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%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np
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from IPython.html.widgets import interact, interactive, fixed
from IPython.display import display
Write a function named random_line that creates x and y data for a line with y direction random noise that has a normal distribution $N(0,\sigma^2)$:
Be careful about the sigma=0.0 case.
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import scipy.stats
After doing some research on stackoverflow, I learned how to use scipy.stats to generate normally distributed random noise for my y-values.
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def random_line(m, b, sigma, size=10):
"""Create a line y = m*x + b + N(0,sigma**2) between x=[-1.0,1.0]
Parameters
----------
m : float
The slope of the line.
b : float
The y-intercept of the line.
sigma : float
The standard deviation of the y direction normal distribution noise.
size : int
The number of points to create for the line.
Returns
-------
x : array of floats
The array of x values for the line with `size` points.
y : array of floats
The array of y values for the lines with `size` points.
"""
x = np.linspace(-1.0,1.0,size)
noise = scipy.stats.norm.rvs(loc=0, scale=sigma, size=size)
y = m*x + b + noise
return x,y
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m = 0.0; b = 1.0; sigma=0.0; size=3
x, y = random_line(m, b, sigma, size)
assert len(x)==len(y)==size
assert list(x)==[-1.0,0.0,1.0]
assert list(y)==[1.0,1.0,1.0]
sigma = 1.0
m = 0.0; b = 0.0
size = 500
x, y = random_line(m, b, sigma, size)
assert np.allclose(np.mean(y-m*x-b), 0.0, rtol=0.1, atol=0.1)
assert np.allclose(np.std(y-m*x-b), sigma, rtol=0.1, atol=0.1)
Write a function named plot_random_line that takes the same arguments as random_line and creates a random line using random_line and then plots the x and y points using Matplotlib's scatter function:
color keyword argument with a default of red.
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def ticks_out(ax):
"""Move the ticks to the outside of the box."""
ax.get_xaxis().set_tick_params(direction='out', width=1, which='both')
ax.get_yaxis().set_tick_params(direction='out', width=1, which='both')
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def plot_random_line(m, b, sigma, size=10, color='red'):
"""Plot a random line with slope m, intercept b and size points."""
x = np.linspace(-1.0,1.0,size)
noise = scipy.stats.norm.rvs(loc=0, scale=sigma, size=size)
y = m*x + b + noise
f = plt.figure(figsize=(7,5))
plt.scatter(x,y, color='%s' % color, marker='o', alpha = .85)
plt.tick_params(right=False, top=False, axis='both', direction='out')
plt.xlim(-1.1,1.1)
plt.ylim(-10.0,10.0)
plt.xlabel('x')
plt.ylabel('y')
plt.title('Random Line Scatter Data')
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plot_random_line(5.0, -1.0, 2.0, 50)
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assert True # use this cell to grade the plot_random_line function
Use interact to explore the plot_random_line function using:
m: a float valued slider from -10.0 to 10.0 with steps of 0.1.b: a float valued slider from -5.0 to 5.0 with steps of 0.1.sigma: a float valued slider from 0.0 to 5.0 with steps of 0.01.size: an int valued slider from 10 to 100 with steps of 10.color: a dropdown with options for red, green and blue.
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interact(plot_random_line, m=(-10.0,10.0,0.1), b=(-5.0,5.0,0.1), sigma=(0.0,5.0,0.01), size=(10,100,10), color={'red':'r',
'green':'g',
'blue':'b'})
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#### assert True # use this cell to grade the plot_random_line interact