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Topics
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Main Story: Web Analytics by Jayesh Borude
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Multiple Regression
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by Ashish Mahadik
News Digest by Piyush Bhanarkar
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Quant Guru: Srinivasa Ramanujan by Raunak Sharma
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Internship Experiences: HDFC
by Vaibhav M and
GEP 10
Piyush Bhanarkar
Curiosity Updates by Arunava Dey
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Quant Fun by Jayant Pansare & Devarshee Ranjan Bora
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Quant Connect
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Editor’s Note July 2017 Heartiest greetings to all! With great excitement and fervour, team Quantinuum presents “Quriosity” - the Quant magazine of SIMSR. In this issue, we have the main story by the Jayesh Borude on “Web Analytics”, which describes how technology is rapidly advancing in the field of analytics. The sub article by Ashish Mahadik on “Multiple Regression” talks about how and where we can use this technique both from an academic and industry point of view. In our Quant guru section, Raunak Sharma writes about Srinivasa Ramanujan, who tried to find proofs of over 6000 theory and hypothesis in the field of mathematics. We are introducing a new section about the Internship Experiences of the second year Quantinuum members. This edition covers the experiences of Piyush Bhanarkar at GEP (Consulting) and Vaibhav M at HDFC (Customer Relationship Management). The News digest features news related to Amzon’s Alexa and the Infosys Finacle covered by Piyush Bhanarkar. Curiosity updates by Arunava Dey cover new ventures and investigations by NASA scientists in earth science fieldwork and space missions. In our Quant Fun section we have an article by Jayant Pansare which talks about interesting and quirky facts about mathematics. Also we have a Sudoku and number puzzle by Devarshee Ranjan Bora at the end. So, look around and enjoy reading about the quantitative aspects around the world.
Happy Learning, Editorial Team!
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Cover Story July 2017 Web Analytics
Web analytics is the collection, reporting, and analysis of website data. The insights gained can be very useful for an organization for fulfilling their objectives of decision making, strategizing and better communication with various stakeholders. The major advantages of web analytics are measuring web traffic, monitoring conversations, visitors count, optimizing marketing campaigns and also identifying target market. Web analytics can also help in better customer relationship management by efficient complaint handling and response. This is the age web analytics plays a central role in market research for every business sector. There are a plethora of tools available nowadays for different kinds of web analytics suited for different needs. Google Analytics is the simplest and most robust web analytics offering. Most of the organizations use this to their benefit and it is easily one of the most popular web analytics tool worldwide. Behavior analysis tools practice serving ads to groups of people who exhibit similarities not in their location, gender, or age, but in how they act and react in their online environment a method to boost sales and increase loyalty. Social media analytics is extremely useful for a marketer for better consumer insights as well as campaign response and reach measurement and competitor analysis. These tools analyze conversations across popular social media tools such as Twitter, Instagram and Facebook. Tools like Facebook insights and Twitterlyzer are dedicated for popular social media sites.
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Competitive analysis tools like compete.com practice assessing and analyzing strengths and weaknesses of competing Web sites, including identifying traffic patterns, major traffic sources, and keyword selection. Web analytics technologies There are at least two categories of web analytics; off-site and on-site web analytics. Off-site web analytics refers to web measurement and analysis regardless of whether you own or maintain a website. It includes the measurement of a website's potential audience (opportunity), share of voice (visibility), and buzz (comments) that is happening on the Internet as a whole. On-site web analytics, the most common, measure a visitor's behavior once on your website. This includes its drivers and conversions; for example, the degree to which different landing pages are associated with online purchases. On-site web analytics measures the performance of your website in a commercial context. This data is typically compared against key performance indicators for performance, and used to improve a website or marketing campaign's audience response. Google Analytics and Adobe Analytics are the most widely used on-site web analytics service; although new tools are emerging that provide additional layers of information, including heat maps and session replay. The traditional qualitative research methods are now gradually getting replaced by web analytics due to the advent of digitization and mobile marketing. The internet and social media shapes the future of a brand. Thus web analytics is the need of the hour. Organizations are recognizing this and spending more of the marketing budget in it. In future more such tools will be introduced and advanced methods will give way to much more effective insights from the worldwide web.
