In this article by Ralph Winters, the author of the book Practical Predictive Analytics we will explore the idea of how to start with predictive analysis.

“In God we trust, all other must bring Data” – Deming

(For more resources related to this topic, see here.)

I enjoy explaining Predictive Analytics to people because it is based upon a simple concept:  Predicting the probability of future events based upon historical data. Its history may date back to at least 650 BC. Some early examples include the Babylonians, who tried to predict short term weather changes based cloud appearances and haloes

Medicine also has a long history of a need to classify diseases.  The Babylonian king Adad-apla-iddina decreed that medical records be collected to form the “Diagnostic Handbook”. Some “predictions” in this corpus list treatments based on the number of days the patient had been sick, and their pulse rate. One of the first instances of bioinformatics!

In later times, specialized predictive analytics were developed at the onset of the Insurance underwriting industries. This was used as a way to predict the risk associated with insuring Marine Vessels. At about the same time, Life Insurance companies began predicting the age that a person would live in order to set the most appropriate premium rates. [i]Although the idea of prediction always seemed to be rooted early in humans’ ability to want to understand and classify, it was not until the 20^th century, and the advent of modern computing that it really took hold.

In addition to aiding the US government in the 1940 with breaking the code, Alan Turing also worked on the initial computer chess algorithms which pitted man vs. machine.  Monte Carlo simulation methods originated as part of the Manhattan project, where mainframe computers crunched numbers for days in order to determine the probability of nuclear attacks.

In the 1950’s Operation Research theory developed, in which one could optimize the shortest distance between two points. To this day, these techniques are used in logistics by companies such as UPS and Amazon.

Non mathematicians have also gotten into the act.  In the 1970’s, Cardiologist Lee Goldman (who worked aboard a submarine) spend years developing a decision tree which did this efficiently.  This helped the staff determine whether or not the submarine needed to resurface in order to help the chest pain sufferer!

What many of these examples had in common was that history was used to predict the future.  Along with prediction, came understanding of cause and effect and how the various parts of the problem were interrelated.  Discovery and insight came about through methodology and adhering to the scientific method.

Most importantly, the solutions came about in order to find solutions to important, and often practical problems of the times.  That is what made them unique.

Predictive Analytics adopted by some many different industries

We have come a long way from then, and Practical Analytics solutions have furthered growth in so many different industries.  The internet has had a profound effect on this; it has enabled every click to be stored and analyzed. More data is being collected and stored, some with very little effort. That in itself has enabled more industries to enter Predictive Analytics.

Marketing has always been concerned with customer acquisition and retention, and has developed predictive models involving various promotional offers and customer touch points, all geared to keeping customers and acquiring new ones.  This is very pronounced in certain industries, such as wireless and online shopping cards, in which customers are always searching for the best deal. Specifically, advanced analytics can help answer questions like “If I offer a customer 10% off with free shipping, will that yield more revenue than 15% off with no free shipping?”.  The 360-degree view of the customer has expanded the number of ways one can engage with the customer, therefore enabling marketing mix and attribution modeling to become increasingly important.  Location based devices have enabled marketing predictive applications to incorporate real time data to issue recommendation to the customer while in the store.

Predictive Analytics in Healthcare has its roots in clinical trials, which uses carefully selected samples to test the efficacy of drugs and treatments.  However, healthcare has been going beyond this. With the advent of sensors, data can be incorporated into predictive analytics to monitor patients with critical illness, and to send alerts to the patient when he is at risk. Healthcare companies can now predict which individual patients will comply with courses of treatment advocated by health providers.  This will send early warning signs to all parties, which will prevent future complications, as well as lower the total costs of treatment.

