Experiment 1: Varying the Number of Points • Fix the uniform noise interval 8 = 1. • Vary the number of points n = : 2, 5, 7, 10, 20, 50, 75, 100. • For each value of n, generate data, fit the model, calculate Err(wo, w†), and plot Err(wt), w₁) as a function of n. • Generate 1 plot with 8 different subplots, one for each value of n, subplot each showing the true model, generated data points with noise, and the predicted model. Experiment 2: Varying the Noise Interval • Fix the number of points n = = 100. • Vary the uniform interval = 0.1, 1, 5, 10. • For each value of 8, generate data, fit the model, calculate Err(wo), w¼), and plot Err(w+), w¼) as a function of S. • Generate 1 plot with 4 subplots, one for each value of 8, each subplot such showing the true model, generated data points with noise, and the predicted model.
import numpy as np
import matplotlib.pyplot as plt
alpha = np.random.uniform(1.0,5.0)
beta = np.random.uniform(0.0,10.0)
def generate_data(n):
x = np.random.uniform(-10, 10, n) # Generate 'n' random x values
epsilon = np.random.uniform(-n, n, n) # 'n' random noise values
y = alpha * x + beta + epsilon
return x, y
def find_optimal_slope(x,y):
x_mean = np.mean(x)
y_mean = np.mean(y)
numerator = np.sum((x - x_mean) * (y - y_mean))
denominator = np.sum((x - x_mean)**2)
if denominator == 0:
slope = 9999999
else:
slope = numerator / denominator
return slope
def find_optimal_intercept(x,y):
slope = find_optimal_slope(x, y)
x_mean = np.mean(x)
y_mean = np.mean(y)
intercept = y_mean - slope * x_mean
return intercept
def calculate_err(x,y):
slope = find_optimal_slope(x, y)
intercept = find_optimal_intercept(x,y)
alpha = np.random.uniform(1.0,5.0)
beta = np.random.uniform(0.0,10.0)
estimation_error = (abs(slope - alpha) ** 2 + abs(slope - beta) ** 2) ** 0.5
def plot_fit(n):
alpha = np.random.uniform(1.0, 5.0)
beta = np.random.uniform(0.0, 10.0)
# Generate data
x, y = generate_data(n)
# Find the optimal slope and intercept for the best-fit line
slope = find_optimal_slope(x, y)
intercept = find_optimal_intercept(x, y)
# Calculate the fitted line and true line
fitted_line = slope * x + intercept
true_line = alpha * x + beta
# Plotting
plt.scatter(x, y, color='blue', label='Data points')
plt.plot(x, fitted_line, color='red', label='Fitted line')
plt.plot(x, true_line, color='green', label='True line', linestyle='--')
plt.legend()
plt.title('True Line vs Fitted Line')
plt.xlabel('x')
plt.ylabel('y')
plt.show()
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