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Home > Data > Predictive Analytics > Mastering Predictive Analytics with R
Mastering Predictive Analytics with R
Mastering Predictive Analytics with R

Mastering Predictive Analytics with R: Master the craft of predictive modeling by developing strategy, intuition, and a solid foundation in essential concepts

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Profile Icon Rui Miguel Forte
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Mastering Predictive Analytics with R

Chapter 2. Linear Regression

We learned from the previous chapter that regression problems involve predicting a numerical output. The simplest but most common type of regression is linear regression. In this chapter, we'll explore why linear regression is so commonly used, its limitations, and extensions.

Introduction to linear regression

In linear regression, the output variable is predicted by a linearly weighted combination of input features. Here is an example of a simple linear model:

Introduction to linear regression

The preceding model essentially says that we are estimating one output, denoted by Introduction to linear regression, and this is a linear function of a single predictor variable (that is, a feature) denoted by the letter x. The terms involving the Greek letter β are the parameters of the model and are known as regression coefficients. Once we train the model and settle on values for these parameters, we can make a prediction on the output variable for any value of x by a simple substitution in our equation. Another example of a linear model, this time with three features and with values assigned to the regression coefficients, is given by the following equation:

Introduction to linear regression

In this equation, just as with the previous one, we can observe that we have one more coefficient than the number of features. This additional coefficient, β0, is...

Simple linear regression

Before looking at some real-world data sets, it is very helpful to try to train a model on artificially generated data. In an artificial scenario such as this, we know what the true output function is beforehand, something that as a rule is not the case when it comes to real-world data. The advantage of performing this exercise is that it gives us a good idea of how our model works under the ideal scenario when all of our assumptions are fully satisfied, and it helps visualize what happens when we have a good linear fit. We'll begin by simulating a simple linear regression model. The following R snippet is used to create a data frame with 100 simulated observations of the following linear model with a single input feature:

Simple linear regression

Here is the code for the simple linear regression model:

> set.seed(5427395)
> nObs = 100
> x1minrange = 5
> x1maxrange = 25
> x1 = runif(nObs, x1minrange, x1maxrange)
> e = rnorm(nObs, mean = 0, sd = 2.0)
> y = 1.67 *...

Multiple linear regression

Whenever we have more than one input feature and want to build a linear regression model, we are in the realm of multiple linear regression. The general equation for a multiple linear regression model with k input features is:

Multiple linear regression

Our assumptions about the model and about the error component ε remain the same as with simple linear regression, remembering that as we now have more than one input feature, we assume that these are independent of each other. Instead of using simulated data to demonstrate multiple linear regression, we will analyze two real-world data sets.

Predicting CPU performance

Our first real-world data set was presented by the researchers Dennis F. Kibler, David W. Aha, and Marc K. Albert in a 1989 paper titled Instance-based prediction of real-valued attributes and published in Journal of Computational Intelligence. The data contain the characteristics of different CPU models, such as the cycle time and the amount of cache memory. When deciding...

Assessing linear regression models

We'll proceed once again with using the lm() function to fit linear regression models to our data. For both of our data sets, we'll want to use all the input features that remain in our respective data frames. R provides us with a shorthand to write formulas that include all the columns of a data frame as features, excluding the one chosen as the output. This is done using a single period, as the following code snippets show:

> machine_model1 <- lm(PRP ~ ., data = machine_train)
> cars_model1 <- lm(Price ~ ., data = cars_train)

Training a linear regression model may be a one-line affair once we have all our data prepared, but the important work comes straight after, when we study our model in order to determine how well we did. Fortunately, we can instantly obtain some important information about our model using the summary() function. The output of this function for our CPU data set is shown here:

> summary(machine_model1)

Call...

Problems with linear regression

In this chapter, we've already seen some examples where trying to build a linear regression model might run into problems. One big class of problems that we've talked about is related to our model assumptions of linearity, feature independence, and the homoscedasticity and normality of errors. In particular we saw methods of diagnosing these problems either via plots, such as the residual plot, or by using functions that identify dependent components. In this section, we'll investigate a few more issues that can arise with linear regression.

Multicollinearity

As part of our preprocessing steps, we were diligent to remove features that were linearly related to each other. In doing this we were looking for an exact linear relationship and this is an example of perfect collinearity. Collinearity is the property that describes when two features are approximately in a linear relationship. This creates a problem for linear regression as we are trying...

