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What is SAS?

SAS stands for Statistical Analysis Software which is used for Data Analytics. It helps you to use qualitative techniques and processes which allows you to enhance employee productivity and business profits. SAS is pronounced as SaaS.

What is mean by R?

R is a programming language is widely used by data scientists and major corporations like Google, Airbnb, Facebook etc. for data analysis.

R language offers a wide range of functions for every data manipulation, statistical model, or chart which is needed by the data analyst. R offers inbuilt mechanisms for organizing data, running calculations on the given information and creating graphical representations of that data sets.

Google Trend SAS vs R


SAS is commercial software, so it needs a financial investment, whereas R is open source software, So, anyone can use it.

SAS is the easiest tool to learn. So, people with limited knowledge of SQL can learn it easily; on the other hand, R programmers need to write tedious and lengthy codes.

SAS is relatively less frequently updated, whereas R is an open-source tool, continuously updated.

SAS has good graphical support, whereas the Graphical support of the R tool is poor.

SAS provides dedicated customer support, whereas R has the biggest online communities but no customer service support.

Why use SAS?

Access raw data files and data in an external database

Analyze data using statics, descriptive, multivariate techniques, forecasting, modeling, and linear programming

Advanced analytics feature allows you to make changes and improvements in business practices.

Helps businesses to know about their historical data

Why use R?

R offers a useful programming constructs for data analytics like conditionals, loops, input and output facilities, user-defined recursive functions, etc.

R has a rich and expanding ecosystem and plenty of documentation available over the internet.

You can run this tool on a variety of platforms including Windows, Unix, and MacOS.

Good graphics capabilities Supported by an extensive user network.

R Vs Sas Stackoverflow Questions

History of SAS

SAS was developed by Jim Goodnight and John Shall in 1970 at N.C. University

Initially, it was developed for Agricultural Research.

Later, it expanded to a gamut of tools to include Predictive Analytics, Data Management, BI, among others.

Today 98 of the world’s top companies in fortune 400 uses SAS data analytical tool for Data analysis.

History of R

1993- R is a programming language developed by Ross Ihaka and Robert Gentleman

1995: R first distributed as an open-source tool under GPL2 license

1997: R core group and CRAN founded

1999: The R website, chúng tôi launched

2000: R 1.0.0 released

2004: R 2.0.0 released

2009: First edition of the R Journal

2013: R 3.0.0 released

2023: New R logo adopted

SAS Vs. R: Key Differences

Differences between SAS and R

Parameters SAS R

Availability / Cost SAS is commercial software, so it needs a financial investment. R is open source software, So, anyone can use it.

Ease of Learning SAS is the easiest tool to learn. So, people with limited knowledge of SQL can learn it easily. R programmers need to write tedious and lengthy codes.

Statistical Abilities SAS offers a powerful package which offers all types of statistical analysis and techniques. R is an open source tool which allows users to submit their own packages/libraries. The latest technologies are often released in R first.

File Sharing You can’t share SAS generated files with another user who does not use SAS. Since anyone uses r, it is much easier to share files with another user.

Updates SAS relatively less frequently updated. R is an open source tool, so it is continuously updated.

Market Share Currently, SAS is facing stiff competition from R, and other Data analytical tool as a result market share of SAS is gradually declining. R has seen exponential growth in the last past five years with its increasing popularity. That is why its market share is increasing rapidly.

Graphical Capabilities SAS has good graphical support. However, it does not offer any customization. Graphical support of R tool is poor.

Customer Support SAS provides dedicated customer support. R has the biggest online communities but no customer service support.

Support for Deep learning Deep Learning in SAS is still in its early stages, and there’s a lot to work for before it matures.

Job Scenario SAS analytic tool is still the market leader as far as corporate jobs are concerned. Many big companies still work on SAS. Jobs on R have been reported to increase over the last few years.

Salary Range The average salary for any SAS programmer is $81,560 per year in the U.S.A. The average salary for an “R” programmer” ranges from approximately $127,937 per year for Data scientists to $147,189 per year.

