def PlotMarathon(data):
"""Plots the marathon data.
data:
"""
print len(data)
xs, ys = zip(*data)
print xs, ys
n = 29
fxs, fys = xs[:n], ys[:n]
sxs, sys = xs[n:], ys[n:]
inter, slope = correlation.LeastSquares(sxs, sys)
print '(inter, slope):', inter, slope
end = 2043
target = 26.21875 / 2
lxs, lys = MakeLine(target, 0, [1965, end])
pyplot.plot(lxs, lys, 'r')
lxs, lys = MakeLine(inter, slope, [1965, end])
pyplot.plot(lxs, lys, 'b')
#pyplot.plot(fxs, fys, 'go')
pyplot.plot(sxs, sys, 'bo')
xticks = range(1980, 2060, 20)
pyplot.xticks(xticks)
myplot.Save(root='world_record_predict',
title='Marathon record projection',
ylabel='mph',
formats=['pdf', 'eps', 'png'])
def NormalPlot(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.LeastSquares(xs, ys)
fit = correlation.FitLine(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 Pvalue(filename='heri.0', delta=0.033, n=100000):
data = ReadData(filename)
count = 0
for i in range(n):
xs, ys = zip(*data)
ys = list(ys)
random.shuffle(ys)
inter, slope = correlation.LeastSquares(xs, ys)
if abs(slope) > delta:
count += 1
return float(count) / n
def FitCdf(cdf):
"""Fits a line to the log CCDF and returns the slope.
cdf: Cdf of RDT
"""
xs, ps = cdf.xs, cdf.ps
cps = [1 - p for p in ps]
xs = xs[1:-1]
lcps = [math.log(p) for p in cps[1:-1]]
_inter, slope = correlation.LeastSquares(xs, lcps)
return -slope
def testLeastSquares(self):
xs = [1, 2, 3]
ys = [3, 6, 8]
inter, slope = correlation.LeastSquares(xs, ys)
self.assertAlmostEquals(inter, 0.66666666)
self.assertAlmostEquals(slope, 2.5)
res = correlation.Residuals(xs, ys, inter, slope)
for got, exp in zip(res, [-0.166666666, 0.33333333, -0.16666666666]):
self.assertAlmostEquals(got, exp)
R2 = correlation.CoefDetermination(ys, res)
self.assertAlmostEquals(R2, 0.986842105263)
def Fit(xs, ys):
"""Find the linear least squares fit between xs and ys."""
inter, slope = correlation.LeastSquares(xs, ys)
print '(inter, slope):', inter, slope
res = correlation.Residuals(xs, ys, inter, slope)
R2 = correlation.CoefDetermination(ys, res)
print 'inter', inter
print 'slope', slope
print 'R^2', R2
print
return inter, slope, R2
def Fit(halfs, fulls):
"""Find the linear least squares fit between halfs and fulls."""
inter, slope = correlation.LeastSquares(halfs, fulls)
print '(inter, slope):', inter, slope
res = correlation.Residuals(halfs, fulls, inter, slope)
R2 = correlation.CoefDetermination(fulls, res)
print 'inter', inter
print 'slope', slope
print 'R^2', R2
print
print 'prediction', inter + slope * ConvertTimeToMinutes('1:34:05')
return inter, slope, R2
def FitLine(xs, ys, fxs):
"""Fits a line to the xs and ys, and returns fitted values for fxs.
Applies a log transform to the xs.
xs: diameter in cm
ys: age in years
fxs: diameter in cm
"""
lxs = [math.log(x) for x in xs]
inter, slope = correlation.LeastSquares(lxs, ys)
# res = correlation.Residuals(lxs, ys, inter, slope)
# r2 = correlation.CoefDetermination(ys, res)
lfxs = [math.log(x) for x in fxs]
fys = [inter + slope * x for x in lfxs]
return fys
def ComputeLeastSquares(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.SpearmanCorr(ages, weights)
# compute least squares fit
inter, slope = correlation.LeastSquares(ages, weights)
print '(inter, slope):', inter, slope
res = correlation.Residuals(ages, weights, inter, slope)
R2 = correlation.CoefDetermination(weights, res)
print 'R^2', R2
print
return inter, slope, R2
def ComputeCorrelations():
resp = brfss_scatter.Respondents()
resp.ReadRecords()
print('Number of records:', len(resp.records))
heights, weights = resp.GetHeightWeight()
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.SpearmanCorr(heights, weights)
print('Spearman correlation (weights):', spearman)
inter, slope = correlation.LeastSquares(heights, log_weights)
print('Least squares inter, slope (log weights):', inter, slope)
res = correlation.Residuals(heights, log_weights, inter, slope)
R2 = correlation.CoefDetermination(log_weights, res)
print('Coefficient of determination:', R2)
print('sqrt(R^2):', math.sqrt(R2))
