Linear regression

Introduction to TensorFlow in Python

Isaiah Hull

Visiting Associate Professor of Finance, BI Norwegian Business School

What is a linear regression?

This image shows a scatter plot of the natural logarithm of house size in square feet against the natural logarithm of house price in dollars.

What is a linear regression?

This image shows a regression line fitted to a scatter plot of the natural logarithm of house size in square feet against the natural logarithm of house price in dollars.

The linear regression model

A linear regression model assumes a linear relationship:
- $price = intercept + size*slope + error$
This is an example of a univariate regression.
- There is only one feature, size.
Multiple regression models have more than one feature.
- E.g. size and location

Linear regression in TensorFlow

# Define the targets and features
price = np.array(housing['price'], np.float32)
size = np.array(housing['sqft_living'], np.float32)

# Define the intercept and slope
intercept = tf.Variable(0.1, np.float32)
slope = tf.Variable(0.1, np.float32)

# Define a linear regression model
def linear_regression(intercept, slope, features = size):
    return intercept + features*slope

# Compute the predicted values and loss
def loss_function(intercept, slope, targets = price, features = size):
    predictions = linear_regression(intercept, slope)
    return tf.keras.losses.mse(targets, predictions)

Linear regression in TensorFlow

# Define an optimization operation
opt = tf.keras.optimizers.Adam()

# Minimize the loss function and print the loss
for j in range(1000):
    opt.minimize(lambda: loss_function(intercept, slope),\
    var_list=[intercept, slope])
    print(loss_function(intercept, slope))

tf.Tensor(10.909373, shape=(), dtype=float32)
...
tf.Tensor(0.15479447, shape=(), dtype=float32)

# Print the trained parameters
print(intercept.numpy(), slope.numpy())

Let's practice!

Introduction to TensorFlow in Python