:(_i==1?pr_max01:(_i==2?pr_max02:(_i==3?pr_max03:(_i==4?pr_max04:(_i==5?pr_max05:(_i==6?pr_max06:(_i==7?pr_max07:(_i==8?pr_max08:(_i==9?pr_max09:pr_max00))))))))))
f_pr_min_line_selector(_i)=>(_i==0?pr_min00:(_i==1?pr_min01:(_i==2?pr_min02:(_i==3?pr_min03:(_i==4?pr_min04:(_i==5?pr_min05:(_i==6?pr_min06:(_i==7?pr_min07:(_i==8?pr_min08:(_i==9?pr_min09:pr_min00))))))))))
f_pr_upper_line_selector(_i)=>(_i==0?pr_upper00:(_i==1?pr_upper01:(_i==2?pr_upper02:(_i==3?pr_upper03:(_i==4?pr_upper04:(_i==5?pr_upper05:(_i==6?pr_upper06:(_i==7?pr_upper07:(_i==8?pr_upper08:(_i==9?pr_upper09:pr_upper00))))))))))
f_pr_lower_line_selector(_i)=>(_i==0?pr_lower00:(_i==1?pr_lower01:(_i==2?pr_lower02:(_i==3?pr_lower03:(_i==4?pr_lower04:(_i==5?pr_lower05:(_i==6?pr_lower06:(_i==7?pr_lower07:(_i==8?pr_lower08:(_i==9?pr_lower09:pr_lower00))))))))))
int pr_fractions = 10
int pr_size = array.size(id=P)
int pr_step = max(pr_size / pr_fractions, 1)
for _i = 0 to pr_size - pr_step - 1 by pr_step
int _next_step_index = _i + pr_step
int _line = _i / pr_step
line.set_xy1(id=f_pr_mid_line_selector(_line), x=array.get(id=indices, index=_i), y=array.get(id=P, index=_i))
line.set_xy2(id=f_pr_mid_line_selector(_line), x=array.get(id=indices, index=_i + pr_step), y=array.get(id=P, index=_i + pr_step))
line.set_xy1(id=f_pr_max_line_selector(_line), x=array.get(id=indices, index=_i), y=array.get(id=P, index=_i) + Pmax)
line.set_xy2(id=f_pr_max_line_selector(_line), x=array.get(id=indices, index=_i + pr_step), y=array.get(id=P, index=_i + pr_step) + Pmax)
line.set_xy1(id=f_pr_min_line_selector(_line), x=array.get(id=indices, index=_i), y=array.get(id=P, index=_i) + Pmin)
line.set_xy2(id=f_pr_min_line_selector(_line), x=array.get(id=indices, index=_i + pr_step), y=array.get(id=P, index=_i + pr_step) + Pmin)
line.set_xy1(id=f_pr_upper_line_selector(_line), x=array.get(id=indices, index=_i), y=array.get(id=P, index=_i) + Pstdev)
line.set_xy2(id=f_pr_upper_line_selector(_line), x=array.get(id=indices, index=_i + pr_step), y=array.get(id=P, index=_i + pr_step) + Pstdev)
line.set_xy1(id=f_pr_lower_line_selector(_line), x=array.get(id=indices, index=_i), y=array.get(id=P, index=_i) - Pstdev)
line.set_xy2(id=f_pr_lower_line_selector(_line), x=array.get(id=indices, index=_i + pr_step), y=array.get(id=P, index=_i + pr_step) - Pstdev)
```