Multiple linear regression

In most cases, performing a univariate linear regression will not yield a model that is useful for making accurate predictions. In this exercise, you will perform a multiple regression, which uses more than one feature.

You will use price_log as your target and size_log and bedrooms as your features. Each of these tensors has been defined and is available. You will also switch from using the the mean squared error loss to the mean absolute error loss: keras.losses.mae(). Finally, the predicted values are computed as follows: params[0] + feature1*params[1] + feature2*params[2]. Note that we've defined a vector of parameters, params, as a variable, rather than using three variables. Here, params[0] is the intercept and params[1] and params[2] are the slopes.

This exercise is part of the course

Introduction to TensorFlow in Python

Exercise instructions

Define a linear regression model that returns the predicted values.
Set loss_function() to take the parameter vector as an input.
Use the mean absolute error loss.
Complete the minimization operation.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Define the linear regression model
def linear_regression(params, feature1 = size_log, feature2 = bedrooms):
	return params[0] + feature1*____ + feature2*____

# Define the loss function
def loss_function(____, targets = price_log, feature1 = size_log, feature2 = bedrooms):
	# Set the predicted values
	predictions = linear_regression(params, feature1, feature2)
  
	# Use the mean absolute error loss
	return keras.losses.____(targets, predictions)

# Define the optimize operation
opt = keras.optimizers.Adam()

# Perform minimization and print trainable variables
for j in range(10):
	opt.minimize(lambda: loss_function(____), var_list=[____])
	print_results(params)

Edit and Run Code

This exercise is part of the course

Introduction to TensorFlow in Python

IntermediateSkill Level

4.8+

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Before you can build advanced models in TensorFlow 2, you will first need to understand the basics. In this chapter, you’ll learn how to define constants and variables, perform tensor addition and multiplication, and compute derivatives. Knowledge of linear algebra will be helpful, but not necessary.

Exercise 1: Constants and variables Exercise 2: Defining data as constants Exercise 3: Defining variables Exercise 4: Basic operations Exercise 5: Performing element-wise multiplication Exercise 6: Making predictions with matrix multiplication Exercise 7: Summing over tensor dimensions Exercise 8: Advanced operations Exercise 9: Reshaping tensors Exercise 10: Optimizing with gradients Exercise 11: Working with image data

In this chapter, you will learn how to build, solve, and make predictions with models in TensorFlow 2. You will focus on a simple class of models – the linear regression model – and will try to predict housing prices. By the end of the chapter, you will know how to load and manipulate data, construct loss functions, perform minimization, make predictions, and reduce resource use with batch training.

Exercise 1: Input data Exercise 2: Load data using pandas Exercise 3: Setting the data type Exercise 4: Loss functions Exercise 5: Loss functions in TensorFlow Exercise 6: Modifying the loss function Exercise 7: Linear regression Exercise 8: Set up a linear regression Exercise 9: Train a linear model Exercise 10: Multiple linear regression

Current Exercise

Exercise 11: Batch training Exercise 12: Preparing to batch train Exercise 13: Training a linear model in batches

The previous chapters taught you how to build models in TensorFlow 2. In this chapter, you will apply those same tools to build, train, and make predictions with neural networks. You will learn how to define dense layers, apply activation functions, select an optimizer, and apply regularization to reduce overfitting. You will take advantage of TensorFlow's flexibility by using both low-level linear algebra and high-level Keras API operations to define and train models.

Exercise 1: Dense layers Exercise 2: The linear algebra of dense layers Exercise 3: The low-level approach with multiple examples Exercise 4: Using the dense layer operation Exercise 5: Activation functions Exercise 6: Binary classification problems Exercise 7: Multiclass classification problems Exercise 8: Optimizers Exercise 9: The dangers of local minima Exercise 10: Avoiding local minima Exercise 11: Training a network in TensorFlow Exercise 12: Initialization in TensorFlow Exercise 13: Defining the model and loss function Exercise 14: Training neural networks with TensorFlow

In the final chapter, you'll use high-level APIs in TensorFlow 2 to train a sign language letter classifier. You will use both the sequential and functional Keras APIs to train, validate, make predictions with, and evaluate models. You will also learn how to use the Estimators API to streamline the model definition and training process, and to avoid errors.

Exercise 1: Defining neural networks with Keras Exercise 2: The sequential model in Keras Exercise 3: Compiling a sequential model Exercise 4: Defining a multiple input model Exercise 5: Training and validation with Keras Exercise 6: Training with Keras Exercise 7: Metrics and validation with Keras Exercise 8: Overfitting detection Exercise 9: Evaluating models Exercise 10: Training models with the Estimators API Exercise 11: Preparing to train with Estimators Exercise 12: Defining Estimators Exercise 13: Congratulations!