scipy

In [2]:

import numpy as np
import matplotlib.pyplot as plt
from scipy import optimize

In [3]:

x = np.linspace(0,10, 21)
x

Out[3]:

array([ 0. ,  0.5,  1. ,  1.5,  2. ,  2.5,  3. ,  3.5,  4. ,  4.5,  5. ,
        5.5,  6. ,  6.5,  7. ,  7.5,  8. ,  8.5,  9. ,  9.5, 10. ])

In [4]:

y = 3*x+4
y

Out[4]:

array([ 4. ,  5.5,  7. ,  8.5, 10. , 11.5, 13. , 14.5, 16. , 17.5, 19. ,
       20.5, 22. , 23.5, 25. , 26.5, 28. , 29.5, 31. , 32.5, 34. ])

In [5]:

fig = plt.figure()
plt.scatter(x,y)
plt.plot(x,y)

Out[5]:

[<matplotlib.lines.Line2D at 0x244c6135cd0>]

In [6]:

y1 = np.random.uniform(low=-1, high=1, size=y.shape)*3
y1 = y1 +y
y1

Out[6]:

array([ 6.98245789,  6.39828999,  7.42999128, 10.67198849, 10.12670086,
        8.87342056, 11.38121752, 14.23830957, 14.95388992, 18.95111325,
       19.13128516, 19.59811703, 21.30199945, 21.37804087, 23.53440182,
       25.56723397, 29.02377325, 28.20930885, 29.07300015, 33.53222   ,
       31.74146698])

In [7]:

plt.scatter(x,y1)

Out[7]:

<matplotlib.collections.PathCollection at 0x244c6248610>

In [8]:

p, cov = optimize.curve_fit(lambda x, m, l: x*m+l, x, y)
print(p, cov)

[3. 4.] [[ 0. -0.]
 [-0.  0.]]

In [9]:

p, cov = optimize.curve_fit(lambda x, m, l: x*m+l, x, y1)
print(p, cov)

[2.77383748 4.80215674] [[ 0.01004133 -0.05020664]
 [-0.05020664  0.34307871]]

In [10]:

y_fit = x*p[0] + p[1]

plt.figure(1, figsize=(5,5))
plt.scatter(x,y1, color="teal")
plt.plot(x,y_fit, color='orange' )

Out[10]:

[<matplotlib.lines.Line2D at 0x244c695e5b0>]

In [18]:

y_fit = x*p[0] + p[1]
fig ,ax= plt.subplots( figsize=(5,10))

plt.title("Linear regression", fontsize=25)
plt.scatter(x,y1, color="teal", s=30,label = 'Input values')
plt.plot(x,y_fit, color='orange',linewidth=1, label = 'Curve fit' )
plt.legend(loc = 'upper left')

plt.xlabel('values x', fontsize=18)
plt.ylabel('values y', fontsize=18)
ax.set_aspect('equal')
plt.grid(axis='y', color='lightgrey')
plt.grid(axis='x', color='lightgrey')
#ax.set_xlim(0,35)
# ax.set_yticks(np.arange(0,37, 2))
# ax.set_xticks(np.arange(0,12, 2))

# ax.set_ylim(0,35)
plt.savefig( 'Exemplo_reg_lin' + '.png', format ='png',  bbox_inches='tight')