Implementation of Univariate Linear Regression

Aim:

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

Equipment’s required:

1. Hardware – PCs
2. Anaconda – Python 3.7 Installation / Moodle-Code Runner

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

import numpy as np 
import matplotlib.pyplot as plt
x = np.array([0,1,2,3,4,5,6,7,8,9])
y = np.array([1,3,2,5,7,8,8,9,10,12])
plt.scatter(x,y)
plt.show()
xmean = np.mean(x)
ymean = np.mean(y)
num=0
den=0
for i in range(len(x)):
    num+=(x[i]-xmean)*(y[i]-ymean)
    den+=(x[i]-xmean)**2
m = num/den
b = ymean - m*xmean
print(m,b)
ypred = m*x+b
print(ypred)

plt.scatter(x,y,color='Red')
plt.plot(x,ypred,color='Blue')
plt.show()

Output

Result

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