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linear regression

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Innocent Iguana answered on May 21, 2022 Popularity 10/10 Helpfulness 2/10

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- Linear regression is a method that let us understand the relationship between dependent and independent variables. 
- It predicts continuous value. example: y = mx + c
- y is target, x is independent feature, m is slope, c is intercept
- By training on many datapoints, the model understands value of c and m. Then taking any value x, the model can estimate the value y.
- Simple linear regression = Use 1 independent variable for predicting 1 dependent variable
- Multiple linear regression = Use multiple independent variables for predicting 1 dependent variable
- Noise : 
    - Error in prediction. 
    - The error is gaussian noise and the residuals show normal distribution properties. 
    - The more the error, the more spread out the normal distribution (sigma or standard deviation in normal distribution)
    - The best fit line has the least noise.
- We define an error function for m and c and choose the line that reduces the error and gain the optimized value for m and c
- Error function = loss function = cost function
- Residual = distance between datapoint and the fitted line
- Our loss function can be RSS (Residual Sum of Squares) the sum of the residuals and our goal is to minimize this value.
- metrics 
    - r-squared : percentage of the variance in target values explained by the features. range is 0 to 1
    - RMSE : Root Mean squared error (Average error in prediction)
- cross validation : do train-test process in multiple folds and take average to consolidate r-squared.
- Regularization : penalizes large co-efficients to reduce overfitting. Some regressions that uses regularizations:
    - Lasso Regression
    - Ridge Regression
- Hyperparameter : Variables used to optimize model parameters

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Contributed on Jan 29 2023

Innocent Iguana

0 Answers Avg Quality 2/10

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# Implementation of gradient descent in linear regression
import numpy as np
import matplotlib.pyplot as plt
 
class Linear_Regression:
    def __init__(self, X, Y):
        self.X = X
        self.Y = Y
        self.b = [0, 0]
     
    def update_coeffs(self, learning_rate):
        Y_pred = self.predict()
        Y = self.Y
        m = len(Y)
        self.b[0] = self.b[0] - (learning_rate * ((1/m) *
                                np.sum(Y_pred - Y)))
 
        self.b[1] = self.b[1] - (learning_rate * ((1/m) *
                                np.sum((Y_pred - Y) * self.X)))
 
    def predict(self, X=[]):
        Y_pred = np.array([])
        if not X: X = self.X
        b = self.b
        for x in X:
            Y_pred = np.append(Y_pred, b[0] + (b[1] * x))
 
        return Y_pred
     
    def get_current_accuracy(self, Y_pred):
        p, e = Y_pred, self.Y
        n = len(Y_pred)
        return 1-sum(
            [
                abs(p[i]-e[i])/e[i]
                for i in range(n)
                if e[i] != 0]
        )/n
    #def predict(self, b, yi):
 
    def compute_cost(self, Y_pred):
        m = len(self.Y)
        J = (1 / 2*m) * (np.sum(Y_pred - self.Y)**2)
        return J
 
    def plot_best_fit(self, Y_pred, fig):
                f = plt.figure(fig)
                plt.scatter(self.X, self.Y, color='b')
                plt.plot(self.X, Y_pred, color='g')
                f.show()
 
 
def main():
    X = np.array([i for i in range(11)])
    Y = np.array([2*i for i in range(11)])
 
    regressor = Linear_Regression(X, Y)
 
    iterations = 0
    steps = 100
    learning_rate = 0.01
    costs = []
     
    #original best-fit line
    Y_pred = regressor.predict()
    regressor.plot_best_fit(Y_pred, 'Initial Best Fit Line')
     
 
    while 1:
        Y_pred = regressor.predict()
        cost = regressor.compute_cost(Y_pred)
        costs.append(cost)
        regressor.update_coeffs(learning_rate)
         
        iterations += 1
        if iterations % steps == 0:
            print(iterations, "epochs elapsed")
            print("Current accuracy is :",
                regressor.get_current_accuracy(Y_pred))
 
            stop = input("Do you want to stop (y/*)??")
            if stop == "y":
                break
 
