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Unformatted text preview: 06.01.1 Chapter 06.01 Statistics Background of Regression Analysis After reading this chapter, you should be able to: 1. review the statistics background needed for learning regression, and 2. know a brief history of regression. Review of Statistical Terminologies Although the language of statistics may be used at an elementary and descriptive level in this chapter, it makes an integral part of our every day discussions. When two friends talk about the weather (whether it will rain or not - probability), or the time it takes to drive from point A to point B (speed - mean or average), or baseball facts (all time career RBI or home runs of a sportsman -sorting, range), or about class grades (lowest and highest score - range and sorting), they are invariably using statistical tools. From the foregoing, it is imperative then that we review some of the statistical terminologies that we may encounter in studying the topic of regression. Some key terms we need to review are sample, arithmetic mean (average), error or deviation, standard deviation, variance, coefficient of variation, probability, Gaussian or normal distribution, degrees of freedom, and hypothesis. Elementary Statistics A statistical sample is a fraction or a portion of the whole (population) that is studied. This is a concept that may be confusing to many and is best illustrated with examples. Consider that a chemical engineer is interested in understanding the relationship between the rate of a reaction and temperature. It is impractical for the engineer to test all possible and measurable temperatures. Apart from the fact that the instrument for temperature measurement have limited temperature ranges for which they can function, the sheer number of hours required to measure every possible temperature makes it impractical. What the engineer does is choose a temperature range (based on his/her knowledge of the chemistry of the system) in which to study. Within the chosen temperature range, the engineer further chooses specific temperatures that span the range within which to conduct the experiments. These chosen temperatures for study constitute the sample while all possible temperatures are the population. In statistics, the sample is the fraction of the population chosen for study. The location of the center of a distribution - the mean or average - is an item of interest in our every day lives. We use the concept when we talk about the average income, the class average for a test, the average height of some persons or about one being overweight (based on the average weight expected of an individual with similar 06.01.2 06....
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- Spring '08