Best features



Nested rules



Data analysis

Graphics and data Flexible statistical analysis

Highly interactive

Famous companies using Airbnb, StacShare, Asana, Hubspot Instacart, Adroll, Opbandit, Custora

TIOBE Rating 22 16

Feature of R

R helps you to connect to many databases and data types

A large number of algorithms and packages for statistics flexible

Offers effective data handling and storage facility

Collect and analyze social media data

Train machines to make predictions

Scrape data from websites

A comprehensive and integrated collection of intermediate tools for data analysis

Interface with other languages and scripting capabilities

Flexible, extensible, and comprehensive for productivity

Ideal platform for data visualization

Features of SAS

Operations Research and Project Management

Report formation with standard graphics

Data updating and modification

Powerful Data handling language

Read and write almost any data format

Best data cleansing functions

Allows you to Interact with multiple host systems

The Final Verdict: R vs SAS

After comparing some main differences between both these tools, we can say that both have their own set of users. There are many companies, who prefer SAS because of data security issues, which show despite a drop in a recent year, there is still a huge demand for SAS certified professionals.

On the other hand, R is an ideal tool for those professionals who want to do deep cost-effective Data analytics jobs. The numbers of startup companies are increasing all over the world. Therefore, the demand for R-certified developers is also increasing. Currently, both have equal potential for growth in the market, and both are equally popular tools.

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Top Certifications For Sas, R, Python, Machine Learning Or Big Data

We released our rankings for various long duration analytics programmes in India for 2014 – 15 last week. They were greeted with unparalleled enthusiasm and response from our audience. We continue our journey to help our audience decide the best analytics trainings and resources.

This week, we will focus on ranking short duration courses or certification courses.

Latest Rankings: Top Certification Rankings of  2023 – 2023

Scope of these rankings:

In this round, we are ranking various short duration certification courses accessible in India. So the consideration set will include courses either run in India or are available online. We will exclude courses / certifications / boot camps running in other countries.

Why rank certification courses and not institutes?

One of the conscious calls, we took while coming up with the rankings was to rank courses and not the institutes. Why? Because that is how we think and that is what we need to make our learning decisions. We usually need to find the best courses specific to learn a language or a tool. You would want to do the course which is best to learn R or SAS or Python. Institute ranking would not be the right way to make these decisions.

Hence, we decided to rank the courses individually and not institutes. So, here are the ranks for various courses:

Certification courses for SAS:

Foundation Course in Analytics by Jigsaw Academy: Foundation course from Jigsaw Academy is an ideal first course for your data science career, if you want to learn SAS. The content is lucid and leaves you with enough knowledge on the subject to start your data science career. The coverage of the course is holistic as well – it covers everything from collecting and cleaning data to how to build various predictive models. What I really like about this course is that it makes the journey of becoming a data scientist easier. With its simple step-by-step approach, it is an ideal course for those who come from a non-statistics or a non-programming background.

SAS Institute – Predictive modeler: Predictive Modeler certification from the SAS institute is probably the best short term certification available on SAS. Typically run over 5 days, this course assumes that you know Base SAS and have been using it for about 6 months (SAS also offers a Base SAS certification separately). The reason why this course has been ranked second is because of the cost. SAS charges INR 75k+ for this certification. There can be travel costs over and above and if you want to learn Base SAS as well, you would double up the cost – pretty hefty for a 10 day course. For the motivated folks, SAS institute has started offering 2 courses online for free. You can do them to start, then practice for a few days and take up this course. This will save the cost to some extent, but you still need to shell out a fortune for this course.

Certified Business Analytics Professional by Edvancer Eduventures: A lower cost option compared to the first 2 courses. This course from Edvancer covers SAS and predictive modeling comprehensively. Edvancer provides a good proposition to get 60 hours of instructor led trainings at a relatively low cost. Definitely check them out if cost is a significant constraint for you.

There are other courses offered in the industry from the likes of AnalytixLabs, EduPristine, Analytics Training Institute which are not comprehensive from the stand point of becoming a predictive modeler. You should only consider them if cost is the only factor for you to decide.

Must Read: A step by step guide to learn SAS from the scratch

Certification courses for R:

Data Science specialization on Coursera: Probably the most definitive set of courses available for free. These are easy to follow, 2 – 3 hours per week per course. You can pick the courses you need and avoid the ones which you don’t need immediately or do them simultaneously, if you have more bandwidth. The only downside to this certification is lack of guidance from a mentor. You need to rely on forums for that role.