Introduction to linear regression

In linear regression, the output variable is predicted by a linearly weighted combination of input features. Here is an example of a simple linear model:

The preceding model essentially says that we are estimating one output, denoted by , and this is a linear function of a single predictor variable (that is, a feature) denoted by the letter x. The terms involving the Greek letter β are the parameters of the model and are known as regression coefficients. Once we train the model and settle on values for these parameters, we can make a prediction on the output variable for any value of x by a simple substitution in our equation. Another example of a linear model, this time with three features and with values assigned to the regression coefficients, is given by the following equation:

In this equation, just as with the previous one, we can observe that we have one more coefficient than the number of features. This additional coefficient, β0, is known as the intercept...

Simple linear regression

Before looking at some real-world data sets, it is very helpful to try to train a model on artificially generated data. In an artificial scenario such as this, we know what the true output function is beforehand, something that as a rule is not the case when it comes to real-world data. The advantage of performing this exercise is that it gives us a good idea of how our model works under the ideal scenario when all of our assumptions are fully satisfied, and it helps visualize what happens when we have a good linear fit. We'll begin by simulating a simple linear regression model. The following R snippet is used to create a data frame with 100 simulated observations of the following linear model with a single input feature:

Here is the code for the simple linear regression model:

> set.seed(5427395)
> nObs = 100
> x1minrange = 5
> x1maxrange = 25
> x1 = runif(nObs, x1minrange, x1maxrange)
> e = rnorm(nObs, mean = 0, sd = 2.0)
> y = 1.67 * x1 - 2...

Multiple linear regression

Whenever we have more than one input feature and want to build a linear regression model, we are in the realm of multiple linear regression. The general equation for a multiple linear regression model with k input features is:

Our assumptions about the model and about the error component ε remain the same as with simple linear regression, remembering that as we now have more than one input feature, we assume that these are independent of each other. Instead of using simulated data to demonstrate multiple linear regression, we will analyze two real-world data sets.

Predicting CPU performance

Our first real-world data set was presented by the researchers Dennis F. Kibler, David W. Aha, and Marc K. Albert in a 1989 paper titled Instance-based prediction of real-valued attributes and published in Journal of Computational Intelligence. The data contain the characteristics of different CPU models, such as the cycle time and the amount of cache memory. When deciding between...

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Description

This book is intended for the budding data scientist, predictive modeler, or quantitative analyst with only a basic exposure to R and statistics. It is also designed to be a reference for experienced professionals wanting to brush up on the details of a particular type of predictive model. Mastering Predictive Analytics with R assumes familiarity with only the fundamentals of R, such as the main data types, simple functions, and how to move data around. No prior experience with machine learning or predictive modeling is assumed, however you should have a basic understanding of statistics and calculus at a high school level.

Who is this book for?

This book is intended for the budding data scientist, predictive modeler, or quantitative analyst with only a basic exposure to R and statistics. It is also designed to be a reference for experienced professionals wanting to brush up on the details of a particular type of predictive model. Mastering Predictive Analytics with R assumes familiarity with only the fundamentals of R, such as the main data types, simple functions, and how to move data around. No prior experience with machine learning or predictive modeling is assumed, however you should have a basic understanding of statistics and calculus at a high school level.

What you will learn

  • Master the steps involved in the predictive modeling process
  • Learn how to classify predictive models and distinguish which models are suitable for a particular problem
  • Understand how and why each predictive model works
  • Recognize the assumptions, strengths, and weaknesses of a predictive model, and that there is no best model for every problem
  • Select appropriate metrics to assess the performance of different types of predictive model
  • Diagnose performance and accuracy problems when they arise and learn how to deal with them
  • Grow your expertise in using R and its diverse range of packages

Product Details

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Publication date, Length, Edition, Language, ISBN-13
Publication date : Jun 17, 2015
Length: 414 pages
Edition : 1st
Language : English
ISBN-13 : 9781783982806
Vendor :
RStudio
Category :
Data
Languages :
R
Concepts :
Predictive Analytics
Tools :
RStudio

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Publication date : Jun 17, 2015
Length: 414 pages
Edition : 1st
Language : English
ISBN-13 : 9781783982806
Vendor :
RStudio
Category :
Data
Languages :
R
Concepts :
Predictive Analytics
Tools :
RStudio

