def project(v, w):
"""return the projection of v onto w"""
coefficient = dot(v, w)
return scalar_multiply(coefficient, w)
def transform_vector(v, components):
return [dot(v, w) for w in components]
def directional_variance_gradient_i(x_i, w):
"""the contribution of row x_i to the gradient of
the direction-w variance"""
projection_length = dot(x_i, direction(w))
return [2 * projection_length * x_ij for x_ij in x_i]
def directional_variance_i(x_i, w):
"""the variance of the row x_i in the direction w"""
return dot(x_i, direction(w))**2
def ridge_penalty(beta, alpha): return alpha * dot(beta[1:], beta[1:])
def predict(x_i, beta):
return dot(x_i, beta)
random.seed(0) # so that you get the same results as me
bootstrap_betas = bootstrap_statistic(zip(x, daily_minutes_good),
estimate_sample_beta,
100)
bootstrap_standard_errors = [
standard_deviation([beta[i] for beta in bootstrap_betas])
for i in range(4)]
print "bootstrap standard errors", bootstrap_standard_errors
print
print "p_value(30.6143, 1.174)", p_value(30.63, 1.174)
print "p_value(0.972, 0.079)", p_value(0.972, 0.079)
print "p_value(-1.868, 0.131)", p_value(-1.868, 0.131)
print "p_value(0.911, 0.990)", p_value(0.911, 0.990)
print
print "regularization"
random.seed(0)
for alpha in [0.0, 0.01, 0.1, 1, 10]:
beta = estimate_beta_ridge(x, daily_minutes_good, alpha=alpha)
print "alpha", alpha
print "beta", beta
print "dot(beta[1:],beta[1:])", dot(beta[1:], beta[1:])
print "r-squared", multiple_r_squared(x, daily_minutes_good, beta)
print