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Published in:
2016 | OriginalPaper | Chapter
1. Introduction
Authors : Cheng-Few Lee, John Lee, Jow-Ran Chang, Tzu Tai
Published in: Essentials of Excel, Excel VBA, SAS and Minitab for Statistical and Financial Analyses
Publisher: Springer International Publishing
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Abstract
A person studies and uses to learn how to study, analyze, and understand a data set of particular interest. But one problem in studying statistics is that it is a very intense computational discipline. We can get a sense of the computational intensity of statistics by looking at the average statistical formula and the correlation coefficient statistical formula shown below.
The average formula looks fairly simple, but it becomes more and more difficult as n increases. The correlation coefficient formula is obviously more complex and tedious to perform—and other computational formulas are even more complicated. Therefore one of the biggest costs in both time and money in studying and using statistics is the implementation costs of implementing statistical concepts on data sets that we are interested in studying, analyzing, and understanding.
$$ \begin{array}{ll}\overline{x}=\frac{{\displaystyle \sum_{i=1}^n{x}_i}}{n}\hfill & r=\frac{\frac{1}{n-1}{\displaystyle \sum_{i=1}^n\left({x}_i-\overline{x}\right)\left({y}_i-\overline{y}\right)}}{{\left[\frac{1}{n-1}{\displaystyle \sum_{i=1}^n{\left({x}_i-\overline{x}\right)}^2}\right]}^{1/2}{\left[\frac{1}{n-1}{\displaystyle \sum_{i=1}^n{\left({y}_i-\overline{y}\right)}^2}\right]}^{1/2}}\hfill \\ {}\mathrm{Average}\hfill & \mathrm{Correlation}\;\mathrm{coefficient}\hfill \end{array} $$