Other examples can be found in just about every other industry.  Here are just a few:

1. Finance:
   •    Fraud detection is a huge area. Financial institutions can monitor clients internal and external transactions for fraud, through pattern recognition, and then alert a customer concerning suspicious activity.
   •    Wall Street program trading. Trading algorithms will predict intraday highs and lows, and will decide when to buy and sell securities.
2. Sports Management
   •    Sports management are able to predict which sports events will yield the greatest attendance and institute variable ticket pricing based upon audience interest.
   •     In baseball, a pitchers’ entire game can be recorded and then digitally analyzed. Sensors can also be attached to their arm, to alert when future injury might occur
3. Higher Education
   •    Colleges can predict how many, and which kind of students are likely to attend the next semester, and be able to plan resources accordingly.
   •    Time based assessments of online modules can enable professors to identify students’ potential problems areas, and tailor individual instruction.
4. Government
   •    Federal and State Governments have embraced the open data concept, and have made more data available to the public. This has empowered “Citizen Data Scientists” to help solve critical social and government problems.
   •    The potential use of using the data for the purpose of emergency service, traffic safety, and healthcare use is overwhelmingly positive.

Although these industries can be quite different, the goals of predictive analytics are typically implement to increase revenue, decrease costs, or alter outcomes for the better.

Skills and Roles which are important in Predictive Analytics

So what skills do you need to be successful in Predictive Analytics? I believe that there are 3 basic skills that are needed:

1. Algorithmic/Statistical/programming skills –These are the actual technical skills needed to implement a technical solution to a problem. I bundle these all together since these skills are typically used in tandem. Will it be a purely statistical solution, or will there need to be a bit of programming thrown in to customize an algorithm, and clean the data?  There are always multiple ways of doing the same task and it will be up to you, the predictive modeler to determine how it is to be done.
2. Business skills –These are the skills needed for communicating thoughts and ideas among groups of all of the interested parties.  Business and Data Analysts who have worked in certain industries for long periods of time, and know their business very well, are increasingly being called upon to participate in Predictive Analytics projects.  Data Science is becoming a team sport, and most projects include working with others in the organization, Summarizing findings, and having good presentation and documentation skills are important.  You will often hear the term ‘Domain Knowledge’ associated with this, since it is always valuable to know the inner workings of the industry you are working in.  If you do not have the time or inclination to learn all about the inner workings of the problem at hand yourself, partner with someone who does.
3. Data Storage / ETL skills:   This can refer to specialized knowledge regarding extracting data, and storing it in a relational, or non-relational NoSQL data store. Historically, these tasks were handled exclusively within a data warehouse.  But now that the age of Big Data is upon us, specialists have emerged who understand the intricacies of data storage, and the best way to organize it.

Related Job skills and terms

Along with the term Predictive Analytics, here are some terms which are very much related:

• Predictive Modeling:  This specifically means using a Mathematical/statistical model to predict the likelihood of a dependent or Target Variable
• Artificial Intelligence:  A broader term for how machines are able to rationalize and solve problems.  AI’s early days were rooted in Neural Networks
• Machine Learning- A subset of Artificial Intelligence. Specifically deals with how a machine learns automatically from data, usually to try to replicate human decision making or to best it. At this point, everyone knows about Watson, who beat two human opponents in “Jeopardy” [ii]
• Data Science – Data Science encompasses Predictive Analytics but also adds algorithmic development via coding, and good presentation skills via visualization.
• Data Engineering – Data Engineering concentrates on data extract and data preparation processes, which allow raw data to be transformed into a form suitable for analytics. A knowledge of system architecture is important. The Data Engineer will typically produce the data to be used by the Predictive Analysts (or Data Scientists)
• Data Analyst/Business Analyst/Domain Expert – This is an umbrella term for someone who is well versed in the way the business at hand works, and is an invaluable person to learn from in terms of what may have meaning, and what may not
• Statistics – The classical form of inference, typically done via hypothesis testing.

Predictive Analytics Software

Originally predictive analytics was performed by hand, by statisticians on mainframe computers using a progression of various language such as FORTRAN etc.  Some of these languages are still very much in use today.  FORTRAN, for example, is still one of the fasting performing languages around, and operators with very little memory.

Nowadays, there are some many choices on which software to use, and many loyalists remain true to their chosen software.  The reality is, that for solving a specific type of predictive analytics problem, there exists a certain amount of overlap, and certainly the goal is the same. Once you get a hang of the methodologies used for predictive analytics in one software packages, it should be fairly easy to translate your skills to another package.