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Table of Contents

12 Chapters
1. Gearing Up for Predictive Modeling Chevron down icon Chevron up icon
1. Gearing Up for Predictive Modeling
Models
Types of models
The process of predictive modeling
Performance metrics
Summary
2. Linear Regression Chevron down icon Chevron up icon
2. Linear Regression
Introduction to linear regression
Simple linear regression
Multiple linear regression
Assessing linear regression models
Problems with linear regression
Feature selection
Regularization
Summary
3. Logistic Regression Chevron down icon Chevron up icon
3. Logistic Regression
Classifying with linear regression
Introduction to logistic regression
Predicting heart disease
Assessing logistic regression models
Regularization with the lasso
Classification metrics
Extensions of the binary logistic classifier
Summary
4. Neural Networks Chevron down icon Chevron up icon
4. Neural Networks
The biological neuron
The artificial neuron
Stochastic gradient descent
Multilayer perceptron networks
Predicting the energy efficiency of buildings
Predicting glass type revisited
Predicting handwritten digits
Summary
5. Support Vector Machines Chevron down icon Chevron up icon
5. Support Vector Machines
Maximal margin classification
Support vector classification
Kernels and support vector machines
Predicting chemical biodegration
Cross-validation
Predicting credit scores
Multiclass classification with support vector machines
Summary
6. Tree-based Methods Chevron down icon Chevron up icon
6. Tree-based Methods
The intuition for tree models
Algorithms for training decision trees
Predicting class membership on synthetic 2D data
Predicting the authenticity of banknotes
Predicting complex skill learning
Summary
7. Ensemble Methods Chevron down icon Chevron up icon
7. Ensemble Methods
Bagging
Boosting
Predicting atmospheric gamma ray radiation
Predicting complex skill learning with boosting
Random forests
Summary
8. Probabilistic Graphical Models Chevron down icon Chevron up icon
8. Probabilistic Graphical Models
A little graph theory
Bayes' Theorem
Conditional independence
Bayesian networks
The Naïve Bayes classifier
Hidden Markov models
Predicting promoter gene sequences
Predicting letter patterns in English words
Summary
9. Time Series Analysis Chevron down icon Chevron up icon
9. Time Series Analysis
Fundamental concepts of time series
Some fundamental time series
Stationarity
Stationary time series models
Non-stationary time series models
Predicting intense earthquakes
Predicting lynx trappings
Predicting foreign exchange rates
Other time series models
Summary
10. Topic Modeling Chevron down icon Chevron up icon
10. Topic Modeling
An overview of topic modeling
Latent Dirichlet Allocation
Modeling the topics of online news stories
Summary
11. Recommendation Systems Chevron down icon Chevron up icon
11. Recommendation Systems
Rating matrix
Collaborative filtering
Singular value decomposition
R and Big Data
Predicting recommendations for movies and jokes
Loading and preprocessing the data
Exploring the data
Other approaches to recommendation systems
Summary
Index Chevron down icon Chevron up icon
Index

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Customer reviews

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Rating distribution
Full star icon Full star icon Full star icon Half star icon Empty star icon 3.9
(18 Ratings)
5 star 55.6%
4 star 16.7%
3 star 5.6%
2 star 5.6%
1 star 16.7%
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Amazon Customer Jun 09, 2017
Full star icon Full star icon Full star icon Full star icon Full star icon 5
well , I like this book . It teach me the basic of modelling as I am shifting from simple programmer to machine learning
Amazon Verified review Amazon
PCTriangle Oct 23, 2015
Full star icon Full star icon Full star icon Full star icon Full star icon 5
I received this book a few days ago and I'm only through 3 chapters but I'm already very impressed with the clarity of the real-world examples it contains. You should know some basic statistics to help you understand various concepts. If you are into seeing mathematical proofs behind algorithms, this book is not for you. However, it gives you enough information to know how to pre-process the data (cleansing, transformations) and items you make assumptions behind analyses. The R codes are well documented and the outputs are well explained. It is one of the best hands-on and concrete PA + R books I've seen.
Amazon Verified review Amazon
MomOfTwo Apr 24, 2016
Full star icon Full star icon Full star icon Full star icon Full star icon 5
I never thought I'd feel so strongly for an academic textbook, but I do. I am currently working on my master's degree at the Harvard Extension School and the assigned book (STAT!) is unnecessarily. I bought the kindle version to help me through the chapters of multiple regression and logistic regression - it was a breath of fresh air. The author has done an excellent job keeping it simple and helping you understand pretty tough concepts. Can't recommend it enough - Kudos.
Amazon Verified review Amazon
AS Aug 20, 2015
Full star icon Full star icon Full star icon Full star icon Full star icon 5
This is a practical application of R and the exercises give you a good sense of the different methods to leverage are with visualizations that extend the predictive capabilities of R. I would highly recommend this book if you are taking a course that leverages R and your textbook does not offer an introduction to the capabilities of R with predictive analytics.
Amazon Verified review Amazon
Riadh Aug 17, 2015
Full star icon Full star icon Full star icon Full star icon Full star icon 5
I do not agree with the book title which sounds as intended for people of intermediate level who want to move forward to master predictive analytics field. A beginner can absolutely find a great material to take advantage of this book to reach indeed an advanced analytics level, even if prior experience in R programming language can be very helpful but not essential. The author treated a huge number of subject in this ~400 pages book which starts from the fundamental principles of predictive analytics (including the typical project life cycle) to advanced methods (neural networks, support vector machines, ensemble methods, probabilistic graphical models …) and subjects (time series analysis, topic modeling, recommendation systems…). The most valuable point of this book is that the main methods and models from the simplest to the most advanced ones are treated very well, the book is balanced and all the covered subjects include numerical examples with perfectly clear and working code resulting in a much larger number of cases studied than the common books treating the same subject ... really much more! One lowlight that I note in this book is the absence of “deep learning” algorithm to complete this important collection of methods especially with the excellent H20 framework from 0xdata, but this is not very weighty as the subject is rather complicated and there is absolutely no R book treating this until today… So 5 stars well deserved!
Amazon Verified review Amazon

