**1**. Making wallpaper with `fromfunction`

Adapted from [Circle Squared](http://igpphome.ucsd.edu/~shearer/COMP233/SciAm_Mandel.pdf)

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.


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


```python

```

**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`


```python

```

e817ca8a9dd91a4a8a80055173057b602a3b989a
ipynb
Jupyter Notebook
notebook/T03_Exercises.ipynb
ashnair1/sta-663-2019
17eb85b644c52978c2ef3a53a80b7fb031360e3d
BSD-3-Clause
2019-01-09T21:53:55.000Z
2022-02-16T17:14:22.000Z
notebook/T03_Exercises.ipynb
ashnair1/sta-663-2019
17eb85b644c52978c2ef3a53a80b7fb031360e3d
BSD-3-Clause
notebook/T03_Exercises.ipynb
ashnair1/sta-663-2019
17eb85b644c52978c2ef3a53a80b7fb031360e3d
BSD-3-Clause
2019-01-09T21:43:48.000Z
2021-11-15T04:26:25.000Z
Qwen/Qwen-72B
1. YES
2. YES