Open Source Software

Open source emphasis agile development, and community sharing.  Of course, open source software is free, but free must also be balance in the context of TCO (Total Cost of Ownership)

R

The R language is derived from the “S” language which was developed in the 1970’s.  However, the R language has grown beyond the original core packages to become an extremely viable environment for predictive analytics.

Although R was developed by statisticians for statisticians, it has come a long way from its early days.  The strength of R comes from its ‘package’ system, which allows specialized or enhanced functionality to be developed and ‘linked’ to the core system.

Although the original R system was sufficient for statistics and data mining, an important goal of R was to have its system enhanced via user written contributed packages.  As of this writing, the R system contains more than 8,000 packages.  Some are of excellent quality, and some are of dubious quality.  Therefore, the goal is to find the truly useful packages that add the most value. 

Most, if not all of the R packages in use, address most of the common predictive analytics tasks that you will encounter.  If you come across a task that does not fit into any category, chances are good that someone in the R community has done something similar.  And of course, there is always a chance that someone is developing a package to do exactly what you want it to do.  That person could be eventually be you!.

Closed Source Software

Closed Source Software such as SAS and SPSS were on the forefront of predictive analytics, and have continued to this day to extend their reach beyond the traditional realm of statistics and machine learning.  Closed source software emphasis stability, better support, and security, with better memory management, which are important factors for some companies. 

There is much debate nowadays regarding which one is ‘better’.  My prediction is that they both will coexist peacefully, with one not replacing the other.  Data sharing and common API’s will become more common.  Each has its place within the data architecture and ecosystem is deemed correct for a company.  Each company will emphasis certain factors, and both open and closed software systems and constantly improving themselves.

Other helpful tools

Man does not live by bread alone, so it would behoove you to learn additional tools in addition to R, so as to advance your analytic skills.

• SQL – SQL is a valuable tool to know, regardless of which language/package/environment you choose to work in. Virtually every analytics tool will have a SQL interface, and a knowledge of how to optimize SQL queries will definitely speed up your productivity, especially if you are doing a lot of data extraction directly from a SQL database. Today’s common thought is to do as much preprocessing as possible within the database, so if you will be doing a lot of extracting from databases like MySQL, Postgre, Oracle, or Teradata, it will be a good thing to learn how queries are optimized within their native framework.
• In the R language, there are several SQL packages that are useful for interfacing with various external databases.  We will be using SQLDF which is a popular R package for interfacing with R dataframes.  There are other packages which are specifically tailored for the specific database you will be working with
• Web Extraction Tools –Not every data source will originate from a data warehouse. Knowledge of API’s which extract data from the internet will be valuable to know. Some popular tools include Curl, and Jsonlite.
• Spreadsheets.  Despite their problems, spreadsheets are often the fastest way to do quick data analysis, and more importantly, enable them to share your results with others!  R offers several interface to spreadsheets, but again, learning standalone spreadsheet skills like PivotTables, and VBA will give you an advantage if you work for corporations in which these skills are heavily used.
• Data Visualization tools: Data Visualization tools are great for adding impact to an analysis, andfor concisely encapsulating complex information.  Native R visualization tools are great, but not every company will be using R.  Learn some third party visualization tools such as D3.js, Google Charts, Qlikview, or Tableau
• Big data Spark, Hadoop, NoSQL Database:  It is becoming increasingly important to know a little bit about these technologies, at least from the viewpoint of having to extract and analyze data which resides within these frameworks. Many software packages have API’s which talk directly to Hadoop and can run predictive analytics directly within the native environment, or extract data and perform the analytics locally.

After you are past the basics

Given that the Predictive Analytics space is so huge, once you are past the basics, ask yourself what area of Predictive analytics really interests you, and what you would like to specialize in.  Learning all you can about everything concerning Predictive Analytics is good at the beginning, but ultimately you will be called upon because you are an expert in certain industries or techniques. This could be research, algorithmic development, or even for managing analytics teams. But, as general guidance, if you are involved in, or are oriented towards data the analytics or research portion of data science, I would suggest that you concentrate on data mining methodologies and specific data modeling techniques which are heavily prevalent in the specific industries that interest you.  For example, logistic regression is heavily used in the insurance industry, but social network analysis is not. Economic research is geared towards time-series analysis, but not so much cluster analysis.

