Using the Matrix Inverse Method

In this recipe, we will use TensorFlow to solve two dimensional linear regressions 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 this is indeed the case, we will generate two-dimensional data, solve it in TensorFlow, and plot the result.

How to do it…

1. First we load the necessary libraries, initialize the graph, and create the data, as follows:

   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 and a column of 1s. Then we create the b matrix from the y-data...