numpy lab(26/02/2024) linear

import numpy as np
import matplotlib.pyplot as plt

def estimate_coef(x, y):
    # number of observations/points
    n = np.size(x)

    # mean of x and y vector
    m_x = np.mean(x)
    m_y = np.mean(y)

    # calculating cross-deviation and deviation about x
    SS_xy = np.sum(y * x) - n * m_y * m_x
    SS_xx = np.sum(x * x) - n * m_x * m_x

    # calculating regression coefficients
    b_1 = SS_xy / SS_xx
    b_0 = m_y - b_1 * m_x
    print("b_0", b_0)
    print("b_1", b_1)
    return (b_0, b_1)

def plot_regression_line(x, y, b):
    # plotting the actual points as scatter plot
    plt.scatter(x, y, color="m", marker="o", s=30)

    # predicted response vector
    y_pred = b[0] + b[1] * x

    # plotting the regression line
    plt.plot(x, y_pred, color="g")

    # putting labels
    plt.xlabel('x')
    plt.ylabel('y')

# observations / data
x = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
y = np.array([1, 3, 2, 5, 7, 8, 8, 9, 10, 12])

# estimating coefficients
b = estimate_coef(x, y)
plot_regression_line(x, y, b)

output:
https://ibb.co/xmMGCbm

# Predict the speed of a 10-year old car.
import matplotlib.pyplot as plt
from scipy import stats

x = [5, 7, 8, 7, 2, 17, 2, 9, 4, 11, 12, 9, 6]
y = [99, 86, 87, 88, 111, 86, 103, 87, 94, 78, 77, 85, 86]

slope, intercept, r, p, std_err = stats.linregress(x, y)

def myfunc(x):
    return slope * x + intercept

mymodel = list(map(myfunc, x))

plt.scatter(x, y)
plt.plot(x, mymodel)
plt.show()

speed = myfunc(10)
print(speed)

# Example of bad-fit
import matplotlib.pyplot as plt
from scipy import stats

x = [89,43,36,36,95,10,66,34,38,20,26,29,48,
     64,6 ,5 ,36 ,66 ,72 ,40]
y = [21 ,46 ,3 ,35 ,67 ,95 ,53 ,72 ,58 ,10 ,
     26 ,34 ,90 ,33 ,38 ,20 ,56 ,2 ,47 ,15]

slope, intercept,r,p,std_err = stats.linregress(x,y)

def myfunc(x):
    return slope * x + intercept

mymodel = list(map(myfunc,x))

plt.scatter(x,y)
plt.plot(x,mymodel)
plt.show()

print(r)

output:
https://ibb.co/3F6nXwZ
https://ibb.co/k3jv8xM