If you are involved more on the data engineering side, concentrate more on data cleaning, being able to integrate various data sources, and the tools needed to accomplish this. 

If you are a manager, concentrate on model development, testing and control, metadata, and presenting results to upper management in order to demonstrate value.

Of course, predictive analytics is becoming more of a team sport, rather than a solo endeavor, and the Data Science team is very much alive.  There is a lot that has been written about the components of a Data Science team, much of it which can be reduced to the 3 basic skills that I outlined earlier.

Two ways to look at predictive analytics

Depending upon how you intend to approach a particular problem, look at how two different analytical mindsets can affect the predictive analytics process.

1. Minimize prediction error goal: This is a very commonly used case within machine learning. The initial goal is to predict using the appropriate algorithms in order to minimize the prediction error. If done incorrectly, an algorithm will ultimately fail and it will need to be continually optimized to come up with the “new” best algorithm. If this is performed mechanically without regard to understanding the model, this will certainly result in failed outcomes.  Certain models, especially over optimized ones with many variables can have a very high prediction rate, but be unstable in a variety of ways. If one does not have an understanding of the model, it can be difficult to react to changes in the data inputs. 
2. Understanding model goal: This came out of the scientific method and is tied closely with the concept of hypothesis testing.  This can be done in certain kinds of models, such as regression and decision trees, and is more difficult in other kinds of models such as SVM and Neural Networks.  In the understanding model paradigm, understanding causation or impact becomes more important than optimizing correlations. Typically, “Understanding” models have a lower prediction rate, but have the advantage of knowing more about the causations of the individual parts of the model, and how they are related. E.g. industries which rely on understanding human behavior emphasize model understanding goals.  A limitation to this orientation is that we might tend to discard results that are not immediately understood

Of course the above examples illustrate two disparate approaches. Combination models, which use the best of both worlds should be the ones we should strive for.  A model which has an acceptable prediction error, is stable over, and is simple enough to understand. You will learn later that is this related to Bias/Variance Tradeoff

R Installation

R Installation is typically done by downloading the software directly from the CRAN site

1. Navigate to https://cran.r-project.org/
2. Install the version of R appropriate for your operating system

Alternate ways of exploring R

Although installing R directly from the CRAN site is the way most people will proceed, I wanted to mention some alternative R installation methods. These methods are often good in instances when you are not always at your computer.

• Virtual Environment: Here are few methods to install R in the virtual environment:
  • Virtual Box or VMware- Virtual environments are good for setting up protected environments and loading preinstalled operating systems and packages.  Some advantages are that they are good for isolating testing areas, and when you do not which to take up additional space on your own machine.
  • Docker – Docker resembles a Virtual Machine, but is a bit more lightweight since it does not emulate an entire operating system, but emulates only the needed processes.  (See Rocker, Docker container)
• Cloud Based- Here are few methods to install R in the cloud based environment:
  • AWS/Azure – These are Cloud Based Environments.  Advantages to this are similar to the reasons as virtual box, with the additional capability to run with very large datasets and with more memory.  Not free, but both AWS and Azure offer free tiers.
• Web Based – Here are few methods to install R in the web based environment:
  • Interested in running R on the Web?  These sites are good for trying out quick analysis etc. R-Fiddle is a good choice, however there are other including: R-Web, ideaone.com, Jupyter, DataJoy, tutorialspoint, and Anaconda Cloud are just a few examples.
• Command Line – If you spend most of your time in a text editor, try ESS (Emacs Speaks Statistics)

How is a predictive analytics project organized?

After you install R on your own machine, I would give some thought about how you want to organize your data, code, documentation, etc. There probably be many different kinds of projects that you will need to set up, all ranging from exploratory analysis, to full production grade implementations.  However, most projects will be somewhere in the middle, i.e. those projects which ask a specific question or a series of related questions.  Whatever their purpose, each project you will work on will deserve their own project folder or directory.

