
import numpy as np
import matplotlib.pyplot as plt
from numpy.linalg import inv


x = np.linspace(0,20,100)
y = [np.sin(i) for i in x]
plt.scatter(x,y)
plt.show()


def y_pred(x,beta_list):
    value = 0
    for i in range(len(beta_list)):
        value += beta_list[i]*(x**i)
    return value


#generate the polynomial regression function of degree = deg (positive integer)
def Poly_reg(x,y,deg):
    n = len(x)
    X = []
    x0 = [1 for i in range(n)]
    X.append(x0)
    for d in range(deg):
        xd = [i**(d+1) for i in x]
        X.append(xd)
    X = np.transpose(np.array(X)) 
    Y = np.array(y) 
    Xt = np.transpose(X)
    XtX = np.matmul(Xt,X)
    XtXi = inv(XtX)
    XtXiXt = np.matmul(XtXi,Xt)
    beta = np.matmul(XtXiXt,Y)
    
    beta = np.transpose(beta)
    y_list = [y_pred(i,beta) for i in x]
    plt.plot(x,y_list,color = 'red',label = 'Regression curve')
    plt.scatter(x,y,s = 20)
    plt.legend(loc = 'upper right')
    plt.xlabel('x')
    plt.ylabel('y')
    plt.show()
    return beta


Poly_reg(x,y,9)

array([-3.60746962e-02,  5.60114854e-01,  1.49460816e+00, -1.50741907e+00,
        5.14307455e-01, -8.72912546e-02,  8.23217625e-03, -4.38788154e-04,
        1.23740082e-05, -1.43538332e-07])

Application of multiple linear regression: polynomial regression¶