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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.
Grouped data For grouped data, the formula applied is σ = Where f = frequency of the variable, μ= population mea
The following dataset is from a study of the effects of second hand smoking in Baltimore, MD, and Washington, DC. For the 25 children involved in this study the outcome variable is
PCA is a linear transformation that transforms the data to a new coordinate system such that the greatest variance by any projection of the data comes to lie on the first coordinat
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Question: (a) (i) Define the term multicollinearity. (ii) Explain why it is important to guard against multicollinearity. (b) (i) Sometimes we encounter missing values
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