08 Calculating the equation of a regression line

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import numpy as np
import pandas as pd
from pandas import Series, DataFrame
import matplotlib.pyplot as plt
import seaborn as sns
from scipy import stats
from sklearn.linear_model import LinearRegression

khanacademy

https://en.wikipedia.org/wiki/Simple_linear_regression

\[ \hat{y} = mx+b \]

\[ m = r \frac{S_{y}}{S_{x}} \]

\[ (\bar{x}, \bar{y}) \]

x = np.array([1, 2, 2, 3])
y = np.array([1, 2, 3, 6])

def reg_line(x, y):
    x_bar = x.mean()
    y_bar = y.mean()
    s_x = x.std(ddof=1)
    s_y = y.std(ddof=1)
    r, _ = stats.pearsonr(x, y)
    m = r * s_y / s_x 
    # from y_hat = mx + b. then b will be equal to
    b = y_bar - m * x_bar
    print(f'yhat = {m}x + {b}')
    return m, b

m, b = reg_line(x, y)

yhat = 2.5x + -2.0

slope, intercept, r_value, p_value, std_err = stats.linregress(x, y)

line = intercept + slope * x

x_test, y_test = x.reshape(-1, 1), y.reshape(-1, 1)
reg = LinearRegression()
reg.fit(x_test, y_test)
y_pred = reg.predict(x_test)

print('slope', reg.coef_, slope, m)
print('intercept', reg.intercept_, intercept, b)
#print('R squard', reg.score(x_, y_), r_squard)
print('line', y_pred, line)

slope [[2.5]] 2.5 2.5
intercept [-2.] -2.0 -2.0
line [[0.5]
 [3. ]
 [3. ]
 [5.5]] [0.5 3.  3.  5.5]

plt.scatter(x, y, label='original data')
plt.plot(x, intercept + slope * x, color='r', label='fitted line')
plt.legend()
plt.show()

plt.scatter(x, y, label='original data')
plt.plot(x, b + m * x, color='r', label='fitted line')
plt.legend()
plt.show()

plt.scatter(x_test, y_test, label='original data')
plt.plot(x_test, y_pred, color='r', label='fitted line')
plt.legend()
plt.show()

sns.scatterplot(x, y, label='original data')
sns.lineplot(x, b + m*x,  color='r', label='fitted line')

/opt/hostedtoolcache/Python/3.9.13/x64/lib/python3.9/site-packages/seaborn/_decorators.py:36: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  warnings.warn(
/opt/hostedtoolcache/Python/3.9.13/x64/lib/python3.9/site-packages/seaborn/_decorators.py:36: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  warnings.warn(

<AxesSubplot:>

sns.scatterplot(x_test.reshape(-1), y_test.reshape(-1), label='original data')
sns.lineplot(x_test.reshape(-1), y_pred.reshape(-1), color='r', label='fitted line')

/opt/hostedtoolcache/Python/3.9.13/x64/lib/python3.9/site-packages/seaborn/_decorators.py:36: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  warnings.warn(

/opt/hostedtoolcache/Python/3.9.13/x64/lib/python3.9/site-packages/seaborn/_decorators.py:36: FutureWarning: Pass the following variables as keyword args: x, y. From version 0.12, the only valid positional argument will be `data`, and passing other arguments without an explicit keyword will result in an error or misinterpretation.
  warnings.warn(

<AxesSubplot:>