Set up your Project and Subfolders

We will start by creating folders for our environment. Create a sub directory named “PracticalPredictiveAnalytics” somewhere on your computer. We will be referring to it by this name throughout this book.

Often project start with 3 sub folders which roughly correspond with 1) Data Source, 2) Code Generated Outputs, and 3) The Code itself (in this case R)

Create 3 subdirectories under this Project Data, Outputs, and R. The R directory will hold all of our data prep code, algorithms etc.  The Data directory will contain our raw data sources, and the Output directory will contain anything generated by the code.  This can be done natively within your own environment, e.g. you can use Windows Explorer to create these folders.

Some important points to remember about constructing projects

• It is never a good idea to ‘boil the ocean’, or try to answer too many questions at once. Remember, predictive analytics is an iterative process.
• Another trap that people fall into is not having their project reproducible.  Nothing is worse than to develop some analytics on a set of data, and then backtrack, and oops! Different results.
• When organizing code, try to write code as building block, which can be reusable.  For R, write code liberally as functions.
• Assume that anything concerning requirements, data, and outputs will change, and be prepared.
• Considering the dynamic nature of the R language. Changes in versions, and packages could all change your analysis in various ways, so it is important to keep code and data in sync, by using separate folders for the different levels of code, data, etc.  or by using version management package use as subversion, git, or cvs

GUI’s

R, like many languages and knowledge discovery systems started from the command line (one reason to learn Linux), and is still used by many.  However, predictive analysts tend to prefer Graphic User Interfaces, and there are many choices available for each of the 3 different operating systems.   Each of them have their strengths and weakness, and of course there is always a matter of preference.  Memory is always a consideration with R, and if that is of critical concern to you, you might want to go with a simpler GUI, like the one built in with R. If you want full control, and you want to add some productive tools, you could choose RStudio, which is a full blown GUI and allows you to implement version control repositories, and has nice features like code completion.   RCmdr, and Rattle’s unique features are that they offer menus which allow guided point and click commands for common statistical and data mining tasks.  They are always both code generators.  This is a good for learning, and you can learn by looking at the way code is generated.

Both RCmdr and RStudio offer GUI’s which are compatible with Windows, Apple, and Linux operator systems, so those are the ones I will use to demonstrate examples in this book.  But bear in mind that they are only user interfaces, and not R proper, so, it should be easy enough to paste code examples into other GUI’s and decide for yourself which ones you like.  

Getting started with RStudio

After R installation has completed, download and install the RStudio executable appropriate for your operating system

Click the RStudio Icon to bring up the program:  The program initially starts with 3 tiled window panes, as shown below. Before we begin to do any actual coding, we will want to set up a new Project.

Create a new project by following these steps:

• Identify the Menu Bar, above the icons at the top left of the screen.
• Click “File” and then “New Project”

   

• Select “Create project from Directory”

  

• Select “Empty Project”

  

• Name the directory “PracticalPredictiveAnalytics”
• Then Click the Browse button to select your preferred directory. This will be the directory that you created earlier
• Click “Create Project” to complete

The R Console 

Now that we have created a project, let’s take a look at of the R Console Window.  Click on the window marked “Console” and perform the following steps:

• Enter getwd() and press enter – That should echo back the current working directory
• Enter dir() – That will give you a list of everything in the current working directory

The getwd() command is very important since it will always tell you which directory you are in. Sometimes you will need to switch directories within the same project or even to another project. The command you will use is setwd().  You will supply the directory that you want to switch to, all contained within the parentheses.

This is a situation we will come across later. We will not change anything right now.  The point of this, is that you should always be aware of what your current working directory is.

The Script Window

The script window is where all of the R Code is written.  You can have several script windows open, all at once.

Press Ctrl + Shift + N  to create a new R script.  Alternatively, you can go through the menu system by selecting File/New File/R Script.   A new blank script window will appear with the name “Untitled1”

Our First Predictive Model

Now that all of the preliminary things are out of the way, we will code our first extremely simple predictive model.

Our first R script is a simple two variable regression model which predicts women’s height based upon weight.  The data set we will use is already built into the R package system, and is not necessary to load externally.   For quick illustration of techniques, I will sometimes use sample data contained within specific R packages to demonstrate.