Source:- https://en.wikipedia.org/wiki/Web_analytics https://www.tutorialspoint.com/web_analytics/google_analytics.htm http://www.webopedia.com/TERM/W/Web_analytics.html
By Jayesh Borude PGDM-FS (2016-18)
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Multiple Regression Regression analysis is used to predict the value of one variable on the basis of other variables. This technique may be most commonly used statistical procedure because one can easily appreciate, almost all companies and government institutions forecast variables such as product demand, interest rates, inflation rates, prices of raw materials and labour costs etc. The earliest form of regression was the method of least squares, which was published by Legendre in 1805, and by Gauss in 1809. Regression methods continue to be an area of active research. In recent decades, new methods have been developed for robust regression, regression involving correlated responses such as time series and growth curves, regression in which the predictor (independent variable) or response variables are curves, images, graphs, or other complex data objects, regression methods accommodating various types of missing data, nonparametric regression, Bayesian methods for regression, regression in which the predictor variables are measured with error, regression with more predictor variables than observations, and causal inference with regression. The technique of regression involves developing a mathematical equation or model that describes the relationship between the variable to be forecasted, which is called the dependent variable and variables that the statistics practitioner believes are related to the dependent variable, called independent variables. If we are trying to identify the dependency of dependent variable on the single independent variable, then it can be achieved through the process called simple linear regression and when the process involves more than one independent variable, we employ multiple regression. Multiple regression allows us to determine the overall fit (variance explained) and the relative contribution of each independent variable to the total variance explained. There are various tools available to perform multiple regression such as R, XLStat, Minitab, SPSS etc. Before employing the process of multiple regression, one need to be certain it the process is applicable to identify the relationship and for that there is a set of assumptions which need to be checked first to get the valid results while doing the test on the real world data. It will always be the case where some assumptions may fail and there are steps to overcome these failures. Following are the assumptions, •
• •
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Dependent variable should be measured on a continuous scale (i.e., it is either an interval or ratio variable). If dependent variable was measured on an ordinal scale, we will need to carry out ordinal regression rather than multiple regression. Independent variables can be either continuous (i.e., an interval or ratio variable) or categorical (i.e., an ordinal or nominal variable). Data should have independence of observations (i.e., independence of residuals), which can be easily checked using the Durbin-Watson statistic, which is a simple test to run using SPSS Statistics. There are guides available online on how to interpret Durbin-Watson statistic. There need to be a linear relationship between (a) the dependent variable and each independent variable, and (b) the dependent variable and the independent variables collectively. Whilst there are a number of ways to check for these linear relationships, we suggest creating scatterplots and partial regression plots using SPSS Statistics, and then visually inspecting these scatterplots and partial regression plots to check for linearity. If the relationship displayed in the scatterplots and partial regression plots are not linear, we will have to either run a non-linear regression analysis, which one can do using SPSS Statistics. 6
• •
•
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The data needs to show homoscedasticity, which is where the variances along the line of best fit remain similar as we move along the line. The data to tested must not show multicollinearity, which occurs when it has two or more independent variables that are highly correlated with each other. This leads to problems with understanding which independent variable contributes to the variance explained in the dependent variable, as well as technical issues in calculating a multiple regression model. There should be no significant outliers, high leverage points or highly influential points. Outliers, leverage and influential points are different terms used to represent observations in the data set that are in some way unusual to perform a multiple regression analysis. These different classifications of unusual points reflect the different impact they have on the regression line. An observation can be classified as more than one type of unusual point. However, all these points can have a very negative effect on the regression equation that is used to predict the value of the dependent variable based on the independent variables. This can change the output that SPSS Statistics produces and reduce the predictive accuracy of results as well as the statistical significance. Finally, we need to check that the residuals (errors) are approximately normally distributed. Two common methods to check this assumption include using: (a) a histogram (with a superimposed normal curve) and a Normal P-P Plot; or (b) a Normal Q-Q Plot of the studentized residuals.
