def Summarize(estimates, actual=None):
mean = thinkstats2.Mean(estimates)
stderr = thinkstats2.Std(estimates, mu=actual)
cdf = thinkstats2.Cdf(estimates)
ci = cdf.ConfidenceInterval(90)
print('mean: ', mean,
'\nSE: ',stderr,
'\nCI: ', ci)
def Summarize(estimates, actual=None):
"""Prints standard error and 90% confidence interval.
estimates: sequence of estimates
actual: float actual value
"""
mean = thinkstats2.Mean(estimates)
stderr = thinkstats2.Std(estimates, mu=actual)
cdf = thinkstats2.Cdf(estimates)
ci = cdf.ConfidenceInterval(90)
print('mean, SE, CI', mean, stderr, ci)
def PlotSamplingDistributions(live):
"""Plots confidence intervals for the fitted curve and sampling dists.
live: DataFrame
"""
ages = live.agepreg
weights = live.totalwgt_lb
inter, slope = thinkstats2.LeastSquares(ages, weights)
res = thinkstats2.Residuals(ages, weights, inter, slope)
r2 = thinkstats2.CoefDetermination(weights, res)
print('rho', thinkstats2.Corr(ages, weights))
print('R2', r2)
print('R', math.sqrt(r2))
print('Std(ys)', thinkstats2.Std(weights))
print('Std(res)', thinkstats2.Std(res))
# plot the confidence intervals
inters, slopes = SamplingDistributions(live, iters=1001)
PlotConfidenceIntervals(ages,
inters,
slopes,
percent=90,
alpha=0.3,
label='90% CI')
thinkplot.Text(42, 7.53, '90%')
PlotConfidenceIntervals(ages,
inters,
slopes,
percent=50,
alpha=0.5,
label='50% CI')
thinkplot.Text(42, 7.59, '50%')
thinkplot.Save(root='linear3',
xlabel='age (years)',
ylabel='birth weight (lbs)',
legend=False)
# plot the confidence intervals
thinkplot.PrePlot(2)
thinkplot.Scatter(ages, weights, color='gray', alpha=0.1)
PlotConfidenceIntervals(ages, inters, slopes, res=res, alpha=0.2)
PlotConfidenceIntervals(ages, inters, slopes)
thinkplot.Save(root='linear5',
xlabel='age (years)',
ylabel='birth weight (lbs)',
title='90% CI',
axis=[10, 45, 0, 15],
legend=False)
# plot the sampling distribution of slope under null hypothesis
# and alternate hypothesis
sampling_cdf = thinkstats2.Cdf(slopes)
print('p-value, sampling distribution', sampling_cdf[0])
ht = SlopeTest((ages, weights))
pvalue = ht.PValue()
print('p-value, slope test', pvalue)
print('inter', inter, thinkstats2.Mean(inters))
Summarize(inters, inter)
print('slope', slope, thinkstats2.Mean(slopes))
Summarize(slopes, slope)
thinkplot.PrePlot(2)
thinkplot.Plot([0, 0], [0, 1], color='0.8')
ht.PlotCdf(label='null hypothesis')
thinkplot.Cdf(sampling_cdf, label='sampling distribution')
thinkplot.Save(root='linear4',
xlabel='slope (lbs / year)',
ylabel='CDF',
xlim=[-0.03, 0.03],
loc='upper left')
def Summarize(estimates, actual=None):
mean = thinkstats2.Mean(estimates)
stderr = thinkstats2.Std(estimates, mu=actual)
cdf = thinkstats2.Cdf(estimates)
ci = cdf.ConfidenceInterval(90)
print('mean: {:.3f} SE: {:.3f} CI: {}'.format(mean, stderr, ci))
thinkplot.Config(xlabel='height (cm)', ylabel='residual weight (kg)')
#%%
# calculate correlation and coefficient of determination
rho = thinkstats2.Corr(heights, logWeight)
r2 = thinkstats2.CoefDetermination(logWeight, res)
# check if R^2 = rho^2
print("Correlation: {:.3f}".format(rho))
print("Coefficent of determination: {:.3f}".format(r2))
print("R^2 - rho^2: {:.3f}".format(rho**2 - r2))
#%%
# calc standard deviation (RMSE) of prediction w/o height
std_ys = thinkstats2.Std(logWeight)
print("Standard deviation w/o height: {:.3f}".format(std_ys))
#%%
# calc standard deviation (RMSE) of prediction w/ height
std_res = thinkstats2.Std(res)
print("Standard deviation w/ height: {:.3f}".format(std_res))
#%%
# How does RMSE get impacted by height info
print("Impact: {:.3f}".format(1 - (std_res / std_ys)))
#%%
# Resampling to compute inter and slope
t = []
for _ in range(100):