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About the author

Profile icon Rui Miguel Forte
Rui Miguel Forte
Rui Miguel Forte is currently the chief data scientist at Workable. He was born and raised in Greece and studied in the UK. He is an experienced data scientist, having over 10 years of work experience in a diverse array of industries spanning mobile marketing, health informatics, education technology, and human resources technology. His projects have included predictive modeling of user behavior in mobile marketing promotions, speaker intent identification in an intelligent tutor, information extraction techniques for job applicant resumes and fraud detection for job scams. He currently teaches R, MongoDB, and other data science technologies to graduate students in the Business Analytics MSc program at the Athens University of Economics and Business. In addition, he has lectured in a number of seminars, specialization programs, and R schools for working data science professionals in Athens. His core programming knowledge is in R and Java, and he has extensive experience working with a variety of database technologies such as Oracle, PostgreSQL, MongoDB, and HBase. He holds a Master's degree in Electrical and Electronic Engineering from Imperial College London and is currently researching machine learning applications in information extraction and natural language processing.
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Can I download the code files for Early Access titles? Chevron down icon Chevron up icon

We try to ensure that all books in Early Access have code available to use, download, and fork on GitHub. This helps us be more agile in the development of the book, and helps keep the often changing code base of new versions and new technologies as up to date as possible. Unfortunately, however, there will be rare cases when it is not possible for us to have downloadable code samples available until publication.

When we publish the book, the code files will also be available to download from the Packt website.

How accurate is the publication date? Chevron down icon Chevron up icon

The publication date is as accurate as we can be at any point in the project. Unfortunately, delays can happen. Often those delays are out of our control, such as changes to the technology code base or delays in the tech release. We do our best to give you an accurate estimate of the publication date at any given time, and as more chapters are delivered, the more accurate the delivery date will become.

How will I know when new chapters are ready? Chevron down icon Chevron up icon

We'll let you know every time there has been an update to a course that you've bought in Early Access. You'll get an email to let you know there has been a new chapter, or a change to a previous chapter. The new chapters are automatically added to your account, so you can also check back there any time you're ready and download or read them online.

I am a Packt subscriber, do I get Early Access? Chevron down icon Chevron up icon

Yes, all Early Access content is fully available through your subscription. You will need to have a paid for or active trial subscription in order to access all titles.

How is Early Access delivered? Chevron down icon Chevron up icon

Early Access is currently only available as a PDF or through our online reader. As we make changes or add new chapters, the files in your Packt account will be updated so you can download them again or view them online immediately.

How do I buy Early Access content? Chevron down icon Chevron up icon

Early Access is a way of us getting our content to you quicker, but the method of buying the Early Access course is still the same. Just find the course you want to buy, go through the check-out steps, and you’ll get a confirmation email from us with information and a link to the relevant Early Access courses.

What is Early Access? Chevron down icon Chevron up icon

Keeping up to date with the latest technology is difficult; new versions, new frameworks, new techniques. This feature gives you a head-start to our content, as it's being created. With Early Access you'll receive each chapter as it's written, and get regular updates throughout the product's development, as well as the final course as soon as it's ready.We created Early Access as a means of giving you the information you need, as soon as it's available. As we go through the process of developing a course, 99% of it can be ready but we can't publish until that last 1% falls in to place. Early Access helps to unlock the potential of our content early, to help you start your learning when you need it most. You not only get access to every chapter as it's delivered, edited, and updated, but you'll also get the finalized, DRM-free product to download in any format you want when it's published. As a member of Packt, you'll also be eligible for our exclusive offers, including a free course every day, and discounts on new and popular titles.