Sources: Statistics for Management and Economics – Gerald Keller https://statistics.laerd.com/spsstutorials/multiple-regression-using-spss-statistics.php https://en.wikipedia.org/wiki/Regression_analysis
By Ashish Mahadik PGDM-FS (2016-18)
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News Digest July 2017 Indian users will soon be able to use Amazon’s voice-based assistant Alexa Amazon plans to turn its website into the largest e-commerce portal within the Indian subcontinent. Reports suggest that Amazon will make its voice-based assistant available, with support for regional languages such as Marathi, Tamil, and Hindi. Indian users will now have the option of conversing with Alexa in three regional languages. The organization will initially offer the voice assistant in English, with support for local languages coming shortly thereafter. The voice-based assistant from Amazon has turned into a robust platform over the last two years, with Alexa touting over 1,200 skills. It can almost do everything from hailing a cab to ordering items on Amazon to sending a text with your voice, and so on. However, there remain a few India-specific hurdles when it comes to using Alexa for purchasing items on Amazon India. This is because all online transactions in the country require two-factor authentication, but it looks like Amazon is exploring workarounds. The organization will use passphrases and other India-specific innovations to address such issues.
Infosys Finacle integrates with Active AI platform to boost conversational services in banks In a recent development around conversational AI in banking and financial services, Infosys Finacle, a part of EdgeVerve Systems collaborated with Singapore based Active.AI that offers enterprise AI platform to banks globally. The integration of Active AI platform with Finacle will help financial institutions to offer conversational solutions via chat and voice interfaces across their digital channels. This step can boost the customer experience and automate the processes for banks. “Elevating customer experience and reducing servicing costs are two of the strategic goals banks across the world are pursuing. The advancement in artificial intelligence technologies offer a significant opportunity to achieve these twin goals�, said Sanat Rao, Chief Business Officer, Infosys Finacle. Source: http://analyticsindiamag.com/
By Piyush Bhanarkar PGDM Operations (2016-18) 8
QuantGuru July 2017 Srinivasa Ramanujam One of the greatest mathematicians of India, Ramanujan’s contribution to the theory of numbers has been profound. He was indeed a mathematical phenomenon of the twentieth century. This legendary genius of India ranks among all-time greats like Euler and Jacobi. Ramanujan produced such theorems and formulae which even today remain unfathomable in the present age of super computers. He left behind him about 4000 formulae and theorems. It is believed that these were the beginning of some great theory that he had at conceptual stage which failed to develop because of his premature and untimely demise. Ramanujan found mathematics as a profound manifestation of the Reality. He was such a great mathematician and genius as transcends all thoughts and imagination. During his four year stay at Cambridge he produced many papers of great mathematical significance in collaboration with his mentor Professor Hardy. His phenomenal and exceptional genius was recognized all over the academic world. Ramanujan's arrival at Cambridge was the beginning of a very successful five-year collaboration with Hardy. In some ways the two made an odd pair: Hardy was a great exponent of rigor in analysis, while Ramanujan's results were (as Hardy put it) "arrived at by a process of mingled argument, intuition, and induction, of which he was entirely unable to give any coherent account". Hardy did his best to fill in the gaps in Ramanujan's education without discouraging him. He was amazed by Ramanujan's uncanny formal intuition in manipulating infinite series, continued fractions, and the like: "I have never met his equal, and can compare him only with Euler or Jacobi." One remarkable result of the Hardy-Ramanujan collaboration was a formula for the number p(n) of partitions of a number n. A partition of a positive integer n is just an expression for n as a sum of positive integers, regardless of order. Thus p(4) = 5 because 4 can be written as 1+1+1+1, 1+1+2, 2+2, 1+3, or 4. The problem of finding p(n) was studied by Euler, who found a formula for the generating function of p(n) (that is, for the infinite series whose nth term is p(n)xn). While this allows one to calculate p(n) recursively, it doesn't lead to an explicit formula. Hardy and Ramanujan came up with such a formula. He was elected Fellow of the Royal Society, London in 1918. He was then 30 years of age. His mastery of certain areas of mathematics was really fantastic and unbelievable. But soon his hard work began to affect his health and he fell seriously ill in April, 1917.He breathed his last on April 26, 1920 at Kumbakonam at the age of 32 years. Source: https://www.usna.edu/Users/math/meh/ramanujan.html
