Write a Python program to generate data that uses the sum of a random variable (which has a Gaussian distribution) and a 4th-degree polynomial equation (3x4+x3+3x2+4x+5). Using least-squares polynomial fit, curve the generated data using a model until your model can accurately predict all values

Check the explanation

Explanation:

Consider a data array x and y be the sum of the random variable (with gaussian distribution) and the 4th degree polynomial.

We shall fit the data arrays X and Y to the 4th degree polynomial.

import random

import numpy as np

import matplotlib. pyploy as plt

poly_coeff=[3,1,3,4,5]

poly=np. poly1d (poly_coeff)

y=poly (random. randint (0,10)) + min (10, max (0, random. gauss (2, 3)))

x=np. arange (-10,10)

curvefit=np. polyfit (x, y, 4)

y_new=np. polyfit (curvefit, x)

plt. plot (x, y, '-or')

plt. plot (x, y_new, '-b')

plt. show ()

See explaination

Explanation:

import random

import matplotlib. pyplot as plt

import numpy as np

def rSquared (obs, predicted):

error = ((predicted - obs) * *2). sum ()

mean = error/len (obs)

return 1 - (mean/np. var (obs))

def generateData (a, b, c, d, e, xvals):

for x in xvals:

calcVal = a*x**4 + b*x**3 + c*x**2 + d*x + e

yvals. append (calcVal + random. gauss (0, 35))

xvals = np. arange (-10, 11, 1)

yvals = []

a, b, c, d, e = 3, 1, 3, 4, 5

generateData (a, b, c, d, e, xvals)

for i in range (5):

model = np. polyfit (xvals, yvals, i)

estYvals = np. polyval (model, xvals)

print ('R-Squared:', rSquared (yvals, estYvals))

plt. plot (xvals, yvals, 'r', label = 'Actual values')

plt. plot (xvals, estYvals, 'bo', label = 'Predicted values')

plt. xlabel ('Variable x values')

plt. ylabel ('Calculated Value of Polynomial')

plt. legend ()

plt. show ()