Fitting Models Exercise 1

Imports



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%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np
import scipy.optimize as opt

For this problem we are going to work with the following model:

$$ y_{model}(x) = a x^2 + b x + c $$

The true values of the model parameters are as follows:



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a_true = 0.5
b_true = 2.0
c_true = -4.0

First, generate a dataset using this model using these parameters and the following characteristics:

For your $x$ data use 30 uniformly spaced points between $[-5,5]$.
Add a noise term to the $y$ value at each point that is drawn from a normal distribution with zero mean and standard deviation 2.0. Make sure you add a different random number to each point (see the size argument of np.random.normal).

After you generate the data, make a plot of the raw data (use points).



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# YOUR CODE HERE
raise NotImplementedError()



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assert True # leave this cell for grading the raw data generation and plot

Now fit the model to the dataset to recover estimates for the model's parameters:



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# YOUR CODE HERE
raise NotImplementedError()



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assert True # leave this cell for grading the fit; should include a plot and printout of the parameters+errors