def test_regress(self):
"""regression slope, intercept should match p 459 Sokal and Rohlf"""
x = [0, 12, 29.5,43,53,62.5,75.5,85,93]
y = [8.98, 8.14, 6.67, 6.08, 5.90, 5.83, 4.68, 4.20, 3.72]
self.assertFloatEqual(regress(x, y), (-0.05322, 8.7038), 0.001)
#higher precision from OpenOffice
self.assertFloatEqual(regress(x, y), (-0.05322215,8.70402730))
def test_regress(self):
"""regression slope, intercept should match p 459 Sokal and Rohlf"""
x = [0, 12, 29.5, 43, 53, 62.5, 75.5, 85, 93]
y = [8.98, 8.14, 6.67, 6.08, 5.90, 5.83, 4.68, 4.20, 3.72]
self.assertFloatEqual(regress(x, y), (-0.05322, 8.7038), 0.001)
#higher precision from OpenOffice
self.assertFloatEqual(regress(x, y), (-0.05322215, 8.70402730))
def plot_regression_line(x,y,line_color='r', axes=None, prob_axes=False, \
axis_range=None):
"""Plots the regression line, and returns the equation.
x and y are the x and y data for a single series
line_color is a matplotlib color, will be used for the line
axes is the name of the axes the regression will be plotted against
prob_axes, if true, forces the axes to be between 0 and 1
range, if not None, forces the axes to be between (xmin, xmax, ymin, ymax).
"""
if axes is None:
axes = gca()
m, b = regress(x, y)
r, significance = correlation(x,y)
#set the a, b, and r values. a is the slope, b is the intercept.
r_str = '%0.3g'% (r**2)
m_str ='%0.3g' % m
b_str = '%0.3g' % b
#want to clip the line so it's contained entirely within the graph
#coordinates. Basically, we need to find the values of y where x
#is at x_min and x_max, and the values of x where y is at y_min and
#y_max.
#if we didn't set prob_axis or axis_range, just find empirical x and y
if (not prob_axes) and (axis_range is None):
x1, x2 = min(x), max(x)
y1, y2 = m*x1 + b, m*x2 + b
x_min, x_max = x1, x2
else:
if prob_axes:
x_min, x_max = 0, 1
y_min, y_max = 0, 1
else: #axis range must have been set
x_min, x_max, y_min, y_max = axis_range
#figure out bounds for x_min and y_min
y_at_x_min = m*x_min + b
if y_at_x_min < y_min: #too low: find x at y_min
y1 = y_min
x1 = (y_min-b)/m
elif y_at_x_min > y_max: #too high: find x at y_max
y1 = y_max
x1 = (y_max-b)/m
else: #just right
x1, y1 = x_min, y_at_x_min
y_at_x_max = m*x_max + b
if y_at_x_max < y_min: #too low: find x at y_min
y2 = y_min
x2 = (y_min-b)/m
elif y_at_x_max > y_max: #too high: find x at y_max
y2 = y_max
x2 = (y_max-b)/m
else: #just right
x2, y2 = x_max, y_at_x_max
#need to check that the series wasn't entirely in range
if (x_min <= x1 <= x_max) and (x_min <= x2 <= x_max):
axes.plot([x1,x2],[y1,y2], color=line_color, linewidth=0.5)
if b >= 0:
sign_str = ' + '
else:
sign_str = ' '
equation=''.join(['y= ',m_str,'x',sign_str,b_str,'\nr$^2$=',r_str])
return equation, line_color
def plot_regression_line(x,y,line_color='r', axes=None, prob_axes=False, \
axis_range=None):
"""Plots the regression line, and returns the equation.
x and y are the x and y data for a single series
line_color is a matplotlib color, will be used for the line
axes is the name of the axes the regression will be plotted against
prob_axes, if true, forces the axes to be between 0 and 1
range, if not None, forces the axes to be between (xmin, xmax, ymin, ymax).
"""
if axes is None:
axes = gca()
m, b = regress(x, y)
r, significance = correlation(x,y)
#set the a, b, and r values. a is the slope, b is the intercept.
r_str = '%0.3g'% (r**2)
m_str ='%0.3g' % m
b_str = '%0.3g' % b
#want to clip the line so it's contained entirely within the graph
#coordinates. Basically, we need to find the values of y where x
#is at x_min and x_max, and the values of x where y is at y_min and
#y_max.
#if we didn't set prob_axis or axis_range, just find empirical x and y
if (not prob_axes) and (axis_range is None):
x1, x2 = min(x), max(x)
y1, y2 = m*x1 + b, m*x2 + b
x_min, x_max = x1, x2
else:
if prob_axes:
x_min, x_max = 0, 1
y_min, y_max = 0, 1
else: #axis range must have been set
x_min, x_max, y_min, y_max = axis_range
#figure out bounds for x_min and y_min
y_at_x_min = m*x_min + b
if y_at_x_min < y_min: #too low: find x at y_min
y1 = y_min
x1 = (y_min-b)/m
elif y_at_x_min > y_max: #too high: find x at y_max
y1 = y_max
x1 = (y_max-b)/m
else: #just right
x1, y1 = x_min, y_at_x_min
y_at_x_max = m*x_max + b
if y_at_x_max < y_min: #too low: find x at y_min
y2 = y_min
x2 = (y_min-b)/m
elif y_at_x_max > y_max: #too high: find x at y_max
y2 = y_max
x2 = (y_max-b)/m
else: #just right
x2, y2 = x_max, y_at_x_max
#need to check that the series wasn't entirely in range
if (x_min <= x1 <= x_max) and (x_min <= x2 <= x_max):
axes.plot([x1,x2],[y1,y2], color=line_color, linewidth=0.5)
if b >= 0:
sign_str = ' + '
else:
sign_str = ' '
equation=''.join(['y= ',m_str,'x',sign_str,b_str,'\nr$^2$=',r_str])
return equation, line_color
