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As one of the oldest multivariate statistical methods of data reduction, Principal Component Analysis (PCA)simplifies a dataset by producing a small number of derived variables that are uncorrelated and that account for most of the variation in the original data set. Eventually, the derived variables are combinations of the original variables. For example, it might be ?hat students take 10 examinations and some students do well in one exam whilst other students do better in another. It is difficult to compare one student with another when we have marks from 10 examinations to consider. One obvious way of comparing students is to calculate tlie mean score. This is a constructed combination of the existing variables,. However. we may get a more useful comparison of overall performances by considering other constructed combinations of the 10 exam marks. The PCA is one way of constructing such combinations, doing so in such ewakas to account for as much as possible of the variation in the original data. One can then compare students' performance by considering this much sn~aller number of variables.
In simple regression the dependent variable Y was assumed to be linearly related to a single variable X. In real life, however, we often find that a dependent variable may depend o
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While there are p original variables the number of principal components is m such that m
Universe or Population The word universe as used in statistics denotes the aggregate from which a sample is to be taken. According to Simpson and Kafka, a universe or populatio
Agreement The degree to which different observers, raters or diagnostic the tests agree on the binary classification. Measures of agreement like that of the kappa coefficient qu
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TYPE I AND II Errors If a statistical hypothesis is tested, we may get the following four possible cases: The null hypothesis is true and it is accepted; The
Betting on sporting events is big business both in the US and abroad. Consider, for instance, next winter’s American football tournament known as the Superbowl. Billions of dollars
Type of Correlation 1. Positive and Negative Correlation: 2. Simple Partial and Multiple Correlations. 3. Linear and Non linear or Correlations
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