Hands-on attempt to visualise Linear Regression and R-Square, using Python and Jupyter

Hands-on attempt to visualise Linear Regression and R-Square, using Python and Jupyter

Visit: https://github.com/namitsharma99/basicLinearRegression

Details: https://youtu.be/bQs8nccZw2s

import numpy as np
import pandas as pd
import csv
import matplotlib.pyplot as plt

plt.rcParams['figure.figsize'] = (40.0, 20.0)

data = pd.read_csv("dummy_data.csv")
print(data.shape)
print(data)

(10, 2)
   X-axis  Y-axis
0       1       2
1       2       2
2       3       5
3       4       4
4       5       3
5       6       6
6       7       6
7       8       9
8       9       8
9      10      11

In [15]:

x = data['X-axis'].values
y = data['Y-axis'].values

x_bar = np.mean(x)
y_bar = np.mean(y)

print(x_bar)
print(y_bar)

5.5
5.6

In [16]:

n = len(x)
print(n)

10

In [17]:

# finding equation y = mx + c

num = 0
den = 0

for i in range(n) :
    num += (x[i] - x_bar) * (y[i] - y_bar)
    den += (x[i] - x_bar) ** 2
    
m = num / den
c = y_bar - m * x_bar

print(m)
print(c)

0.9212121212121213
0.5333333333333323

In [39]:

# trying linear regression model

plt.rcParams.update({'font.size': 50})

#actual points
plt.scatter(x, y, color='red', label='actual scatter plot', s=150)

# for line y = mx + c
# translating variables x and y as u and v, as v = mu + c

u = x
v = m * u + c
plt.plot(u, v, color='green', label='predicted line')

plt.xlabel('X-axis')
plt.ylabel('Y-axis')
plt.legend()
plt.show()

[ 1  2  3  4  5  6  7  8  9 10]
[1.45454545 2.37575758 3.2969697  4.21818182 5.13939394 6.06060606
 6.98181818 7.9030303  8.82424242 9.74545455]

In [42]:

# checking the accuracy of this model using R^2 technique
# using line v = m * u + c

num = 0
den = 0

for i in range(n):
    # y axis predicted :
    v_p = m * u[i] + c
    num += (v_p - y_bar) ** 2
    den += (y[i] - y_bar) ** 2
    
print(num/ den)

0.8496616651956459