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A Quick Guide To Predictive Analytics

A Quick Guide To Predictive Analytics

Ever since the world woke up to discover the significance of data, there has been tremendous advancement in this field each taking us further towards the utilization of accumulated data to achieve a higher level of efficiency. Predictive analytics is all about extracting hidden information in data and combining technologies like machine learning, artificial intelligence, data analysis, statistical modeling to predict future trends.

Sifting through stored datasets comprising structured and unstructured data, predictive analytics identifies the patterns hidden and analyzes those patterns to make predictions about trends and thereby helps to identify opportunities as well as risk factors. Not just forecasting, but predictive analytics also helps you find associations that could lead you to a new breakthrough. Having undergone big data training in gurgaon, could actually prove to be a big boost for someone planning on working in this specialized field. Now, when you have access to data-based forecasting, it is easy for you to identify both negative and positive trends and in turn, it helps you take the right decisions.

Businesses especially rely heavily on predictive analytics for market analysis, targeting their customers, and assessing risk factors. Unlike before when these business strategies were based on mere guesswork, now the think-tank has access to data to anticipate an outcome.

Predictive analytics models: Predictive analytics models could be classified into two broad categories as follows

Classification models: In this model data is categorized on the basis of some specified criterion. 

Regression models: Regression models focus on identifying patterns that already exist, or, that has been continuing for a while.

So, what are the processes involved in Predictive analytics?

Predictive analytics process could be broken down to different stages and let’s take a look at what the steps are

Defining the Project: This is the first stage when you decide what kind of outcome you are expecting. Besides setting out clear business objectives you also need to be clear about the deliverables as these will have a bearing on your data collection.

Collecting all Data: This is the second stage where data from different sources are collected.

Analyzing Data: In this stage, the data collected is cleaned and gets structured and also gets transformed and modeled.

Statistics: A statistical model is used to test the assumptions, hypotheses, as well as findings.

Modeling: Through multi-model evaluation best option is chosen from an array of available options.  So, the idea is to create an accurate predictive model.

Deployment: This is the stage of deploying the predictive model and create an option for deploying the results for productive purposes in reality.

monitoring: the final and an important stage where the models created are monitored and tested with new data sets to check whether the models still have relevance.

The applications of predictive analytics

Predictive analytics models have found usage across industries

  • In the financial sector, predictive analytics could be used for credit risk measurement, detecting fraud as well as for minimizing the risk, and also for retaining customers.
  • In the field of healthcare predictive analytics could be used for detecting severe health complications that might develop in a patient in the future.
  • In business predictive analytics could be used for short-term or, long-term sales forecasting. In fact, the reaction of the customer could be anticipated and changes could be made accordingly.
  • When a huge investment is involved predictive analytics could help to identify the problematic areas that could pose risk. Accurate risk assessment could help a company secure a better ROI.
  • Predictive analytics could help companies with their customer service, marketing campaigns, sales goals. Companies can strategize better to retain customers and improve their relations with them.
  • With predictive analytics in place, it would be easier to predict equipment maintenance needs and it could also be used for forecasting an equipment failure.

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Predictive analytics is being adopted in a number of industries ranging from insurance to healthcare. The forecasting that one gets is highly accurate. However, building a reliable dataset and building a reliable model is essential. Having trained personnel on the team who have done data analyst course in delhi, could be helpful.


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Data Science: What Are The Challenges?

Data Science: What Are The Challenges?

Big data is certainly is getting a lot of hype and for good reasons. Different sectors ranging from business to healthcare are intent on harnessing the power of data to find solutions to their most imminent problems. Huge investments are being made to build models, but, there are some niggling issues that are not being resolved.

So what are the big challenges the data science industry is facing?

Managing big data

Thanks to the explosion of information now the amount of data being created every year is adding to the already overstocked pile, and, most of the data we are talking about here is unstructured data.  So, handling such a massive amount of raw data that is not even in a particular database is a big challenge that could only be overcome by implementing advanced tools.

