def _coef_determination(ys, res):
"""
Computes the coefficient of determination (R^2) for given residuals.
Args:
ys: dependent variable
res: residuals
Returns:
float coefficient of determination
"""
ybar, vary = _03_thinkstats._mean_var(ys)
resbar, varres = _03_thinkstats._mean_var(res)
return 1 - varres / vary
def _corr(xs, ys):
"""
Computes Corr(X, Y).
Args:
xs: sequence of values
ys: sequence of values
Returns:
Corr(X, Y)
"""
xbar, varx = _03_thinkstats._mean_var(xs)
ybar, vary = _03_thinkstats._mean_var(ys)
corr = _cov(xs, ys, xbar, ybar) / math.sqrt(varx * vary)
return corr
def _least_squares(xs, ys):
"""
Computes a linear least squares fit for ys as a function of xs.
Args:
xs: sequence of values
ys: sequence of values
Returns:
tuple of (intercept, slope)
"""
xbar, varx = _03_thinkstats._mean_var(xs)
ybar, vary = _03_thinkstats._mean_var(ys)
slope = _cov(xs, ys, xbar, ybar) / varx
inter = ybar - slope * xbar
return inter, slope
def _test(actual1, actual2, model, iters=1000):
"""
Estimates p-values based on differences in the mean.
Args:
actual1:
actual2: sequences of observed values for groups 1 and 2
model: sequences of values from the hypothetical distribution
"""
n = len(actual1)
m = len(actual2)
# compute delta
mu1, mu2, delta = hypothesis._difference_in_mean(actual1, actual2)
delta = abs(delta)
print('n:', n)
print('m:', m)
print('mu1', mu1)
print('mu2', mu2)
print('delta', delta)
# compute the expected distribution of differences in sample mean
mu_pooled, var_pooled = _03_thinkstats._mean_var(model)
print('(Mean, Var) of pooled data', mu_pooled, var_pooled)
f = 1.0 / n + 1.0 / m
mu, var = (0, f * var_pooled)
print('Expected Mean, Var of deltas', mu, var)
# compute the p-value of delta in the observed distribution
sigma = math.sqrt(var)
left = _16_erf._normal_cdf(-delta, mu, sigma)
right = 1 - _16_erf._normal_cdf(delta, mu, sigma)
pvalue = left + right
print('Tails:', left, right)
print('p-value:', pvalue)
# compare the mean and variance of resamples differences
deltas = [hypothesis._resample(model, model, n, m) for i in range(iters)]
mean_var = _03_thinkstats._mean_var(deltas)
print('(Mean, Var) of resampled deltas', mean_var)
return pvalue
def _make_uniform_prior(t, num_points, label, spread=3.0):
"""
Makes a prior distribution for mu and sigma based on a sample.
Args:
t: sample
num_points: number of values in each dimension
label: string label for the new Pmf
spread: number of standard errors to include
Returns:
Pmf that maps from (mu, sigma) to prob.
"""
# estimate mean and stddev of t
n = len(t)
xbar, S2 = _03_thinkstats._mean_var(t)
sighat = math.sqrt(S2)
print(xbar, sighat, sighat / xbar)
# compute standard error for mu and the range of ms
stderr_xbar = sighat / math.sqrt(n)
mspread = spread * stderr_xbar
ms = numpy.linspace(xbar - mspread, xbar + mspread, num_points)
# compute standard error for sigma and the range of ss
stderr_sighat = sighat / math.sqrt(2 * (n - 1))
sspread = spread * stderr_sighat
ss = numpy.linspace(sighat - sspread, sighat + sspread, num_points)
# populate the PMF
pmf = _04_Pmf.Pmf(name=label)
for m in ms:
for s in ss:
pmf._set((m, s), 1)
return ms, ss, pmf
def _summarize(srcs):
"""Computes the number of edges for each source."""
lens = [len(t) for t in srcs.itervalues()]
mu, sigma2 = _03_thinkstats._mean_var(lens)
print(mu, math.sqrt(sigma2))
return lens
