/Find-the-best-fit-line-using-Least-Squares-Method

BSD 3-Clause "New" or "Revised" LicenseBSD-3-Clause

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.

image

4. Compute the y -intercept of the line by using the formula:

image

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:

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:

image

Result:

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