    #final best-fit line
    regressor.plot_best_fit(Y_pred, 'Final Best Fit Line')
 
    #plot to verify cost function decreases
    h = plt.figure('Verification')
    plt.plot(range(iterations), costs, color='b')
    h.show()
 
    # if user wants to predict using the regressor:
    regressor.predict([i for i in range(10)])
 
if __name__ == '__main__':
    main()

Popularity 10/10 Helpfulness 2/10 Language python

Source: www.geeksforgeeks.org

Tags: linear-regression linear-regressio

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Contributed on May 21 2022

Alvin Saini

0 Answers Avg Quality 2/10

regression linear

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// This source code is subject to the terms of the Mozilla Public License 2.0 at https://mozilla.org/MPL/2.0/
// © x11joe
// Credit given to @midtownsk8rguy for original source code.  I simply modified to add Pearson's R

//@version=4
study("Linear Regression Trend Channel With Pearson's R", "LRTCWPR", true, format.inherit)
period     = input(     20, "Period"       , input.integer, minval=3)
deviations = input(    2.0, "Deviation(s)" , input.float  , minval=0.1, step=0.1)
extendType = input("Right", "Extend Method", input.string , options=["Right","None"])=="Right" ? extend.right : extend.none
periodMinusOne = period-1
Ex = 0.0, Ey = 0.0, Ex2 = 0.0,Ey2 =0.0, Exy = 0.0, for i=0 to periodMinusOne
    closeI = nz(close[i]), Ex := Ex + i, Ey := Ey + closeI, Ex2 := Ex2 + (i * i),Ey2 := Ey2 + (closeI * closeI), Exy := Exy + (closeI * i)
ExT2 = pow(Ex,2.0) //Sum of X THEN Squared
EyT2 = pow(Ey,2.0) //Sym of Y THEN Squared
PearsonsR = (Exy - ((Ex*Ey)/period))/(sqrt(Ex2-(ExT2/period))*sqrt(Ey2-(EyT2/period)))
ExEx = Ex * Ex, slope = Ex2==ExEx ? 0.0 : (period * Exy - Ex * Ey) / (period * Ex2 - ExEx)
linearRegression = (Ey - slope * Ex) / period
intercept = linearRegression + bar_index * slope
deviation = 0.0, for i=0 to periodMinusOne
    deviation := deviation + pow(nz(close[i]) - (intercept - slope * (bar_index[i])), 2.0)
deviation := deviations * sqrt(deviation / periodMinusOne)
startingPointY = linearRegression + slope * periodMinusOne
var label pearsonsRLabel = na
label.delete(pearsonsRLabel[1])
pearsonsRLabel := label.new(bar_index,startingPointY - deviation*2,text=tostring(PearsonsR), color=color.black,style=label.style_labeldown,textcolor=color.white,size=size.large)
var line upperChannelLine = na  , var line medianChannelLine = na  , var line lowerChannelLine = na
line.delete(upperChannelLine[1]), line.delete(medianChannelLine[1]), line.delete(lowerChannelLine[1])
upperChannelLine  := line.new(bar_index - period + 1, startingPointY + deviation, bar_index, linearRegression + deviation, xloc.bar_index, extendType, color.new(#FF0000, 0), line.style_solid , 2)
medianChannelLine := line.new(bar_index - period + 1, startingPointY            , bar_index, linearRegression            , xloc.bar_index, extendType, color.new(#C0C000, 0), line.style_solid , 1)
lowerChannelLine  := line.new(bar_index - period + 1, startingPointY - deviation, bar_index, linearRegression - deviation, xloc.bar_index, extendType, color.new(#00FF00, 0), line.style_solid , 2)

Popularity 10/10 Helpfulness 1/10 Language whatever

Source: stackoverflow.com

Tags: regression r

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Contributed on Oct 17 2022

Peck Ijo

0 Answers Avg Quality 2/10

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