Test_Assumptions_p12.py

from statistics import mean
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import style
import random

style.use('fivethirtyeight')

# xs=np.array([1,2,3,4,5,6])
# ys=np.array([5,4,6,5,6,7])

def create_dataset(hm, variance, step=2, correlation=False):
    val=1
    ys=[]
    for i in range (hm):
        y=val+random.randrange(-variance,variance)
        ys.append(y)
        if correlation and correlation == 'pos':
            val+=step
        elif correlation and correlation == 'neg':
            val-=step
    
    xs=[i for i in range(len(ys))]

    return np.array(xs),np.array(ys)


def best_fit_slope_and_intercept(xs,ys):
    m=(((mean(xs)*mean(ys))-mean(xs*ys))
       /((mean(xs)**2)-mean(xs**2)))
    b=mean(ys)-m*mean(xs)
    return m,b


xs,ys=create_dataset(40,80,2,correlation=False)

m,b=best_fit_slope_and_intercept(xs,ys)
#print(m,b)

def squared_error(ys_orig,ys_line):
    return sum((ys_line-ys_orig)**2)

def coefficient_of_determination(ys_orig,ys_line):
    y_mean_line=[mean(ys_orig) for y in ys_orig]
    squared_error_regr=squared_error(ys_orig,ys_line)
    squared_error_y_mean=squared_error(ys_orig,y_mean_line)
    return 1-(squared_error_regr/squared_error_y_mean)


regression_line=[(m*x)+b for x in xs] 
predict_x=8
predict_y=m*predict_x+b
###same as 
# for x in xs:
#     regression_line=m*x+b

r_squared=coefficient_of_determination(ys,regression_line)
print(r_squared)
plt.scatter(xs,ys)
plt.scatter(predict_x,predict_y,s=100,color='g')
plt.plot(xs,regression_line)
plt.show()