By Raunak Sharma MMS (2016-18)
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Internship Experience July 2017 GEP GEP was one of the first companies to visit the campus; and after a long rigorous process, I was one of the lucky few to get an opportunity to work with GEP as a Global Delivery Consultant. After a fantastic on-boarding process followed by a week-long induction, we were assigned to our respective clients. GEP has got a very open work culture. People on my floor were very friendly and interactive. Apart from the project mentor GEP also assigned me a Buddy, who constantly guided me throughout the internship duration. Workwise, I was exposed to a new challenge every single day which involved ample amount of research and reaching out to people in the consulting bay. GEP gave me a perfect a perfect platform to analyze data, find key insights and covert these insights into sourcing strategies for the client. I was really impressed by the structured evaluation process GEP followed. Here you can practically see your theoretical concepts being applied to the business world. In the end, I would just like to say that it was an experience which started with a bang and ended with a blast! By Piyush Bhanarkar PGDM Operations (2016-18)
HDFC It all began in October when I was placed in HDFC Bank Limited. I was ecstatic as I did not go home during Diwali vacation to sit for various companies coming to the campus and it paid off. In the month of April, my internship began. We received training for four days where we were taught about various processes and products of HDFC also we were given insights on the business of HDFC. At the end of training we were asked to give a test and then we were allocated branches were we had to report. My project was based on digitalization in which I had to conduct a market research. The research involved gathering of data through both primary research and secondary research. The main objective was to understand why current account holders are not shifting online. Along with research we were asked to convert any possible leads or poach any client of competitor banks. There were constant reviews carried out by my mentor on my project so that the project met the standards. After the collection was over I used tools like Excel and SPSS to analyze the data. Apart from my Project objective I learned various things at HDFC like the work in various profiles of bank and the functioning of retail and corporate bank, and most important was I got valuable insights from some of very experienced employees of HDFC. By Vaibhav M PGDM Marketing (2016-18) 10
Curiosity Updates July 2017 NASA's Juno Spacecraft Spots Jupiter's Great Red Spot Images of Jupiter's Great Red Spot reveal a tangle of dark, venous clouds weaving their way through a massive crimson oval. The JunoCam imager aboard NASA's Juno mission snapped pics of the most iconic feature of the solar system's largest planetary inhabitant during its Monday (July 10) flyby. The images of the Great Red Spot were downlinked from the spacecraft's memory on Tuesday and placed on the mission's JunoCam website Wednesday morning.
Curiosity Mars Rover Begins Study of Ridge Destination The car-size NASA rover on a Martian mountain, Curiosity, has begun its long-anticipated study of an iron-bearing ridge forming a distinctive layer on the mountain's slope. Since before Curiosity's landing five years ago next month, this feature has been recognized as one of four unique terrains on lower Mount Sharp and therefore a key mission destination. Curiosity's science team informally named it "Vera Rubin Ridge" this year, commemorating astronomer Vera Cooper Rubin (1928-2016).
Source: https://www.jpl.nasa.gov/news/
By Arunava Dey PGDM-FS (2016-18)
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QUANT FUN July 2017
Interesting Facts about Mathematics 1) The Fibonacci spiral It is an approximation of the spiral created by drawing circular arcs connecting the opposite corners of squares in the Fibonacci tiling; this one uses squares of sizes 1, 1, 2, 3, 5, 8, 13, 21, 34‌
Fibonacci tiling – It is the plane covered with non-overlapping squares of Fibonacci numbers. The Fibonacci spiral is most common in nature. Examples- Hurricanes structure, Galaxies, Elephant trunk, Pinecone, pattern of Sunflower seeds, Rose petals, Cut In Half Snail Shell, Fingers, Fingerprint, Ear, Egg. Source: https://math.temple.edu/~reich/Fib/fibo.html 2) Golden ratio
If their ratio is the same as the ratio of their sum to the larger of the two quantities i.e. 1.618 In mathematics, two quantities are in the golden ratio (Phi) if their ratio is the same as the ratio of their sum to the larger of the two quantities.