Paste the following code into the “Untitled1” scripts that was just created:

require(graphics)
data(women)
head(women)
utils::View(women)
plot(women$height,women$weight)

Click Ctrl+Shift+Enter to run the entire code.  The display should change to something similar as displayed below.

Code Description

What you have actually done is:

• Load the “Women” data object. The data() function will load the specified data object into memory. In our case, data(women)statement says load the ‘women’ dataframe into memory.
• Display the raw data in three different ways:
  1. utils::View(women) – This will visually display the dataframe. Although this is part of the actual R script, viewing a dataframe is a very common task, and is often issued directly as a command via the R Console. As you can see in the figure above, the “Women” data frame has 15 rows, and 2 columns named height and weight.
  2. plot(women$height,women$weight) – This uses the native R plot function which plots the values of the two variables against each other.  It is usually the first step one does to begin to understand the relationship between 2 variables. As you can see the relationship is very linear.
  3. Head(women) – This displays the first N rows of the women  data frame to the console. If you want no more than a certain number of rows, add that as a 2^nd argument of the function.  E.g.  Head(women,99) will display UP TO 99 rows in the console. The tail() function works similarly, but displays the last rows of data.

The very first statement in the code “require” is just a way of saying that R needs a specific package to run.  In this case require(graphics) specifies that the graphics package is needed for the analysis, and it will load it into memory.  If it is not available, you will get an error message.  However, “graphics” is a base package and should be available

To save this script, press Ctrl-S (File Save) , navigate to the PracticalPredictiveAnalytics/R folder that was created, and name it Chapter1_DataSource

Your 2^nd script

Create another Rscript by Ctrl + Shift + N  to create a new R script.  A new blank script window will appear with the name “Untitled2”

Paste the following into the new script window

lm_output <- lm(women$height ~ women$weight)
summary(lm_output)
prediction <- predict(lm_output)
error <- women$height-prediction
plot(women$height,error) 

Press Ctrl+Shift+Enter to run the entire code.  The display should change to something similar to what is displayed below.

Code Description

Here are some notes and explanations for the script code that you have just ran:

• lm() function: This functionruns a simple linear regression using lm() function. This function  predicts woman’s height based upon the value of their weight.  In statistical parlance, you will be ‘regressing’ height on weight. The line of code which accomplishes this is:

  lm_output <- lm(women$height ~ women$weight

There are two operations that you will become very familiar with when running Predictive Models in R.

1. The ~ operator (also called the tilde) is a shorthand way for separating what you want to predict, with what you are using to predict.   This is expression in formula syntax. What you are predicting (the dependent or Target variable) is usually on the left side of the formula, and the predictors (independent variables, features) are on the right side. Independent and dependent variables are height and weight, and to improve readability, I have specified them explicitly by using the data frame name together with the column name, i.e. women$height and women$weight
2. The <- operator (also called assignment) says assign whatever function operators are on the right side to whatever object is on the left side.  This will always create or replace a new object that you can further display or manipulate. In this case we will be creating a new object called lm_output, which is created using the function lm(), which creates a Linear model based on the formula contained within the parentheses.
   

   Note that the execution of this line does not produce any displayed output.  You can see if the line was executed by checking the console.  If there is any problem with running the line (or any line for that matter) you will see an error message in the console.

3. summary(lm_output): The following statement displays some important summary information about the object lm_output and writes to output to the R Console as pictured above

   summary(lm_output) 

The results will appear in the Console window as pictured in the figure above.

Look at the lines market (Intercept), and women$weight which appear under the Coefficients line in the console.  The Estimate Column shows the formula needed to derive height from weight.  Like any linear regression formula, it includes coefficients for each independent variable (in our case only one variable), as well as an intercept. For our example the English rule would be “Multiply weight by 0.2872 and add 25.7235 to obtain height”.