Lack of skilled personnel

 One of the biggest challenges the data science industry has to deal with is the shortage of skilled professionals that are well equipped with Data Science training. The companies need somebody with specific training to manage and process the datasets and present them with the insight which they can channelize to develop business strategies. Sending employees to a Data analyst training institute can help companies address the issue and they could also consider making additional efforts for retaining employees by offering them a higher remuneration.

Communication gap

One of the challenges that stand in the way, is the lack of understanding on the part of the data scientists involved in a project. They are in charge of sorting, cleaning, and processing data, but before they take up the responsibility they need to understand what is the goal that they are working towards. When they are working for a business organization they need to know what the set business objective is, before they start looking for patterns and build models.

Data integration

When we are talking about big data, we mean data pouring from various sources. The myriad sources could range from emails, documents, social media, and whatnot. In order to process, all of this data need to be combined, which can be a mammoth task in itself. Despite there being data integration tools available, the problem still persists.  Investment in developing smarter tools is the biggest requirement now.

Data security

Just the way integrating data coming from different sources is a big problem, likewise maintaining data security is another big challenge especially when interconnectivity among data sources exists. This poses a big risk and renders the data vulnerable to hacking. In the light of this problem, procuring permission for utilizing data from a source becomes a big issue. The solution lies in developing advanced machine learning algorithms to keep the hackers at bay.

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Data validity

Gaining insight from data processing could only be possible when that data is free from any sort of error. However, sometimes data hailing from different sources could show disparity regardless of being about the same subject. Especially in healthcare, for example, patient data when coming from two different sources could often show dissimilarity. This poses a serious challenge and it could be considered an extension of the data integration issue.  Advanced technology coupled with the right policy changes need to be in place to address this issue, otherwise, it would continue to be a roadblock.

The challenges are there, but, recognizing those is as essential as continuing research work to finding solutions. Institutes are investing money in developing data science tools that could smoothen the process by eliminating the hurdles.  Accessing big data courses in delhi, is a good way to build a promising career in the field of data science, because despite there being challenges the field is full big opportunities.

 


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An Introduction To The 5 V’s of Big Data

An Introduction To The 5 V’s of Big Data

The term big data refers to the massive amount of data being generated from various sources that need to be sorted, processed, and analyzed using advanced data science tools to derive valuable insight for different industries. Now, big data comprises structured, semi-structured, and mostly unstructured data. Processing this huge data takes skill and expertise and which only someone with Data Science training would be able to do.

The concept of big data is relatively new and it started emerging post the arrival of internet closely followed by the proliferation of advanced mobile devices, social media platforms, IoT devices, and all other myriad platforms that are the breeding grounds of user-generated data. Managing and storing this data which could be in text, audio, image formats is essential for not just businesses but, for other sectors as well. The information data holds can help in the decision-making process and enable people to understand the vital aspects of an issue better.

The characteristics of big data

Now, any data cannot be classified as big data, there are certain characteristics that define big data and getting in-depth knowledge regarding these characteristics can help you grasp the concept of big data better. The main characteristics of big data could be broken down into 5Vs.

What are the 5Vs of data?

The 5Vs of data basically refers to the core elements of big data, the presence of which acts as a differentiating factor. Although many argue in favor of the essential 3 VS, other pundits prefer dissecting data as per 5Vs. These 5Vs denote Volume, Velocity, Variety, Veracity, Value the five core factors but, not necessarily in that order. However, Volume would always be the element that lays the foundation of big data. Pursuing a Data Science course would further clarify your idea of big data.

Volume

This concept is easier to grasp as it refers to the enormous amount of data being generated and collected every day. This amount is referred to as volume, the size of data definitely plays a crucial role as storing this data is posing a serious challenge for the companies. Now the size of the data would vary from one industry to the other, the amount of data an e-commerce site generates would vary from the amount generated on a popular social media platform like Facebook. Now, only advanced technology could handle and process and not to mention deal with the cost and space management issue for storing such large volumes of data.

