a1

#program 1
from math import sqrt
# Calculate root mean squared error
def rmse(actual, predicted):
 errors = [(predicted[i] - actual[i]) ** 2 for i in
range(len(actual))]
 return sqrt(sum(errors) / len(actual))
# Calculate mean
def mean(values):
 return sum(values) / len(values)
# Calculate covariance
def covariance(x, y):
 mean_x, mean_y = mean(x), mean(y)
 return sum((x[i] - mean_x) * (y[i] - mean_y) for i in
range(len(x)))
# Calculate variance
def variance(values):
 mean_val = mean(values)
 return sum((x - mean_val) ** 2 for x in values)
# Calculate coefficients
def coefficients(data):
 x = [row[0] for row in data]
 y = [row[1] for row in data]
 b1 = covariance(x, y) / variance(x)
 b0 = mean(y) - b1 * mean(x)
 return b0, b1
# Simple linear regression
def simple_linear_regression(train, test):
 b0, b1 = coefficients(train)
 return [b0 + b1 * row[0] for row in test]
# Test dataset
data = [[1, 1], [2, 3], [4, 3], [3, 2], [5, 5]]
# Evaluate model
x, y = [row[0] for row in data], [row[1] for row in data]
print(f"x stats: mean={mean(x):.3f}, variance={variance(x):.3f}")
print(f"y stats: mean={mean(y):.3f}, variance={variance(y):.3f}")
print(f"Covariance: {covariance(x, y):.3f}")
predicted = simple_linear_regression(data, data)
print(f"Predicted: {predicted}")
print(f"RMSE: {rmse(y, predicted):.3f}")
b0, b1 = coefficients(data)
print(f"Coefficients: B0={b0:.3f}, B1={b1:.3f}")