Created
December 19, 2019 04:47
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Linear Regression from Scratch
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from statistics import mean | |
import numpy as np | |
import random | |
import matplotlib.pyplot as plt | |
from matplotlib import style | |
style.use('ggplot') | |
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, dtype=np.float64),np.array(ys,dtype=np.float64) | |
def best_fit_slope_and_intercept(xs,ys): | |
m = (((mean(xs)*mean(ys)) - mean(xs*ys)) / | |
((mean(xs)*mean(xs)) - mean(xs*xs))) | |
b = mean(ys) - m*mean(xs) | |
return m, b | |
def coefficient_of_determination(ys_orig,ys_line): | |
y_mean_line = [mean(ys_orig) for y in ys_orig] | |
squared_error_regr = sum((ys_line - ys_orig) * (ys_line - ys_orig)) | |
squared_error_y_mean = sum((y_mean_line - ys_orig) * (y_mean_line - ys_orig)) | |
print(squared_error_regr) | |
print(squared_error_y_mean) | |
r_squared = 1 - (squared_error_regr/squared_error_y_mean) | |
return r_squared | |
xs, ys = create_dataset(40,40,2,correlation='pos') | |
m, b = best_fit_slope_and_intercept(xs,ys) | |
regression_line = [(m*x)+b for x in xs] | |
r_squared = coefficient_of_determination(ys,regression_line) | |
print(r_squared) | |
plt.scatter(xs,ys,color='#003F72', label = 'data') | |
plt.plot(xs, regression_line, label = 'regression line') | |
plt.legend(loc=4) | |
plt.show() |
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