def _normal_plot(ys, label, color='b', jitter=0.0, **line_options):
"""
Makes a normal probability plot.
Args:
ys: sequence of values
label: string label for the plotted line
color: color string passed along to pyplot.plot
jitter: float magnitude of jitter added to the ys
line_options: dictionary of options for pyplot.plot
"""
n = len(ys)
xs = [random.gauss(0.0, 1.0) for i in range(n)]
xs.sort()
ys = [y + random.uniform(-jitter, +jitter) for y in ys]
ys.sort()
inter, slope = correlation._least_squares(xs, ys)
fit = correlation._fit_line(xs, inter, slope)
pyplot.plot(*fit, color=color, linewidth=0.5, alpha=0.5)
pyplot.plot(sorted(xs), sorted(ys),
color=color,
marker='.',
label=label,
markersize=3,
alpha=0.1,
**line_options)
def _compute_least_squares(ages, weights):
"""
Computes least squares fit for ages and weights.
Prints summary statistics.
"""
# compute the correlation between age and weight
print('Pearson correlation', correlation._corr(ages, weights))
print('Spearman correlation', correlation._spearman_corr(ages, weights))
# compute least squares fit
inter, slope = correlation._least_squares(ages, weights)
print('(inter, slope):', inter, slope)
res = correlation._residuals(ages, weights, inter, slope)
R2 = correlation._coef_determination(weights, res)
print('R^2', R2)
print
return inter, slope, R2
def _compute_correlations():
resp = brfss_scatter.Respondents()
resp._read_records()
print('Number of records:', len(resp.records))
heights, weights = resp._get_height_weight()
pearson = correlation._corr(heights, weights)
print('Pearson correlation (weights):', pearson)
log_weights = _log(weights)
pearson = correlation._corr(heights, log_weights)
print('Pearson correlation (log weights):', pearson)
spearman = correlation._spearman_corr(heights, weights)
print('Spearman correlation (weights):', spearman)
inter, slope = correlation._least_squares(heights, log_weights)
print('Least squares inter, slope (log weights):', inter, slope)
res = correlation._residuals(heights, log_weights, inter, slope)
R2 = correlation._coef_determination(log_weights, res)
print('Coefficient of determination:', R2)
print('sqrt(R^2):', math.sqrt(R2))
