This is my first story in medium, in this story I am going to explain “How to Implement simple linear regression using python without any library?”.

Although I have used some basic libraries like *pandas*, *numpy* and *matplotlib* to get dataset, to solve equation and to visualize the data respectively.

You will find the notebook which I have created using sklearn and the dataset in github repository.

I have explained the code below.

import numpy as np

import matplotlib.pyplot as plt

class Regression:

def __init__(self):

pass

def find_sum(l, p):

res = 0

for i in l:

res += i**p

return res

def find_mul_sum(l1, l2):

res = 0

for i in range(len(l1)):

res += (l1[i]*l2[i])

return res

def solve_equ(sum_x, sum_x2, sum_y, sum_xy):

# Equation no 1

# Ey = a * Ex + b * n

# Equation no 2

# Exy = a * Ex^2 + b * Ex

n = 30

p = np.array([[sum_x,n], [sum_x2,sum_x]])

q = np.array([sum_y, sum_xy])

res = np.linalg.solve(p, q)

return res

def predict(x, res):

y_pred = []

for i in x:

y_pred.append(res[0] * i + res[1])

return y_pred

def main():

x = [1.1,1.3,1.5,2,2.2,2.9,3,3.2,3.2,3.7,3.9,4,4,4.1,4.5,4.9,5.1,5.3,5.9,6,6.8,7.1,7.9,8.2,8.7,9,9.5,9.6,10.3,10.5]

y = [39343,46205,37731,43525,39891,56642,60150,54445,64445,57189,63218,55794,56957,57081,61111,67938,66029,83088,81363,93940,91738,98273,101302,113812,109431,105582,116969,112635,122391,121872]

r = Regression

sum_x = r.find_sum(x, 1)

sum_y = r.find_sum(y, 1)

sum_x2 = r.find_sum(x, 2)

sum_xy = r.find_mul_sum(x, y)

res = []

res = r.solve_equ(sum_x, sum_x2, sum_y, sum_xy)

y_pred = r.predict(x, res)

plt.scatter(x, y, color = 'red')

plt.plot(x, y_pred, color = 'blue')

plt.title('Ownression')

plt.xlabel('X')

plt.ylabel('Y')

plt.show()

if __name__ == "__main__":

main()

Here as you might get the idea that I have created the class Regression with necessary method and for sake of simplicity I have used the basic sample data in X and Y.

First method in class I have created finds the sum of the list with power if you know how to get regression co-efficient on paper then it should not be a problem for you.

After getting all the sum we have to create two equations as we are using Least Square Method.

To solve the equation I have used *numpy’s* method named *linalg.solve.* By solving the equation we will get one constant which we will use to get the value from x for test dataset. My method to solve equation will return the list of two unknowns** “y = a * x + b”** here it’ll return

**a**and

**b.**

In predict method it will create the list named *y_pred *is a list of predicted values of the values that is been passed as a test.

Finally, in the main method it will apply all the methods that I have used and will also plot the graph where points in red color shows the actual values and the blue line shows the predicted values.

Hope you liked the article. If you have any kind of question related to this article let me know.

**Thank you for reading. :)**