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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Fitting Models Exercise 1
Imports
Step1:  Fitting a quadratic curve
For this problem we are going to work with the following model
Step2:  First, generate a dataset using this model using these parameters and the following characteristics
Step3:  Now fit the model to the dataset to recover estimates for the model's parameters
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Python Code:
%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np
import scipy.optimize as opt
Explanation: Fitting Models Exercise 1
Imports
End of explanation
a_true = 0.5
b_true = 2.0
c_true = -4.0
Explanation: Fitting a quadratic curve
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:
End of explanation
# YOUR CODE HERE
raise NotImplementedError()
assert True # leave this cell for grading the raw data generation and plot
Explanation: 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).
End of explanation
# YOUR CODE HERE
raise NotImplementedError()
assert True # leave this cell for grading the fit; should include a plot and printout of the parameters+errors
Explanation: Now fit the model to the dataset to recover estimates for the model's parameters:
Print out the estimates and uncertainties of each parameter.
Plot the raw data and best fit of the model.
End of explanation
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