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  25.723456   1.043746   24.64 2.68e-12 ***
women$weight  0.287249   0.007588   37.85 1.09e-14 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.44 on 13 degrees of freedom
Multiple R-squared:  0.991,	Adjusted R-squared:  0.9903 
F-statistic:  1433 on 1 and 13 DF,  p-value: 1.091e-14

We have already assigned the output of the lm() function to the lm_output object. Let’s apply another function to lm_output as well. The predict() function “reads” the output of the lm function and predicts (or scores the value), based upon the linear regression equation.  In the code we have assigned the output of this function to a new object named “prediction”.

Switch over to the console area, and type “prediction” to see the predicted values for the 15 women. The following should appear in the console.

> prediction
       1        2        3        4        5        6        7 
58.75712 59.33162 60.19336 61.05511 61.91686 62.77861 63.64035 
       8        9       10       11       12       13       14 
64.50210 65.65110 66.51285 67.66184 68.81084 69.95984 71.39608 
      15 
72.83233

There are 15 predictions.  Just to verify that we have one for each of our original observations we will use the nrow() function to count the number of rows.

At the command prompt in the console area, enter the command: nrow(women) 

The following should appear:

>nrow(women)
[1] 15 

The error object is a vector that was computed by taking the difference between the predicted value of height and the actual height.  These are also known as the residual errors, or just residuals.

Since the error object is a vector, you cannot use the nrows() function to get its size.   But you can use the length() function:

>length(error)
[1] 15 

In all of the above cases, the counts all compute as 15, so all is good.

• plot(women$height,error) :This plots the predicted height vs. the residuals.  It shows how much the prediction was ‘off’ from the original value.  You can see that the errors show a non-random pattern.  This is not good.  In an ideal regression model, you expect to see prediction errors randomly scatter around the 0 point on the why axis.

Some important points to be made regarding this first example:

The R-Square for this model is artificially high. Regression is often used in an exploratory fashion to explore the relationship between height and weight.  This does not mean a causal one.  As we all know, weight is caused by many other factors, and it is expected that taller people will be heavier.

A predictive modeler who is examining the relationship between height and weight would want probably want to introduce additional variables into the model at the expense of a lower R-Square. R-Squares can be deceiving, especially when they are artificially high

After you are done, press Ctrl-S (File Save), navigate to the PracticalPredictiveAnalytics/R folder that was created, and name it Chapter1_LinearRegression

Installing a package

Sometimes the amount of information output by statistic packages can be overwhelming. Sometime we want to reduce the amount of output and reformat it so it is easier on the eyes. Fortunately, there is an R package which reformats and simplifies some of the more important statistics. One package I will be using is named “stargazer”.

Create another R script by Ctrl + Shift + N  to create a new R script. 

Enter the following lines and then Press Ctrl+Shift+Enter to run the entire script. 

install.packages("stargazer")
library(stargazer)
stargazer(lm_output, title="Lm Regression on Height", type="text")

After the script has been run, the following should appear in the Console:

Code Description

install.packages("stargazer")

This line will install the package to the default package directory on your machine.  Make sure you choose a CRAN mirror before you download.

library(stargazer) 

This line loads the stargazer package

stargazer(lm_output, title="Lm Regression on Height", type="text")

The reformatted results will appear in the R Console. As you can see, the output written to the console is much cleaner and easier to read 

After you are done, press Ctrl-S (File Save), navigate to the PracticalPredictiveAnalytics/Outputs folder that was created, and name it Chapter1_LinearRegressionOutput

Installing other packages

The rest of the book will concentrate on what I think are the core packages used for predictive modeling. There are always new packages coming out. I tend to favor packages which have been on CRAN for a long time and have large user base. When installing something new, I will try to reference the results against other packages which do similar things.  Speed is another reason to consider adopting a new package.

Summary

In this article we have learned a little about what predictive analytics is and how they can be used in various industries. We learned some things about data, and how they can be organized in projects.  Finally, we installed RStudio, and ran a simple linear regression, and installed and used our first package. We learned that it is always good practice to examine data after it has been brought into memory, and a lot can be learned from simply displaying and plotting the data.

Resources for Article:

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Further resources on this subject:

• Stata as Data Analytics Software [article]
• Metric Analytics with Metricbeat [article]
• Big Data Analytics [article]

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