Velocity

Another crucial feature of big data is velocity which basically refers to the speed at which data is generated and processed, analyzed, and moved across platforms to deliver insight in real-time if possible. Especially, in a field like healthcare the speed matters, crucial trading decisions that could result in loss or profit, must also be taken in an instant. Only the application of advanced data science technology can collect data points in an instant and process those at a lightning speed to deliver results. Another point to be noted here is the fact that just like volume the velocity of data is also increasing.

Variety

The 3rd V refers to the variety, a significant aspect of big data that sheds light on the diversity of data and its sources. As we already know that the data now hails from multiple sources, including social media platforms, IoT devices, and whatnot. The problem does not stop there, the data is also diverse in terms of format such as videos, texts, images, audios and it is a combination of structured and unstructured data. In fact, almost 80%-90% of data is unstructured in nature. This poses a big problem for the data scientists as sorting this data into distinct categories for processing is a complicated task. However, with advanced data science technologies in place determining the relationship among data is a lot hassle-free process now.

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Veracity

It is perhaps the most significant aspect of all other elements, no matter how large datasets you have and in what variety, if the data is messy and inaccurate then it is hardly going to be of any use. Data quality matters and dirty data could be a big problem especially because of the fact that data comes from multiple sources. So, you have apparently no control, the problems range from incomplete data to inconsistency of information. In such situations filtering the data to extract quality data for analysis purposes is essential. Pursuing Data science using python training can help gain more skill required for such specific tasks.

Value

The 5th V of big data refers to the value of the data we are talking about. You are investing money in collecting, storing, and processing the big data but if it does not generate any value at the end of the day then it is completely useless. Managing this massive amount of data requires a big investment in advanced infrastructure and additional resources, so, there needs to be ROI. The data teams involved in the process of collecting, sorting, and analyzing the data need to be sure of the quality of data they are handling before making any move.

The significance of big data in generating valuable insight is undeniable and soon it would be empowering every industry. Further research in this field would lead to the development of data science tools for handling big data issues in a more efficient manner. The career prospects in this field are also bright, training from a Data analyst training institute can help push one towards a rewarding career.

 


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A Quick Guide to Data Visualization

A Quick Guide to Data Visualization

The growing significance of big data and the insight it imparts is of utmost significance. Data scientists are working round the clock to process the massive amount of data generated every day. However, unless you have been through Data Science training, it would be impossible for you to grasp even an iota of what is being communicated through data.

The patterns, outliers every single important factor that emerged through decoding must be presented in a coherent format for the untrained eyes. Data visualization enables the researchers to present data findings visually via different techniques and tools to enable people to grasp that information easily.

Why data visualization is so vital?

The complicated nuances of data analysis is not easier for anybody to understand. As we humans are programmed to gravitate towards a visual representation of any information, it makes sense to convey the findings through charts, graphs, or, some other way. This way it takes only a couple of moments for the marketing heads to process what is the trend to watch out for. 

We are used to seeing and processing the information presented through bars and pie charts in company board meetings, people use these conventional models to represent company sales data.

It only makes sense to narrate what the scientists have gathered from analyzing complex raw data sets, via visual techniques to an audience who needs that information to form data-driven decisions for the future.

So what are the different formats and tools of data visualization?

Data visualization can take myriad forms which may vary in the format but, these all have one purpose to serve representing data in an easy to grasp manner. The data scientist must be able to choose the right technique to relate his data discovery which should not only enlighten the audience but, also entertain them.

The popular data visualization formats are as follows

Area Chart
Bubble Cloud/Chart
 Scatter Plot
Funnel Chart
Heat Map
The formats should be adopted in accordance with the information to be communicated

Data scientists also have access to smart visualization tools which are

  • Qlikview
  • Datawrapper
  • Sisense
  • FusionCharts
  • Plotly
  • Looker
  • Tableau

A data scientist must be familiar with the tools available and be able to decide on which suits his line of work better.

What are the advantages of data visualization?