The Analytics Edge on edX: One of the most intensive course to pursue, this course requires you to spend 15 – 16 hours every week. And if you do put them, it covers everything you need to learn with R in less than 4 months. By end of this course, you will be competing on a competition on Kaggle!

Data Science Certification from Jigsaw Academy: Again a comprehensive offering from Jigsaw with good quality content and instructors. This course provides you with all you need to know to become a data scientist. The only complain I have about the course is the cost – INR 26K for self paced and INR 42k for Instructor led might seem high, given that there are a lot of free resources available on R. On the flip side, this course will expose you to business case studies and real world problems better than any other course I have come across. If you are confident about your ability to pick up complex knowledge, stick to the free courses. But, if you are intimidated by statistics or programming and feel you need some hand holding, Jigsaw is the ideal place to learn.

Business Analytics with R from Edureka: A cost effective instructor led offering from Edureka, which covers the concepts well. You can also consider the data science offering from them for slightly higher fees and get functional knowledge about Hadoop and Machine Learning with R as well.

Certified R Programmer from Edvancer: This offering from Edvancer tries to serve people in the middle – those who are motivated enough to learn by self paced tutorials, but still need on demand support to help them out at times. Given that there is no dearth of self paced videos / tutorials on R, you should consider this course for its on demand support.

Data Analysis with R from Udacity also covers basic exploratory data analysis in R, but does not provide enough learning to build predictive models.

Must Read: A step by step guide to learn data science in R Programming

Certification courses for Python:

Mastering Python by Edureka: I personally like Python as a tool for data science. The ecosystem for Python is still evolving. Hence, it is difficult to find courses as comprehensive in Python as this one from Edureka. The course starts from basics of Python and goes on to make sure that you can apply machine learning using Python. One of the best offering to learn Python for data science.

Intro to Data Science by Udacity: Udacity has a whole bunch of courses which assume that you know Python. This particular course is a good introduction to Pandas and data wrangling using Pandas. While the course is a good introduction, it falls short on comprehensiveness and does not cover all your needs as a data scientist through this course.

Must Read: A comprehensive guide which teaches Python from the scratch

Certification courses for Machine Learning:

Machine Learning by Andrew Ng on Coursera: I would probably not be wrong, if I call this course as the most popular course on Machine Learning. Prof. Andrew Ng explains even the most complicated topics in easy to understand manner. A must do course if you want to learn Machine Learning from scratch

Learning from Data on edX: One of the most intensive course run by Prof. Abu-Mustafa. The course contains some really intensive exercises and assignments. The course is not for the people with light heart, but for those who can endure – this is the best course on the subject.

Machine Learning courses from Udacity: The machine learning offerings from Udacity fall some where in between the two courses mentioned above. They don’t simplify the subject matter to the extent Prof. Andrew Ng did and the problem sets are also not as intensive as the course on edX.

Must Read: A beginners guide to conquer Machine Learning

Certification courses for Big Data:

Big Data and Hadoop from Edureka: Although the course does not come with Wiley certification, it is a very cost effective option. The course covers Big Data and Hadoop ecosystem in good details and is clearly the most popular course from Edureka offerings.

A few other courses worth mentioning here are MongoDB fundamentals on Udacity and Mining massive datasets on Coursera. As the name suggests, the course on MongoDB provides you all the basics of working with MongoDB. Mining massive datasets on the other hand is a blend of machine learning and Big Data.

Short note about the methodology:

You can read more details about our methodology here. We ranked the courses on 4 parameters:

Breadth of the coverage

Quality of the content

Industry recognition

Value for Money

End Notes: If you like what you just read & want to continue your analytics learning, subscribe to our emails, follow us on twitter or like our facebook page.


Sas Training (18 Courses Bundle, Online Certification)

Goals Objectives

The objective of the sales training program is to assist people who are willing to learn SAS from the beginning. It will help to improve accessibility, scalability, and reliability while it also minimizes overhead and maintenance costs of the infrastructure. It will also help the trainees to understand easier and quicker integration with other platforms and which will eliminate the requirements of any expensive hardware. After the end of this program trainees will be able to work effectively and efficiently on SAS.

Course Highlights

This course includes almost 13units which consists of the training units as well as projects.

