114 lines
5.4 KiB
TeX
114 lines
5.4 KiB
TeX
\documentclass[a4paper]{article}
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% To compile PDF run: latexmk -pdf {filename}.tex
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% Math package
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\usepackage{amsmath}
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%enable \cref{...} and \Cref{...} instead of \ref: Type of reference included in the link
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\usepackage[capitalise,nameinlink]{cleveref}
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% Enable that parameters of \cref{}, \ref{}, \cite{}, ... are linked so that a reader can click on the number an jump to the target in the document
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\usepackage{hyperref}
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% UTF-8 encoding
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\usepackage[T1]{fontenc}
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\usepackage[utf8]{inputenc} %support umlauts in the input
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% Easier compilation
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\usepackage{bookmark}
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\usepackage{graphicx}
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\begin{document}
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\title{Week 9 - Correlation and Regression}
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\author{
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Jai Bheeman \and Kelvin Davis \and Jip J. Dekker \and Nelson Frew \and Tony
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Silvestere
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}
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\maketitle
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\section{Introduction} \label{sec:introduction}
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We present a report on the relationship between the heights and weights of the
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top tennis players as catalogued in provided data. We use statistical analysis
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techniques to numerically describe the characteristics of the data, to see how
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trends are exhibited within the data set. We conclude the report with a brief
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discussion of the implications of the analysis and provide insights on
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potential correlations that may exist.
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\section{Method} \label{sec:method}
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Provided with a set of 132 unique records of the top 200 male tennis players,
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we sought to investigate the relationship between the height of particular
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individuals with their respective weights. We conducted basic statistical
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correlation analyses of the two variables with both Pearson's and Spearman's
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correlation coefficients to achieve this. Further, to understand the
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correlations more deeply, we carried out these correlation tests on the full
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population of cleaned data (removed duplicates etc), alongside several random
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samples and samples of ranking ranges within the top 200. To this end, we made
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use of Microsoft Excel tools and functions of the Python library SciPy.
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We specifically have made use of these separate statistical analysis tools in the
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interest of sanity checking our findings. To do this, we simply replicated the
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correlation tests within other software environments.
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\section{Results} \label{sec:results}
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We performed separate statistical analyses on 10 different samples of the
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population, as well as the population itself. This included 11 separate
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subsets of the rankings:
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\begin{itemize}
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\item The top 20 entries
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\item The middle 20 entries
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\item The bottom 20 entries
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\item The top 50 entries
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\item The bottom 50 entries
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\item 5 randomly chosen sets of 20 entries
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\end{itemize}
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\vspace{1em}
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Table \ref{tab:excel_results} shows the the results for the conducted tests.
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\begin{table}[ht]
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\centering
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\label{tab:excel_results}
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\begin{tabular}{|l|r|r|}
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\hline
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\textbf{Test Set} & \textbf{Pearson's Coefficient} & \textbf{Spearman's Coefficient} \\
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\hline
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\textbf{Full Population} & 0.77953 & 0.73925 \\
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\textbf{Top 20} & 0.80743 & 0.80345 \\
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\textbf{Middle 20} & 0.54134 & 0.36565 \\
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\textbf{Bottom 20} & 0.84046 & 0.88172 \\
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\textbf{Top 50} & 0.80072 & 0.78979 \\
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\textbf{Bottom 50} & 0.84237 & 0.81355 \\
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\textbf{Random Set \#1} & 0.84243 & 0.80237 \\
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\textbf{Random Set \#2} & 0.56564 & 0.58714 \\
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\textbf{Random Set \#3} & 0.59223 & 0.63662 \\
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\textbf{Random Set \#4} & 0.65091 & 0.58471 \\
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\textbf{Random Set \#5} & 0.86203 & 0.77832
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\\ \hline
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\end{tabular}
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\caption{Table showing the correlation coefficients between height and
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weight using different test sets. All data is rounded to 5 decimal
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places}
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\end{table}
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\begin{figure}[ht]
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\centering
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\label{fig:scipy}
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\includegraphics[width=0.6\textwidth]{pearson.png}
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\includegraphics[width=0.6\textwidth]{spearman.png}
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\caption{The Pearsion (top) and Spearman (bottom) correlations coefficients
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of the data set as computed by the Pandas Python library}
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\end{figure}
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\section{Discussion} \label{sec:discussion}
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The results generally indicate that there is a fairly strong positive
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correlation between the weight and weight of an individual tennis player,
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within the top 200 male players. The population maintains a strong positive
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correlation with both Pearson's and Spearman's correlation coefficients,
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indicating that a relationship may exist. Our population samples show
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promising consistency with this, with 6 seperate samples having values above
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0.6 with both techniques. The sample taken from the middle 20 players,
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however, shows a relatively weaker correlation compared with the top 20 and
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middle 20, which provides some insight into the distribution of the strongest
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correlated heights and weights amongst the rankings. All five random samples
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of 20 taken from the population indicate however that there does appear to be
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a consistent trend through the population, which corresponds accurately with
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the coefficients on the general population.
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\end{document}
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