Data visualization is a tricky process while ensuring that the audience does not fall asleep during a presentation, data scientists also need to identify the best visualization techniques, which they can learn during big data training in gurgaon to represent the relationship, comparison or, some other data dynamic.
If and when done right data visualization  has several benefits to offer

Enables efficient analysis of data

In business, efficient data interpretation can help companies understand trends. Data visualization allows them quickly identify and grasp the information regarding company performance hidden in the data and enables them to make necessary changes to the strategy.

Identify connections faster

While representing information regarding the operational issues of an organization,  data visualization technique can be of immense help as it allows to show connections among different data sets with more clarity. Thereby enabling the management to quickly identify the connecting factors. 

Better performance analysis

Using certain visualizing techniques it is easier to present a product or, customer-related data in a multi-dimensional manner. This could provide the marketing team with the insight to understand the obstacles they are facing. Such as the reaction of a certain demographic to a particular product, or, it could also be the demand for certain products in different areas.  They are able to act faster to solve the niggling issues this way.

Adopt the latest trends

 Data processing can quickly identify the emerging trends, and with the help of data visualization techniques, the findings could be quickly represented in an appealing manner to the team. The visual element can immediately communicate which trends are to watch out for and which might no longer work.

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 Encourages interaction

Visual representation of data allows the strategists to not just look at numbers but, actually understand the story being told through the patterns. It encourages interaction and allows them to delve deeper into the patterns, instead of just merely looking at some numbers and making assumptions.

Data visualization is certainly aiding the businesses to gain an insight that was lost to them earlier. A data scientist needs to be familiar with the sophisticated data visualization tools and must strike a balance between the data and its representation. Identifying what is unimportant and which needs to be communicated as well as finding an engaging visual technique to quickly narrate the story is what makes him an asset for the company.  A premier Data analyst training institute can help hone the skills of an aspiring data scientist through carefully designed courses.

 


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How Legal Analytics Can Benefit Law Firms?

How Legal Analytics Can Benefit Law Firms?

As different sectors are waking up to realize the significance of big data, the law firms are also catching up. After all it is one of the sectors that have to deal with literally massive amounts of data.

The popularity of legal analytics software like Premonition is a pointer to the fact that even though the industry was initially slow on the uptake, it is now ready to harness the power of big data to derive profit.

 So what exactly is legal analytics?

Legal analytics involves application of data analysis to mine legal documents and dockets to derive valuable insight. Now there is no need to confuse it with legal research or, to think that it is an alternative to the popular practice. Legal analytics is all about detecting patterns in past case records to enable firms strategize better in future. It basically aims to offer aid in legal research. Training received in an analytics lab could help a professional achieve proficiency.

Legal analytics platform combines sophisticated technologies of machine learning, NLP. It goes through past unstructured data and via cleaning and organizing that data into a coherent structure it analyzes the data to detect patterns.

How law firms can benefit from legal analytics?

Law firms having to deal with exhaustive data holding key information can truly gain advantage with the application of legal analytics. Primarily because of the fact it would enable them to anticipate what the possible outcome might be in order to strategize better and increase their chances of turning a case in their favor. Data Science training could be of immense value for firms willing to adopt this technology.

Not just that but implementation of legal analytics could also help the law firms whether big or, small run their operations and market their service in a more efficient manner and thereby increasing the percentage of ROI.

The key advantages of legal analytics could be as followed

  • The chances of winning a case could be better as by analyzing the data of past litigations, useful insight could be derived regarding the key issues like duration, judge’s decision and also certain trends that might help the firm develop a smarter strategy to win a particular case.
  • Cases often continue for a long period before resulting in a loss. To save money and time spent on a particular case, legal analytics could help lawyers decide whether to continue on or, to settle.
  • Often legal firms need to hire outside expertise to help with their case, the decision being costly in nature must be backed by data. With legal analytics it would be easier to go through data regarding a particular candidate and his performance in similar cases in the past.
  • There could be a significant improvement in the field of operational efficiency. In most of the situations lawyers spend huge amount of time in sorting through case documents and other data. This way they are wasting their time in finding background information when they could be spending time in offering consultation to a potential client and securing another case thereby adding financial benefit to the firm. The task of data analysis should better be handled by the legal analytics software.
  • At the end of the day a law firm is just another business, so, to ensure that the business operations of the firm are being managed with efficiency, legal analytics software could come in handy. Whether it’s budgeting or, recruiting or retaining old staff valuable insight could be gained, which could be channeled to rake in more profit.

