1. Making wallpaper with fromfunction

Adapted from Circle Squared

Create a \(400 \times 400\) array using the function lambda i, j:  0.27**2*(i**2 + j**2) % 1.5. Use imshow from matplotlib.pyplot with interpolation='nearest' and the YlOrBr colormap to display the resulting array as an image.

%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt

2. Find t least squares solution for \(\beta_0, \beta_1, \beta_2\) using the normal equations \(\hat{\beta} = (X^TX)^{-1}x^Ty\).

\begin{align} 10 &= \beta_0 + 3 \beta_1 + 7 \beta_2 \\ 11 &= \beta_0 + 2 \beta_1 + 8 \beta_2 \\ 9 &= \beta_0 + 3 \beta_1 + 7 \beta_2 \\ 10 &= \beta_0 + 1 \beta_1 + 9 \beta_2 \\ \end{align}

You can find the inverse of a matrix by using np.linalg.inv and the transpose with X.T