def correlation(x, y):
stdev_x = standard_deviation(x)
stdev_y = standard_deviation(y)
if stdev_x > 0 and stdev_y > 0:
return covariance(x, y) / stdev_x / stdev_y
else:
return 0
def correlation(x, y):
standard_dev_x = standard_deviation(x)
standard_dev_y = standard_deviation(y)
if (standard_dev_x is 0 or standard_dev_y is 0):
return 0
else:
return covariance(x,
y) / (standard_deviation(x) * standard_deviation(y))
def correlation(x, y):
"""
Covariance values are sometimes difficult to interprete. For this reason,
correlation is a more common measure.
Correlation is always unitless and always lies between -1 (perfect anti-correlation)
and 1 (perfect correlation). Correlation is sensitive to outliers.
"""
stdev_x = standard_deviation(x)
stdev_y = standard_deviation(y)
if stdev_x > 0 and stdev_y > 0:
return covariance(x, y) / stdev_x / stdev_y
else:
return 0 # if no variation, correlation is zero
def correlation(x, y):
"""
Covariance values are sometimes difficult to interprete. For this reason,
correlation is a more common measure.
Correlation is always unitless and always lies between -1 (perfect anti-correlation)
and 1 (perfect correlation). Correlation is sensitive to outliers.
"""
stdev_x = standard_deviation(x)
stdev_y = standard_deviation(y)
if stdev_x > 0 and stdev_y > 0:
return covariance(x, y) / stdev_x / stdev_y
else:
return 0 # if no variation, correlation is zero
def scale(data_matrix):
# data matrix e.g. [[63,67,70], [160,170.2,177.8], [150,160,171]]
"""returns the means and standard deviations of each column"""
num_rows, num_cols = shape(data_matrix)
means = [mean(get_column(data_matrix, j))
for j in range(num_cols)]
stdevs = [standard_deviation(get_column(data_matrix, j))
for j in range(num_cols)]
return means, stdevs
# Repeatedly take a bootstrap sample
# If coefficient of one of the indpendent vars doesn't vary much across samples,
# then we can be confident that our estimate is relatively tight.
# If the coefficient varies greatly across samples, then we can't be at all
# confident in our estimate.
random.seed(0)
bootstrap_betas = bootstrap_statistic(
list(zip(trainer_party_stats, trainer_badge_counts)), estimate_sample_beta,
10)
print('bootstrap betas:')
for beta in bootstrap_betas:
print('beta = %s' % beta)
bootstrap_standard_errors = [
standard_deviation([beta[index] for beta in bootstrap_betas])
for index in range(3)
]
print('standard errors: %s' % bootstrap_standard_errors)
# We can then evaluate the meaningfulness of the betas
# with the following calculations
def p_value(beta_hat_j, sigma_hat_j):
if beta_hat_j > 0:
return 2 * (1 - normal_cdf(beta_hat_j / sigma_hat_j))
else:
return 2 * normal_cdf(beta_hat_j / sigma_hat_j)
def least_squares_fit(xs, ys):
beta = correlation(xs,
ys) * standard_deviation(ys) / standard_deviation(xs)
alpha = mean(ys) - beta * mean(xs)
return alpha, beta