Hemaatchu / 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: HEMAVATHY S
RegisterNumber: 212223230076
*/
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='red') 
plt.show()

Output:

Result:

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