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It can be represented in continued fraction form as
PhiMatrix golden ratio software is used to confirm that Golden ratio has been used to confirm it. Golden pyramid A regular square pyramid is determined by its medial right triangle, whose edges are the pyramid's apothem (a), semi-base (b), and height (h).
If mathematical proportions of b: h: a is
, then it is called as Golden pyramid.
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Apothem is the slant height of a lateral face; that is, the shortest distance from apex to base on a given face. Source: https://www.mathsisfun.com/numbers/golden-ratio.html 3) Kaprekar's routine 6174 is known as Kaprekar's constant Take any four-digit number, using at least two different digits. (Leading zeros are allowed.) Arrange the digits in descending and then in ascending order to get two four-digit numbers, adding leading zeros if necessary. Subtract the smaller number from the bigger number. Go back to step 2. The above process, known as Kaprekar's routine, will always reach its fixed point, 6174, in at most 7 iterations. For example, choose 3524: 5432 – 2345 = 3087 8730 – 0378 = 8352 8532 – 2358 = 6174 7641– 1467 = 6174 Source:- http://mathworld.wolfram.com/KaprekarRoutine.html 4) Honeycombs
Bees build these hexagonal constructions. It is the shape most efficient for storing the largest possible amount of honey while using the least amount of wax. For same perimeter, circle is the shape which has highest area. It is the shape most efficient for storing the largest possible amount of honey while using the least amount of wax Honeycombs are based on optimal use of wax. Although the strongest column shape is the cylinder (circular cell), shapes like circles would leave gaps between the cells because they don’t fit perfectly together. Source: http://aperiodical.com/2015/01/apiological-mathematical-speculations-about-bees-part-1-honeycombgeometry/
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5) Mathematical Clock using only 9
It is the representation of all the numbers of Clock i.e. 1 to 12 by using only number 9 with arithmetic representations. No of 9 used are restricted to 3 times.
Source: https://puzzling.stackexchange.com/questions/2515/clock-values-using-just-9-and-some-operators
By Jayant Pansare PGDM FS (2016-18) 15
Sudoku
Number Puzzle A blind-folded man is handed a deck of 52 cards and told that exactly 10 of these cards are facing up.He is asked to divide those cards into two piles, each with the same number of cards facing up. He can't peek, get help, or damage the cards, but may use any strategy that occurs to him to do so. How can he do it?
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Quant Connect July 2017 Quantinuum, the Quant forum of KJ Somaiya Institute of Management Studies and Research aims to empower students and professionals alike to organize and understand numbers and, in turn, to make good and rational decisions as future managers. The newsletter published monthly consists of a gamut of articles for readers ranging from beginners to advanced learners so as to further enrich the young minds understand the contributions made to the field of mathematics along with a couple of brain- racking sections of Sudoku to tickle the gray cells. For any further queries and feedback, please contact the following address: KJ Somaiya Institute of Management Studies and Research, Vidya Nagar, VidyaVihar, Ghatkopar East, Mumbai -400077 Mentor Prof. N.S.Nilakantan (+919820680741) – Email – nilakantan@somaiya.edu
Team Leaders:
Vaibhav M (+917708521382) Maheshwaran Kumar (+919566173411) Rishita Shah (+919867290018)
Editorial Team:
Rupal Doshi (+919831427640) Amod Kulkarni (+919833701015) Arunava Dey (+917720093053) Milcah George (+917406186087)
Designing Team:
Shreyas Kulkarni (+918600106378) Ashish Mohadik (+919819741018)
Follow us on https://www.facebook.com/simsr.quantinuum. For any queries, drop us a mail at newsletter.quantinuum@gmail.com
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