Linear Regression

Regression analysis is a form of predictive modelling technique which investigates the relationship between a dependent and independent variable. 

Mathematical Part,

Y = aX + b

            Y – random variable (response, dependent)

            X – random variable (predictor, independent)

a, b - regression coefficients, that are to be learned

a = S_i=1:s (x_i – x¢) (y_i- y¢) / S_i=1:s  (x_i – x¢)² , 

b = y¢ - ax¢,

where ,

x¢ = average of x₁, x₂, … , x_s , 

y¢ = average of y₁, y₂, … , y_s ,

given sample data points (x₁, y₁), (x₂, y₂),  …, (x_s, y_s).

Dataset: The dataset we use is iris.data  

From https://www.kaggle.com/uciml/iris 

Source Code: 

1. # -*- coding: utf-8 -*-  
2. """ 
3. Created on Mon Sep 30 03:12:40 2019 
4.  
5. @author: nowshad 
6. """  
7. import numpy as np  
8. import matplotlib.pyplot as plt  
9. import pandas as pd  
10.   
11. dataset = pd.read_csv('headbrain.csv')  
12. print(dataset.shape)   
13. print(dataset.head(5))    
14.   
15. X = dataset['Head Size(cm^3)'].values  
16. Y = dataset['Brain Weight(grams)'].values  
17. mean_x = np.mean(X)  
18. mean_y= np.mean(Y)  
19.   
20. n=len(X)  
21.   
22. numer=0  
23. denom=0  
24. for i in range(n):  
25.     numer += (X[i]-mean_x)*(Y[i]-mean_y)  
26.     denom += (X[i]-mean_x)**2  
27.       
28. m= numer/denom  
29. c= mean_y - (m*mean_x)  
30. print("m= ",m)  
31. print("c= ",c)  
32.   
33. max_x = np.max(X)+1  
34. min_x= np.min(X)-1  
35. x=np.linspace(min_x,max_x,5)  
36. y=m*x+c  
37.   
38. plt.plot(x,y,color='green',label='Regression Line')  
39. plt.scatter(X,Y,color='red',label='Scatter Plot')  
40. plt.xlabel('Head Size')  
41. plt.ylabel('Brain Weight')  
42. plt.legend()  
43. plt.show()  
44.   
45. err_nm=0  
46. err_dn=0  
47. for i in range(n):  
48.     y_predict=m*X[i]+c  
49.     err_nm += (Y[i]-y_predict) **2  
50.     err_dn += (Y[i]-mean_y)**2  
51. r2= (1-(err_nm/err_dn))*100  
52. print("\nR2 = ",r2,"%")  

Output

R square value is more than 0.50 and its good enough.

Reference

https://www.edureka.co/python