SAS Business Analytics for Beginners is the first module in which how SAS business analytics can be used by the beginners is explained. The information about this module is covered by a video tutorial of almost nine-hour long.

SAS Statistics will be the next unit in which how SAS software can perform statistical analyses using SAS/STAT software is explained, It focuses on t-tests, ANOVA, and linear regression, and includes a brief introduction to logistic regression. It will be explained step by step in the video tutorials.

SAS Output Delivery System(ODS) will be about how we can manipulate and customize your output. It will provide trainees the method of delivering output in a variety of formats and makes the formatted output easy to access. It will be briefed step by step in the video tutorials.

SAS Macros Tutorials is next which is about how SAS macros can make our life easier by reducing the redundancy or repetitiveness of a code. It will be very helpful for the trainees to reduce their workload using the software. The detailed information about this module is covered through a video tutorial.

Project Highlights

Project on SAS – Predictive Modeling with SAS Enterprise Miner is the first project in which a solution is to be created accurately predictably and descriptive models on large volumes of data can be easily studied. More information about the project will be explained through video tutorials.

Project on SAS – Quantitative Finance will be the next project where you need to use SAS to solve mathematical models and extremely large datasets to analyze quantitative financial markets and securities without any difficulty. The concepts will be explained through videos and all kinds of queries will also be solved by the mentor.

Project on SAS – SAS Graph is next in which SAS GRAPH will be used to give data different structures by using colors, fonts, and graphics for the user interface to be studied easily by the users. It will help the trainees to study and explore both network and non-network relational data and to reopened with a single menu command.

Project – SAS SQL is the next project which will be prepared after the fourth module in which multiple studies of graphs and tables. The concepts will be explained through videos in detail.

SAS Advanced Project – Macros will be the last project of the module which will be about how to reduce the tendency of the repetitiveness of coding. More information about the project will be explained through video tutorials.

6  More Projects and courses are there according to the course adopted. After completing all of these training programs and projects, you will be able to work effectively with SAS and will be able to face all your problems in practical life.

What Is The Difference Between A Proxy And A Vpn?

A Virtual Private Network (VPN) is a network that protects user identifications by rerouting the traffic and helps you to connect to a remote computer. If we talk about a Proxy, it also does the same job as like VPN. But there is a difference. This guide helps you to find the difference between a proxy and a VPN. Also, it explains why VPN is a more reliable and stronger service than that of the Proxy, so read on.

Difference between a Proxy and a VPN

In order to abstain from these snooping things, we use a VPN software or a Proxy service that provides a higher level of privacy. Both services allow you to access the internet services anonymously by concealing the Internet Protocol address in various ways.

So, the question arises that if proxy servers and VPN connections perform the same job then why they are called different. Basically, they are different and here the similarities come to end.

What is a Proxy Server?

Proxy software makes it easier for people to overcome Internet censorship. It can make you anonymous on the internet, making the connections more secure and private.

A proxy server is a server that acts as a middle man between your computer and the server that you are trying to access. In this case, the websites can’t detect your original IP address and it seems to come from any other location.

For example, suppose you are currently located in Mumbai city and you need to access the website that is only limited to the people located in the United States. In this case, you need to connect to a proxy server that is located in the United States. After that, connect to that website. That way, the traffic coming from your web browser looks like coming from the remote computer.

Proxy service is quite helpful for the region-restricted websites and it is highly reliable for the task related to low-stakes. As we mentioned earlier, the proxy server uses anonymous network ID, so it bypasses the simple contents filters and services that are based on IP restrictions.

In order to make it more clear, let us take an example. Assume you are five friends and playing an online game where you receive a daily in-game incentive bonus when you vote the game server on a server ranking site. But according to the game policy, you can only vote with your IP address notwithstanding whether other player names are used. Luckily, there is a proxy service using which all the five friends can easily log in their vote and get the in-game incentive bonus. It could happen because the web browser of each person appears to be originating from any other IP address.

Apart from these plus points, there is also some downside to the proxy server. The proxy server is not much reliable for high-leveled tasks. Although, it hides the IP address and works as a mute man lies in the middle for Internet traffic. But, it does not support the encryption protection to encrypt data between your device and the proxy server. Therefore, a proficient and experienced programmer can quickly block sensitive data in transit and keep it.

The proxy service is basically based on an application by application basis. It means that you can’t configure the entire PC while connecting to the proxy.

