# Ch `03`: Concept `02`

## Polynomial regression

Import the relevant libraries and initialize the hyper-parameters

``````

In [1]:

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

learning_rate = 0.01
training_epochs = 40

``````

Set up some fake raw input data

``````

In [2]:

trX = np.linspace(-1, 1, 101)

``````

Set up raw output data based on a degree 6 polynomial

``````

In [3]:

num_coeffs = 6
trY_coeffs = [1, 2, 3, 4, 5, 6]
trY = 0
for i in range(num_coeffs):
trY += trY_coeffs[i] * np.power(trX, i)

``````

``````

In [4]:

trY += np.random.randn(*trX.shape) * 1.5

``````

Plot the raw data

``````

In [5]:

plt.scatter(trX, trY)
plt.show()

``````
``````

``````

Define the nodes to hold values for input/output pairs

``````

In [6]:

X = tf.placeholder("float")
Y = tf.placeholder("float")

``````

Define our polynomial model

``````

In [7]:

def model(X, w):
terms = []
for i in range(num_coeffs):
term = tf.multiply(w[i], tf.pow(X, i))
terms.append(term)

``````

Set up the parameter vector to all zero

``````

In [8]:

w = tf.Variable([0.] * num_coeffs, name="parameters")
y_model = model(X, w)

``````

Define the cost function just as before

``````

In [9]:

cost = tf.reduce_sum(tf.square(Y-y_model))

``````

Set up the session and run the learning algorithm just as before

``````

In [10]:

sess = tf.Session()
init = tf.global_variables_initializer()
sess.run(init)

for epoch in range(training_epochs):
for (x, y) in zip(trX, trY):
sess.run(train_op, feed_dict={X: x, Y: y})

w_val = sess.run(w)
print(w_val)

``````
``````

[ 1.10158885  2.36433625  3.30378437  4.43473864  3.75751448  4.60356045]

``````

Close the session when done

``````

In [11]:

sess.close()

``````

Plot the result

``````

In [12]:

plt.scatter(trX, trY)
trY2 = 0
for i in range(num_coeffs):
trY2 += w_val[i] * np.power(trX, i)
plt.plot(trX, trY2, 'r')
plt.show()

``````
``````

``````