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There has been an increase in the percentage of law firms which have adopted legal analytics, but, overall this industry is still showing reluctance in fully embracing the power. The professionals who have apprehension they need to set aside the bias they have and recognize the potential of this technology. May be they should consider enrolling in a Data analyst training institute to gain sharper business insight.

 


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A Deep Dive Into The US Healthcare System in New York

A Deep Dive Into The US Healthcare System in New York

Unlike India’s healthcare system wherein both public and private entities deliver healthcare facilities to citizens, in the US, the healthcare sector is completely privatised.

The aim of this notebook is to study some of the numerical data we have for the US and especially data for New York. Most of us know about New York’s situation that is one of the worst in the world.

Therefore, analysing data may clarify a few things. We will be using three sets of data – urgent care facilities, US county healthcare rankings 2020 and Covid sources for counties.

For the data and codesheet click below.

 

Now pick key column names for your study with ‘.keys’ as the function name. We are interested in a few variables from health rankings so we take only the ones we think will be useful in a new data frame.

We will study each data set one by one so that we can get an understanding of the data before combining them. For this we call the plotly library that has very interactive graphs. We use the choropleth to generate a heat map over the country in question.

Fig. 1.

It is clear form the heat map that New York has a very high incidence of infections vis a vis other states. We then begin working with data on the number of ICU beds in each state. Since each state will have different populations, we cannot compare the absolute number of ICU beds. We need the ratio of ICU beds per a given number of inhabitants.

Fig. 2.

The generated heat map (Fig. 2.) shows the ICU density per state in the US. For more on this do watch the complete video tutorial attached herewith.

This tutorial was brought to you by DexLab Analytics. DexLab Analytics is a premiere data analyst training institute in Gurgaon.

 


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Statistical Application in R & Python: EXPONENTIAL DISTRIBUTION

Statistical Application in R & Python: EXPONENTIAL DISTRIBUTIONStatistical Application in R & Python: EXPONENTIAL DISTRIBUTION

In this blog, we will explore the Exponential distribution. We will begin by questioning the “why” behind the exponential distribution instead of just looking at its PDF formula to calculate probabilities. If we can understand the “why” behind every distribution, we will have a head start in figuring out its practical uses in our everyday business situations.

Much could be said about the Exponential distribution. It is an important distribution used quite frequently in data science and analytics. Besides, it is also a continuous distribution with one parameter “λ” (Lambda). Lambda as a parameter in the case of the exponential distribution represents the “rate of something”. Essentially, the exponential distribution is used to model the decay rate of something or “waiting times”.

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For instance, you might be interested in predicting answers to the below-mentioned situations:

  • The amount of time until the customer finishes browsing and actually purchases something in your store (success).
  • The amount of time until the hardware on AWS EC2 fails (failure).
  • The amount of time you need to wait until the bus arrives (arrival).

In all of the above cases if we can estimate a robust value for the parameter lambda, then we can make the predictions using the probability density function for the distribution given below:

Application:-

Assume that a telemarketer spends on “average” roughly 5 minutes on a call. Imagine they are on a call right now. You are asked to find out the probability that this particular call will last for 3 minutes or less.

 

 

Below we have illustrated how to calculate this probability using Python and R.

Calculate Exponential Distribution in R:

In R we calculate exponential distribution and get the probability of mean call time of the tele-caller will be less than 3 minutes instead of 5 minutes for one call is 45.11%.This is to say that there is a fairly good chance for the call to end before it hits the 3 minute mark.

Calculate Exponential Distribution in Python:

We get the same result using Python.