There are two main types of proxy that are commonly used. These proxy server protocols are HTTP and SOCKS. The HTTP Proxy is the oldest and most wide-spread proxy server. It has been designed basically for web-based traffic so that it could detect the suspicious content easily. The most interesting thing of an HTTP proxy is that it allows you the encryption protection using the SSL certificate, whereas the SOCKS server doesn’t support encryption security.

Read: Free Proxy software for Windows 10.

What is a VPN server?

A VPN or a Virtual Private Network is essential to stay invisible or anonymous on the chúng tôi will encrypt all the data that your device sends so that it will not be hackable. It hides and protects your identity online.

Virtual Private Networks is somewhat similar to the Proxy server, herewith it also offers an extra layer of privacy and security to the internet activity. The VPN functions at the OS level where it occupies the entire traffic connection of the computer it is configured on. That indicates, the VPN captures the network traffic of each application running on your computer that extends far beyond a single web browser.

Additionally, the VPN server encrypts the network traffic between the internet and the computer due to which the whole process passes through an extremely encrypted tunnel. It provides 100% assurance to the protection of data from the Internet Service Providers and the prying eyes of Intruder on internet activity. And that way, sensitive and private information of every single user would remain preserved.

Read: Free VPN software for Windows 10.

VPN vs Proxy

The actual difference between a proxy and a VPN is that a Proxy service lets you hide your IP (Internet Protocol) address and it reroutes the entire network connections anonymous. Whereas a VPN connection has major benefits over the proxy. It not only hides your IP but also provides better encryption to the network between the computer and its servers so that no snoopers or hackers could harm your device.

Python Vs C++: Difference Between Them

Key Difference Between Python and C++

Python code runs through an interpreter while C++ code is pre-compiled

Python supports Garbage Collection whereas C++ does not support Garbage Collection

Python is slower, on the other hand, C++ is faster than Python

In Python, Rapid Prototyping is possible because of the small size of the code while in C++, Rapid Prototyping not possible because of larger code size

Python is easy to learn language whereas C++ has a stiff learning curve as it has lots of predefined syntaxes and structure

What is C++?

C++ is widely used in general-purpose programming languages. The language allows you to encapsulates high and low-level language features. So, it is seen as an intermediate-level language. It also used to develop complex systems where the hardware level coding requires.

What is Python?

Python is a high-level object-oriented programming language. It has built-in data structures, combined with dynamic binding and typing, which makes it an ideal choice for rapid application development. Python also offers support for modules and packages, which allows system modularity and code reuse.

It is one of the fastest programming languages as it requires very few lines of code. Its emphasis is on readability and simplicity, which make it a great choice for beginners.

Stack Overflow Questions c++ VS. Python

Why Python?

Here, are reasons for using Python language:

Very simple syntax compared to Java, C, and C++ languages.

It is used for Machine Learning, Deep Learning, and the general overarching AI field.

Very useful in data analysis and visualization.

Extensive library and handy tools for developers/programmer

Python is cross-compatible

Python has its auto-installed shell

Compared with the code of other languages, python code is easy to write and debug. Therefore, its source code is relatively easy to maintain.

Python is a portable language so that it can run on a wide variety of Operating systems and platforms.

Python comes with many prebuilt libraries, which makes your development task easy.

Python helps you to make complex programming simpler. As it internally deals with memory addresses, garbage collection.

Python provides an interactive shell that helps you to test the things before it’s actual implementation.

Python offers database interfaces to all major commercial DBMS systems.

Supports imperative and functional programming

Python is famous for its use in IoT.

Why C++?

Here, are reasons for using C++

C++ is multi-paradigm means it follows three paradigms Generic, Imperative, and Object-Oriented.

C++ provides performance and memory efficiency.

It provides high-level abstraction.

C++ is compatible with C.

The language allows the reusability of code.

Features of C++

Here, are important features of C++

The program should be simple, object-oriented and easy to understand

Development should be conducted in a robust and secure environment.

Code should follow the specific architecture and must be portable.

Code should be easily “interpreted and dynamic “

Features of Python

Here, are important features of Python

Easy to learn, read, and maintain

It can run on various hardware platforms using the same interface.

You can include low-level modules to the Python interpreter.

