Using the matrix inverse method

In this recipe, we will use TensorFlow to solve two-dimensional linear regression with the matrix inverse method.

Getting ready

Linear regression can be represented as a set of matrix equations, say 

. Here, we are interested in solving the coefficients in matrix x. We have to be careful if our observation matrix (design matrix) A is not square. The solution to solving x can be expressed as 

. To show that this is indeed the case, we will generate two-dimensional data, solve it in TensorFlow, and plot the result.

How to do it...

We proceed with the recipe as follows:

1. First, we load the necessary libraries, initialize the graph, and create the data. See the following code:

import matplotlib.pyplot as plt 
import numpy as np 
import tensorflow as tf 
sess = tf.Session() 
x_vals = np.linspace(0, 10, 100) 
y_vals = x_vals + np.random.normal(0, 1, 100) 

2. Next, we create the matrices to use in the inverse method. We create the A matrix first, which will be a column of x data...