Conclusion:

We use exponential distribution to predict the amount of waiting time until the next event (i.e., success, failure, arrival, etc).

Here we try to predict that the probability of the mean call time of the telemarketer will be less than 3 minutes instead of 5 minutes for one call, with the help of Exponential Distribution. Similarly, the exponential distribution is of particular relevance when faced with business problems that involve the continuous rate of decay of something. For instance, when attempting to model the rate with which the batteries will run out. 

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Hopefully, this blog has enabled you to gather a better understanding of the exponential distribution. For more such interesting blogs and useful insights into the technologies of the age, check out the best Analytics Training institute Gurgaon, with extensive Data Science Courses in Gurgaon and Data analyst course in Delhi NCR.

Lastly, let us know your opinions about this blog through your comments below and we will meet you with another blog in our series on data science blogs soon.

 

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How to Start a Successful Data Science Career?

How to Start a Successful Data Science Career?

The most common question we come across in DexLab Analytics HQ is how to take a step into the world of analytics and data science. Of course, grabbing a data science job isn’t easy, especially when there is so much hype going around. This is why we have put together top 5 ways to bag the hottest job in town. Follow these points and swerve towards your dream career.

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Enhance Your Skills

At present, LinkedIn in the US alone have 24,697 vacant data scientist positions. Python, SQL and R are the most common skills in demand followed by Tensorflow, Jupyter Notebooks and AWS. Gaining statistical literacy is the best way to grab these hot positions but for that, you need hands-on training from an expert institute.

If interested, you can check out analytics courses in Delhi NCR delivered by DexLab Analytics. They can help you stay ahead of the curve.

Create an Interesting Portfolio

A portfolio filled with machine learning projects is the best bet. Companies look for candidates who have prior work experience or are involved in data science projects. Your portfolio is the potential proof that you are capable enough to be hired. Thus, make it as attractive as possible.

Include projects that qualify you to be a successful data scientist. We would recommend including a programming language of your choice, your data visualization skill and your ability to employ SQL.

Get Yourself a Website

Want to standout from the rest? Build up your website, create a strong online presence and continuously add and update your Kaggle and GitHub profile to exhibit your skills and command over the language. Profile showcasing is of utmost importance to get recognized by the recruiters. A strong online presence will not only help you fetch the best jobs but also garner the attention of the leads of various freelance projects.

Be Confident and Apply for Jobs You Are Interested In

It doesn’t matter if you possess the skills or meet the job requirements mentioned on the post, don’t stop applying for the jobs that interest you. You might not know every skill given on a job description. Follow a general rule, if you qualify even half of the skills, you should apply.

However, while job hunting, make sure you contact recruiters, well-versed in data science and boost your networking skills. We would recommend you visit career fairs, approach family, friends or colleagues and scroll through company websites. These are the best ways to look for data science jobs. 

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Improve Your Communication Skills

One of the key skills of data scientists is to communicate insights to different users and stakeholders. Since data science projects run across numerous teams and insights are often shared across a large domain, hence superior communication skill is an absolute must-have.

Want more information on how to become a data scientist? Follow DexLab Analytics. We are a leading data analyst training institute in Delhi offering in-demand skill training courses at affordable prices.

 

The blog has been sourced fromwww.forbes.com/sites/louiscolumbus/2019/04/14/how-to-get-your-data-scientist-career-started/#67fdbc0e7e5c

 

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Basics of a Two-Variable Regression Model: Explained

Basics of a Two-Variable Regression Model: Explained

In continuation of the previous Regression blog, here we are back again to discuss the basics of a two-variable regression model. To read the first blog from the Regression series, click here www.dexlabanalytics.com/blog/a-regression-line-is-the-best-fit-for-the-given-prf-if-the-parameters-are-ols-estimations-elucidate.