Python offers an ideal structure and support for large programs.

Python offers support for automatic garbage collection.

It supports an interactive mode of testing and debugging.

It offers high-level dynamic data types and also supports dynamic type checking.

Python language can be integrated with Java, C, and C++ programming code

Applications of C++

Here, are important applications of C++:

C++ is used to develop all kinds of embedded systems like smartwatches, multimedia systems in automobiles, lot devices, etc.

C++ also allows you to develop the servers and the high-performance microcontroller programs

Game development is the key to C++. That’s why C++ is becoming more popular among game developers.

Applications of Python

Here, are some important Applications of Python

Python is widely used in machine learning

The language allows you to manage a huge amount of data with an easy and cost-effective way.

Data analysts use Python to analyze the data and statistical information.

It is also useful in big data technologies. In fact, most of the significant data functions can be performed using python programming.

Web developers use python language for developing the complex web application; that’s because Python offers the Django framework, which helps you to create the entire sites using Python.

Python vs. C++: Differences Between Python and C++

Here, are the major difference between Python and C++

Python C++

Supports Garbage Collection Does not support Garbage Collection

Python programs are easier to write Not easy in contrast to Python because of its complex syntax.

Run through interpreter C++ is pre-compiled

Rapid Prototyping is possible because of the small size of the code Rapid Prototyping not possible because of larger code size

Python is difficult to be installed on a windows box Not have an issue while installing in the windows system.

Python is nearer to plain English language. Therefore, it is easy to learn language. C++ has a stiff learning curve as it has lots of predefined syntaxes and structure

Python is slower. C++ is faster than Python

Python has more English like syntax, so readability is very high. C++ code readability is weak when compared with Python code.

In Python, variables are accessible outside the loop. The scope of the C++ variables is limited within the loops.

Famous companies using Python are Google, Lyft, Twitch, Telegram. Famous companies using C++ are Uber technologies, Netflix, Spotify, Instagram.

TIOBE rating is 3 TIOBE rating is 4

The average salary for a Python Developer is $120,359 per year in the United States of America. The average salary for a C++ Developer is $108,809 per year in the United States.

Here, are cons/drawbacks of using C++ language

It offers no security for your code

Complex language to use in a very large high-level program.

It is used for platform-specific applications commonly.

When C++ used for web applications it is complex and difficult to debug.

C++ can’t support garbage collection.

C++ is not as portable as other high-level programming languages. So, when you want to compile the C++ code, you need to run it on another machine.

If the same operation has to be executed more than one time, the same sequence has to copy at some places, which increases code redundancy.

Here, are cons/drawbacks of using Python language

Used in fewer platforms.

Weak in mobile computing, hence not used in app development

As Python is dynamic, so it shows more errors at run-time

Under-developed and primitive database access layer

Absence of commercial support

Google Trends C++ vs. Python

The Game Of Increasing R

This article was published as a part of the Data Science Blogathon.


After building a Machine Learning model, the next and very crucial step is to evaluate the model performance on the unseen or test data and see how good our model is against a benchmark model.

The evaluation metric to be used would depend upon the type of problem you are trying to solve —whether it is a supervised, unsupervised problem, or a mix of these (like semi-supervised), and if it is a classification or a regression task.

In this article, we will discuss two important evaluation metrics used for regression problem statements and we will try to find the key difference between them and learn why these metrics are preferred over Mean Squared Error (MSE) and Root Mean Squared Error (RMSE) for a regression problem statement.

Some Important questions which we are trying to understand in this article are as follows:

👉 The Game of increasing R-squared (R2)

👉 Why we go for adjusted-R2?

 👉 When to use which from R2 and adjusted-R2?

Let’s first understand what exactly is R Squared?

R-squared, which sometimes is also known as the coefficient of determination, defines the degree to which the variance in the dependent variable (target or response) can be explained by the independent variable (features or predictors).

Let us understand this with an example — say the R2 value for a regression model having  Income as an Independent variable (predictor) and, Expenditure as a dependent variable (response) comes out to be 0.76.

– In general terms, this means that 76% of the variation in the dependent variable is explained by the independent variables.

But for our defined regression problem statement, it can be understood as,

👉 76% variability in expenditure is associated or related with the regression equation and 24% variations are due to other factors.

