def _calculate_confidence_interval(self,
x,
observations,
model,
rx,
rmodel,
confidence=95):
alpha = 1.0 - confidence / 100.0
n = len(observations)
if n > 2:
xm = x.mean()
observations = array(observations)
model = array(model)
# syx = math.sqrt(1. / (n - 2) * ((observations - model) ** 2).sum())
# ssx = ((x - xm) ** 2).sum()
# ssx = sum([(xi - xm) ** 2 for xi in x])
ti = tinv(alpha, n - 2)
syx = self.syx
ssx = self.ssx
# for i, xi in enumerate(rx):
def _calc_interval(xi):
d = 1.0 / n + (xi - xm) ** 2 / ssx
return ti * syx * math.sqrt(d)
cors = [_calc_interval(xi) for xi in rx]
return cors
def calculate_CI(values): count = len(values) average = numpy.mean(values) variance = numpy.var(values) std_err = math.sqrt(float(variance) / float(count)) degs_freedom = count - 1 t_value = tinv.tinv(1 - confidence_alpha, degs_freedom) margin_error = std_err * t_value #margin_error = std_err #??? return (average - margin_error, average, average + margin_error)
def _calculate_confidence_interval(self,
x,
observations,
rx,
confidence=95):
alpha = 1.0 - confidence / 100.0
n = len(observations)
if n > 2:
xm = x.mean()
ti = tinv(alpha, n - 1)
syx = self.get_syx()
ssx = self.get_ssx(xm)
d = n**-1 + (rx - xm)**2 / ssx
cors = ti * syx * d**0.5
# print rx, cors[0]
return cors
def _calculate_confidence_interval(self,
x,
observations,
rx,
confidence=95):
alpha = 1.0 - confidence / 100.0
n = len(observations)
if n > 2:
xm = x.mean()
ti = tinv(alpha, n - 2)
syx = self.get_syx()
ssx = self.get_ssx(xm)
d = n ** -1 + (rx - xm) ** 2 / ssx
cors = ti * syx * d ** 0.5
return cors
def calc_confidence_interval(self, confidence, x, observations, model, rx, rmodel):
'''
http://people.stfx.ca/bliengme/ExcelTips/RegressionAnalysisConfidence2.htm
'''
alpha = 1.0 - confidence / 100.0
lower = []
upper = []
n = len(observations)
if n > 2:
xm = x.mean()
observations = array(observations)
model = array(model)
syx = math.sqrt(1. / (n - 2) * ((observations - model) ** 2).sum())
ssx = ((x - xm) ** 2).sum()
# ssx = sum([(xi - xm) ** 2 for xi in x])
ti = tinv(alpha, n - 2)
for i, xi in enumerate(rx):
d = 1.0 / n + (xi - xm) ** 2 / ssx
cor = ti * syx * math.sqrt(d)
lower.append(rmodel[i] - cor)
upper.append(rmodel[i] + cor)
# see http://mathworld.wolfram.com/LeastSquaresFitting.html
# error_a = syx * ((1.0 / n + xm ** 2 / ssx)) ** 0.5
# error_b = syx / (ssx) ** 0.5
return array(lower), array(upper)
