Model Components

Previously, you have been given a pre-defined model to work with. In this exercise, you will implement a model function that returns model values for y, computed from input x data, and any input coefficients for the "zero-th" order term a0, the "first-order" term a1, and a quadratic term a2 of a model (see below).

\(y = a_0 + a_1 x + a_2 x^2\)

Recall that "first order" is linear, so we'll set the defaults for this general linear model with a2=0, but later, we will change this for comparison.

This exercise is part of the course

Introduction to Linear Modeling in Python

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Exercise instructions

Complete the function definition model() so it takes x, and default inputs a0=3, a1=2, a2=0 as input, and returns y.
Create an array of values x using the numpy method np.linspace().
Pass x into your model() without specifying a0, a1, a2, to get default predicted y values.
Use the pre-defined plot_prediction() to see a plot of the resulting data x and y.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Define the general model as a function
def model(x, a0=____, a1=____, a2=____):
    return a0 + (a1*____) + (a2*____*____)

# Generate array x, then predict y values for specific, non-default a0 and a1
x = np.____(-10, 10, 21)
y = model(____)

# Plot the results, y versus x
fig = plot_prediction(____, ____)

Edit and Run Code