👉76% variability in expenditure is explained by its linear relationship with income while 24% variations are uncounted for.

👉 76% variation in expenditure due to variation in income while we can’t say anything about the 24% variations. God knows better about it.

Image Source: link

Important points about R Squared 

👉 Ideally, we would want the independent variables to explain the complete variations in the target variable. In that scenario, the R2 value would be equal to 1. Thus we can say that the higher the R2 value, the better is our model.

👉 In simple terms, the higher the R2, the more variation is explained by your input variables, and hence better is your model. Also, the R2 would range from [0,1]. Here is the formula for calculating R2–

The R2 is calculated by dividing the sum of squares of residuals from the regression model (given by SSRES) by the total sum of squares of errors from the average model (given by SSTOT) and then subtracting it from 1.

Fig. Formula for Calculating R2

Image Source: link

Drawbacks of using R Squared :

👉 Every time if we add Xi (independent/predictor/explanatory) to a regression model, R2 increases even if the independent variable is insignificant for our regression model.

👉 R2 assumes that every independent variable in the model helps to explain variations in the dependent variable. In fact, some independent variables don’t help to explain the dependent variable. In simple words, some variables don’t contribute to predicting the dependent variable.

👉 So, if we add new features to the data (which may or may not be useful), the R2 value for the model would either increase or remain the same but it would never decrease.

So, to overcome all these problems, we have adjusted-R2 which is a slightly modified version of R2.

Let’s understand what is Adjusted R2?

👉 Similar to R2,  Adjusted-R2 measures the proportion of variations explained by only those independent variables that really help in explaining the dependent variable.

👉 Unlike R2, the Adjusted-R2 punishes for adding such independent variables that don’t help in predicting the dependent variable (target).

Let us mathematically understand how this feature is accommodated in Adjusted-R2. Here is the formula for adjusted R2

Fig. Formula for Calculating adjusted-R2

Image Source: link

Let’s take an example to understand the values changes of these metrics in a Regression model

For Example,

      Independent Variable                    R2              Adjusted-R2

                   X1                  67.8                   67.1

                   X2                  88.3                   85.6

                   X3                  92.5                   82.7

In this example for a regression problem statement, we observed that the independent variable X3 is insignificant or it doesn’t contribute to explain the variation in the dependent variable. Hence, adjusted-R2 is decreased because the involvement of in-significant variable harms the predicting power of other variables that are already included in the model and declared significant.

 R2 vs Adjusted-R2

👉 Adjusted-R2 is an improved version of R2.

👉 Adjusted-R2 includes the independent variable in the model on merit.

👉 Adjusted-R2 < R2

👉 R2 includes extraneous variations whereas adjusted-R2 includes pure variations.

👉 The difference between R2 and adjusted-R2 is only the degrees of freedom.

The Game of Increasing R2

Sometimes researchers tried their best to increase R2 in every possible way.

👉 One way to include more and more explanatory (independent) variables in the model because:

R2 is an increasing function of the number of independent variables i.e, with the inclusion of one more independent variable R2 is likely to increase or at least will not decrease.

When to use which?

Comparing models using R2

Comparing two models just based on R2 is dangerous as,

👉 Models having a different number of independent variables may have an equal value of R2.

👉 Total sample size and respective degrees of freedom are ignored.

Hence, there is a likelihood that one would choose the wrong model.

Problem solved by adjusted-R2

To compare two different models, or choose the best model, the adjusted-R2 is used because:

👉 It is adjusted for the respective degree of freedom.

👉 It takes into account the total sample size and number of independent variables.

👉 It is not an increasing function of the number of independent variables.

👉 It only increases if newly independent variables have an impact on the dependent variable.


So, concluding the discussion we say that,

👉 R2 can be used to access the goodness of fit of a single model whereas,

👉Adjusted-R2 is used to compare two models and to see the real impact of newly added independent variables.

👉 Adjusted-R2 should be used while selecting important predictors for the regression model.

End Notes

Thanks for reading!

Please feel free to contact me on Linkedin, Email.

About the author Chirag Goyal

Currently, I am pursuing my Bachelor of Technology (B.Tech) in Computer Science and Engineering from the Indian Institute of Technology Jodhpur(IITJ). I am very enthusiastic about Machine learning, Deep Learning, and Artificial Intelligence.

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