我自己的线性回归

Question

I have some data:

x_data = 0.603 + np.array(range(1,5))
y_data = np.array([22.8,78.6,129.7,181.3,])3

now I want to create my own function for linear regression:

import numpy as np
import sympy as sp

def linear_fit(xi,yi):
    a = sp.Symbol("a")
    b = sp.Symbol("b")
    data = np.transpose(np.array([xi,yi]))
    res_sum = sum(np.array([(a * i + b - j)**2 for i, j in data]))

I am not sure how to derivate this sum and then how to solve the equations for "a" and "b". And I wonder if there is a better way to define linear regression instead of using sympy.

Answer 1

I like that spirit to make your own regression model instead of using other libraries. You can try this code i wrote and update it as you wish.

import numpy as np
import time
"""
m is the coeficient and b0 is the y intercrept(the y obstacle in the y-axis) and 
x_pred is the predicting data
in this model we predict the y by x so we should feed some xs to the data and some ys 
and then we predict the y to the given x
"""
class Linear:
     m = 0;#the coef
     b0 = 0;#the y-intercrept
     def train(x,y):#train data set simply we do is fit the xs to the ys
         global b0;
         global m;
         pred = [];
         c = 0;
         m_x = np.mean(x);#mean of x
         m_y = np.mean(y);#mean of y
         s = len(x); #length of x
         num,den = 0,0;#the denominator and the numerator
         for i in range(s):
             num += (x[i]-m_x)*(y[i]-m_y);#numerator #find m; m= (x[i]m_x(y[i]m_y)/(x[i]-m_x)**2 -->do this for s number of times(the number of xs in the data set) do this for number of xs in the data set
         den += (x[i]-m_x)**2;#denominator
         m = num/den;#find m; m= (x[i]-m_x)*(y[i]-m_y)/(x[i]-m_x)**2  
         b0 = m_y-(m*m_x);#find b0(the y-intercrept)
         return pred;

    def predict(x_pred):#predict model
        global b0,m;
        x_test = m*x_pred+b0;#y = m*x+b is the predicting equation
        print("y={}*{}+{}".format(m,x,b0));
        return x_test;
y = [3,6,9];
x = [5,10,15];
train = Linear.train(x,y);
p1 = Linear.predict(5);
print("y is:",p1);

This is all YOURS!!!! -From TOEKNEEHARSH

Answer 2

In short, you need to implement all the functions for computing the hypothesis, the cost and the gradient, and then combine them to create your model.

You can take a look at this notebook implemented from scratch using NumPy .

Although this notebook implements Logistic Regression and not Linear Regression, you can get a fair idea about how to implement Linear Regression.