%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt

points = np.array([(1, 1), (2, 4), (3, 1), (9, 3)])
# get x and y vectors
x = points[:,0]
y = points[:,1]

# calculate polynomial
z = np.polyfit(x, y, 3)
f = np.poly1d(z)

# calculate new x's and y's
x_new = np.linspace(x[0], x[-1], 50)
y_new = f(x_new)

plt.plot(x,y,'o', x_new, y_new)
plt.xlim([x[0]-1, x[-1] + 1 ])
plt.show()

import matplotlib.pyplot as plt
xp = np.linspace(-2, 6, 100)
_ = plt.plot(x, y, '.', xp, p(xp), '-', xp, p30(xp), '--')
plt.ylim(-2,2)
plt.show()

from numpy import *
import pylab

# data to fit
x = random.rand(6)
y = random.rand(6)

# fit the data with a 4th degree polynomial
z4 = polyfit(x, y, 4) 
p4 = poly1d(z4) # construct the polynomial 

z5 = polyfit(x, y, 5)
p5 = poly1d(z5)

xx = linspace(0, 1, 100)
pylab.plot(x, y, 'o', xx, p4(xx),'-g', xx, p5(xx),'-b')
pylab.legend(['data to fit', '4th degree poly', '5th degree poly'])
pylab.axis([0,1,0,1])
pylab.show()
print p4

from numpy import *
import pylab

# data to fit
x = [0,20,40,60,80,120,160,180]
y = [24.5,41.5,52.1,61.4,73.5,86,92.8,94]

# fit the data with a 2nd degree polynomial
z2 = polyfit(x, y, 2) 
p2 = poly1d(z2) # construct the polynomial 

xx = linspace(0, 200, 1000)
pylab.plot(x, y, 'o', xx, p2(xx),'-g')
pylab.axis([-20,200,0,100])
pylab.xlabel('Pounds of Nitrogen per Acre')
pylab.ylabel('Crop Yield (Bushels)')
pylab.title('Effect of Nitrogen Fertilizer on Corn Yield')
pylab.show()
print p2

import scipy as scipy
t = linspace(0, 500, 1000)
#import seaborn as sns
#sns.residplot(x,y)
scipy.stats(x,y)

from numpy import *
import pylab

# data to fit
x = [0,20,40,60,80,120,160,180]
y = [24.5,41.5,52.1,61.4,73.5,86,92.8,94]

# fit the data with a 2nd degree polynomial
z2 = polyfit(x, y, 2) 
p2 = poly1d(z2) # construct the polynomial 

xx = linspace(0, 500, 1000)
pylab.plot(x, y, 'o', xx, p2(xx),'-g')
pylab.axis([-20,500,0,100])
pylab.xlabel('Pounds of Nitrogen per Acre')
pylab.ylabel('Crop Yield (Bushels)')
pylab.title('Effect of Nitrogen Fertilizer on Corn Yield')
pylab.show()
print p2