{"id":8700,"date":"2016-09-10T14:36:25","date_gmt":"2016-09-10T09:06:25","guid":{"rendered":"http:\/\/ucanalytics.com\/blogs\/?p=8700"},"modified":"2018-07-10T11:28:05","modified_gmt":"2018-07-10T05:58:05","slug":"principal-component-analysis-step-step-guide-r-regression-case-study-example-part-4","status":"publish","type":"post","link":"https:\/\/ucanalytics.com\/blogs\/principal-component-analysis-step-step-guide-r-regression-case-study-example-part-4\/","title":{"rendered":"Principal Component Analysis: Step-by-Step Guide using R- Regression Case Study Example (Part 4)"},"content":{"rendered":"
\"Death<\/a>

Death and Principal Component Analysis – by Roopam<\/p><\/div>\n

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Principal component analysis is a wonderful technique for data reduction without losing critical information. Yes, you could reduce the size of 2GB data to a few MBs without losing a lot of information. This is like a mp3 version of music. Many, including some experienced data scientists, find principal component analysis (PCA) difficult to understand. However, I believe that after reading this article you will understand PCA and appreciate that it is a highly intuitive and powerful data science technique with several business applications. This article is a continuing part of our regression case study example<\/a> <\/strong>where you are helping an investment firm make money through price arbitrage. In this article, I will help you gain the intuitive understanding of principal component analysis by highlighting both practical applications and the underlying mathematical fundamentals. Principal component analysis is also extremely useful while dealing with multicollinearity in regression models. In the subsequent article, we will use this property of PCA for the development of a model to estimate property price.<\/p>\n

Before we explore further nuances of principal component analysis, in the true tradition of YOU CANalytics, let’s digress a bit and create links between:<\/p>\n

Principal Component Analysis and Death<\/span><\/h2>\n

\"Human<\/a>What happens when people die? Where do they go? All of us have pondered this at some point or other. There are several religious and a few non-religious theories to explain events after death. A theory which makes sense to me is: after death, we go back to our fundamental elements. Here, I am not talking about metaphysical or divine elements but chemistry. There are close to 120 known elements including lithium, oxygen, uranium, hydrogen, argon, and carbon. These elements form the periodic table we learned in the chemistry lessons in high-school. Despite the choice of roughly 120 elements, the human body does not have all of them in the same proportion. Incidentally, six elements, as shown in the chart, constitute close to 99% of the human body. Think of these elements as the principal components of the human body. The remaining ~1% of the human body has a little over 20 other elements. This means, around three-fourth of the elements in the periodic table are completely absent in the human body.<\/p>\n

We noticed that about 1% of the human body has formed with ~ 20 elements. The idea with PCA is that if you remove these 20 elements you will lose just 1% of the essence of the human body. This will also mean that your information load will decline by ~77% (20\/26). These ideas will form the basis of our understanding of principal component analysis as we progress with our pricing case study example. You could find the previous parts at this link: regression case study example<\/a>.<\/p>\n

Principal Component Analysis – Case Study Example<\/span><\/h2>\n

You had got a stern message from your client last evening. They want you to turn around the price estimation model soon so that they can integrate it into their business operations. Luckily, you have made a good progress while preparing your data for the regression modeling. The original data had some outliers and missing observations which you have decided to drop for this analysis. You can download the cleaned data from this link: regression-clean-data<\/a>. In this analysis, you are trying to estimate the response variable (house price) through the other numeric and categoric predictor variables. This estimation will be used by your client, a property investment firm, to make money through price arbitrage.<\/p>\n

In the previous part using bivariate analysis<\/a><\/strong>, we noticed that there is a significantly high correlation between some of the numeric predictor variables. This, you know, will create a problem of multicollinearity while regression model development. One of the most effective methods for elimination of multicollinearity is principal component analysis. I suggest you go back and read that article to get a good understanding of results of PCA (bivariate analysis<\/a>). You have six numeric predictor variables in your dataset i.e.<\/p>\n

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