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multiple_linear_regression_from_scratch.py
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multiple_linear_regression_from_scratch.py
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import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
data = pd.read_csv('student.csv')
print(data.shape)
data.head()
math = data['Math'].values
read = data['Reading'].values
write = data['Writing'].values
# Ploting the scores as scatter plot
fig = plt.figure()
ax = Axes3D(fig)
ax.scatter(math, read, write, color='#ef1234')
plt.show()
m = len(math)
x0 = np.ones(m)
X = np.array([x0, math, read]).T
# Initial Coefficients
B = np.array([0, 0, 0])
Y = np.array(write)
alpha = 0.0001
def cost_function(X, Y, B):
m = len(Y)
J = np.sum((X.dot(B) - Y) ** 2)/(2 * m)
return J
inital_cost = cost_function(X, Y, B)
print("Initial Cost")
print(inital_cost)
def gradient_descent(X, Y, B, alpha, iterations):
cost_history = [0] * iterations
m = len(Y)
for iteration in range(iterations):
# Hypothesis Values
h = X.dot(B)
# Difference b/w Hypothesis and Actual Y
loss = h - Y
# Gradient Calculation
gradient = X.T.dot(loss) / m
# Changing Values of B using Gradient
B = B - alpha * gradient
# New Cost Value
cost = cost_function(X, Y, B)
cost_history[iteration] = cost
return B, cost_history
# 100000 Iterations
newB, cost_history = gradient_descent(X, Y, B, alpha, 100000)
# New Values of B
print("New Coefficients")
print(newB)
# Final Cost of new B
print("Final Cost")
print(cost_history[-1])
# Model Evaluation - RMSE
def rmse(Y, Y_pred):
rmse = np.sqrt(sum((Y - Y_pred) ** 2) / len(Y))
return rmse
# Model Evaluation - R2 Score
def r2_score(Y, Y_pred):
mean_y = np.mean(Y)
ss_tot = sum((Y - mean_y) ** 2)
ss_res = sum((Y - Y_pred) ** 2)
r2 = 1 - (ss_res / ss_tot)
return r2
Y_pred = X.dot(newB)
print("RMSE")
print(rmse(Y, Y_pred))
print("R2 Score")
print(r2_score(Y, Y_pred))