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 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))