linear_regression_from_scratch(OLS)

from math import sqrt
#some utility function 
def mean(values):
  mean_value=sum(values) / float(len(values))
  return mean_value
# Calculate the variance of a list of numbers
def variance(values, mean):
  var=0
  for i in range(len(values)):
    var+=(values[i]-mean)**2  
  return var
# Calculate covariance between x and y
def covariance(x, mean_x, y, mean_y):
  covar = 0.0
  for i in range(len(x)):
    covar += (x[i] - mean_x) * (y[i] - mean_y)
  return covar
# Calculate coefficients(betas)
def coefficients(dataset):
  x = [row[0] for row in dataset]
  y = [row[1] for row in dataset]
  x_mean, y_mean = mean(x), mean(y)
  b1 = covariance(x, x_mean, y, y_mean) / variance(x, x_mean)
  b0 = y_mean - b1 * x_mean
  return [b0, b1]
# Simple linear regression algorithm
def simple_linear_regression(train, test):
	predictions = []
	b0, b1 = coefficients(train)
	for row in test:
		yhat = b0 + b1 * row[0]
		predictions.append(yhat)
	return predictions
# Evaluate regression algorithm on training dataset
def evaluate_algorithm(dataset, algorithm):
	test_set = []
	for row in dataset:
		row_copy = list(row)
		row_copy[-1] = None
		test_set.append(row_copy)
	predicted = algorithm(dataset, test_set)
	actual = [row[-1] for row in dataset]
	rmse = rmse_metric(actual, predicted)
	return predicted,rmse
  # Test simple linear regression
dataset = [[1, 1], [2, 3], [4, 3], [3, 2], [5, 5]]
predicton,rmse = evaluate_algorithm(dataset, simple_linear_regression)
print('RMSE: %.3f' % (rmse))