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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.
Formation of Continuous Frequency Distribution: Continuous frequency distribution is most popular in practice. With reference to the formation of this type of frequency distr
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
There are two diagnostic tests for a disease. Among those who have the disease, 10% give negative results on the first test, and independently of this, 5% give negative results on
Test for Equality of Proportions For example, we may want to test whether the percentage of smokers (p 1 ) among the males equals the percentage of female smokers (p 2 ). W
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(a) At a stream gauging station, the following discharges and stage measurements were taken for the purpose of the rating curve at that section: Stage (m) 1
For the following claim, find the null and alternative hypotheses, test statistic, P-value, critical value and draw a conclusion. Assume that a simple random sample has been selec
This probability rule determined by the research of the two mathematicians Bienayme' and Chebyshev, explains the variability of data about its mean when the distribution of the dat
HOW WOULD YOU INTERPRET THIS PROBABILITY:P(a)=1.05
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