yogaraj2 / find-the-best-fit-line-using-least-squares-method

Implementation of Univariate Linear Regression

AIM:

To implement univariate Linear Regression to fit a straight line using least squares.

Equipments Required:

1. Hardware – PCs
2. Anaconda – Python 3.7 Installation / Jupyter notebook

Algorithm

1. Get the independent variable X and dependent variable Y.
2. Calculate the mean of the X -values and the mean of the Y -values.
3. Find the slope m of the line of best fit using the formula.
4. Compute the y -intercept of the line by using the formula:
5. Use the slope m and the y -intercept to form the equation of the line.
6. Obtain the straight line equation Y=mX+b and plot the scatterplot.

Program:

/*
Program to implement univariate Linear Regression to fit a straight line using least squares.
Developed by: YOGARAJ S
RegisterNumber:  212223040248
*/

import numpy as np

import matplotlib.pyplot as plt

X = np.array(eval(input()))

Y = np.array(eval(input()))

X_mean =np.mean(X)

Y_mean=np.mean(Y)

num=0

denom=0

for i in range(len(X)):

num+=(X[i] -X_mean)*(Y[i]-Y_mean)

denom+= (X[i]-X_mean)**2

m=num/denom

b=Y_mean-m*X_mean

print(m,b)

y_predicted=m*X+b print(y_predicted)

plt.scatter(X,Y)

plt.plot(X,y_predicted,color='green')

plt.show()

Output:

Result:

Thus the univariate Linear Regression was implemented to fit a straight line using least squares using python programming.