Table of Contents

• Introduction
• Data Collection Process
• Analysis
• Conclusion
• References

Introduction

My task for this project was to select an occurrence which I could model into an analyzable form. The process I was to analysis was to have a large ( more than 80 ) number of data points to be recorded. I selected the occurrence of my long distance phone calls over the course of a year. Particularly, I wanted to find patterns of calls. For example, I wanted to know if there were high probabilities that I would make certain calls after I made calls to particular individuals. At first, I thought I knew my own calling patterns - but, when looking at all the data collected in one table - I couldn't see the expected patterns. Therefore I created several joint matrices that, when processed using probability and entropy analysis, would reveal patterns.

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Data Collection Process

Interestingly when data is tabulated together in one table it takes on a new form; where before the subtle patterns are not noticeable, patterns are detected - also, is a lack of certain patterns noticeable; which, in my analysis, prompted me to re-tabulate the data. Because of this I was forced to sift through my phone call data three times before I came up with a collection of bits that could be transferred into analyzable matrices.

My first task was to put my phone bills in order and write down the calls I made restrained to four constraints: calls to Laura, calls to Anne, calls to Texas, and other calls. I went back more than 14 months - since I wanted to simplify my analysis, along with expressing the table in a binary format, I made a second table that only listed the data in binary format when a call occurred. This second table also restricted calls going back one year. But this only gave information if a call was made - I needed more information; specifically, I wanted to know when, during the year's time, I made a call and when I did not. As my professor pointed out, this added dimension to the data. So I referred to the original phone bills and created a third table which accounted the days which no calls were made.

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Analysis

Group analysis taken from the number of consecutive days times the number of calls - this creates a value that includes information about the number of consecutive calls and their consecutive nature.

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Conclusion

Although not being able to analyze the data as much as I would like, certain conclusions can be extracted from the tabulated data. Within the last year, for any day there was: 57.85 % chance I would not make a call, 8.26 % chance I would call Anne, 13.49 % chance I would call Laura, 4.40 % chance I would call home, and 4.68 % chance I would call someone different. More interestingly: the chance I would call both Laura and Anne is 3.85 %, and the chance I would call all four categories is only 0.275 %.

I next created a function that multiplied the number of consecutive calls multiplied times the number of calls in order to analyze the grouping of calls and the associated probability. From this tabulation I notice that I either make only separate or limited calls consecutively (35 % of only making one call a day) or I make many calls consecutively (the function values jump from around "12" to "35" very quickly).

References

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