In Data Science, regression models are the major driver to interpret the model with necessary statistical methods, practically as well as theoretically. One, who works extensively with business data metrics, will be able to solve various tough problems with the help of a regression theory. The key insight of the regression models lies in interpreting the fitness of the models. But it differs from the standard machine learning techniques such that, for improvement in the performance of the model being predicted, the major interpretable coefficients are never sacrificed. Thus, a sense in regression models can be considered as the most important tool to be chosen for solving any practical problem.

2

Let’s consider a simple example to understand regression analysis from scratch. Say, we want to predict the sales of a Softlines eCommerce company for this year during the festivals of Diwali. There are a lot of factors to generate impacts on the sales value, as there are hundreds of factors persisting within the model. We can consider our own judgement to get the impacting factors. Now, here in our model, the value of sales that we want to predict is the dependent variable, whereas the impacting factors are considered as the independent variables. To analyse this model in terms of regression, we need to gather all the information about the independent variables from the past few years, and then act on it according to the regression theory.

Before getting into the core theory, there are some basic assumptions for such a two-variable regression model and they are as follows:

  • Variables are linearly related: The variables in a 2-variable Regression Model are linearly related, the linearity being in parameters, though not always in variables, i.e. the power in which the parameters appear should be of 1 only and should not be multiplied or divided by any other parameters. These linearly related variables are basically of two types (i) independent or explanatory variables & (ii) dependent or response variables.
  • Variables can be represented graphically: The idea behind this assumption guarantees that observations must be real numbers represented on graph papers.
  • Residual term and the estimated value of the variables are uncorrelated.
  • Residual terms and explanatory variables are uncorrelated.
  • Error variables are uncorrelated with mean 0 & common variance σ2

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Now, how can a PRF for expanding an economic relationship between 2 variables be specified?

Well, Population regression function, or more generally, the population regression curve, is defined as the locus of the conditional means of the dependent variables, for a fixed value of the explanatory variables. More simply, it is the curve connecting the means of the sub-populations of Y corresponding to the given values of the regressor X.

Formally, a PRF is the locus of all conditional means of the dependent variables for a given value of the explanatory variables. Thus; the PRF as economic theory would suggest would be:

Where 9(X) is expected to be an increasing function of X, if the conditional expectation is linear in X. then

Hence, for any ith observations:

However, the actual observation for the dependent variable is Yi. Therefore; Yi – E(Y/Xi) = ui, which is the disturbance term or the stochastic term of the Regression Model.

Thus,

…………………… (A)

  • is the population regression function and this form of specifying the population regression function is called the stochastic specification of the PRF.

Stochastic Specification of the Model:

Yi = α + βXi + ui is referred to as the stochastic specification of the Population Regression Function, where ui is the stochastic or the random disturbance term. It explains everything’s net influence other than X variable on the ith observation. Thus, ui is a surrogate or proxy for all omitted or neglected variables which may affect Y but is not included in the model. The random disturbance term is incorporated into the model with the following assumptions:-

Proof:

Taking conditional expectation as both sides, we get:

Hence; E(ui) = 0

cov(ui,uj) = E(ui uj ) = 0 ∀ i ≠ j i.e. the disturbance terms are distributed independently of each other.

Proof:

Two variables are said to be independently distributed, or stochastically independent; if the conditional distributions are equal to the corresponding marginal distributions.

Hence; cov(ui,uj )= E(ui uj ) = 0 Thus, no auto correction is present among ui,s i.e. ui,s. s are identically and independently distributed Random Variables. Hence, ui,s are all Random Samples.

Proof:

The conditional variance between two error terms can be given as given independence &

 

 

All these assumptions can be embodied in the simple statement: ui~N(0,σ2) where ui,s are iid’s ∀ I, Which heads “the ui are independently distributed identically distributed with mean 0 & variance σ2”.

Last Notes

The benefits of regression analysis are immense. Today’s business houses literally thrive on such analysis. For more information, follow us at DexLab Analytics. We are a leading data science training institute headquartered in Delhi NCR and our team of experts take pride in crafting the most insight-rich blogs. Currently, we are working on Regression Analysis. More blogs are to be followed on this model. Keep watching!

 

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