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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.
Read the following data on the economy of Angoia and answer/respond to the questions/instructions that follow. Unless otherwise stated, the monetary figures are in real billions o
2 bidders have identical valuations of an object for sale. The value of the object is either 0; 50 or 100, with equal probabilities. The object is allocated to one of the bidders i
Henry Kaiser suggested a rule for selecting a number of components m less than the number needed for perfect reconstruction: set m equal to the number of eigenvalues greater than I
For each of the following situations choose the statistical model that you find to be the most appropriate. Justify your choice. a) We are interested in assessing the effects of
We are interested in assessing the effects of temperature (low, medium, and high) and technical configuration on the amount of waste output for a manufacturing plant. Suppose that
For each of the following scenarios, explain how graph theory could be used to model the problem described and what a solution to the problem corresponds to in your graph model.
The file Midterm Data.xls has a tab labeled "Many vs. S&P" which presents historical price data for several assets, a volatility condition (VIDX = 1 if the NYSE volatility is grea
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Geometric Mean The geometric mean of numbers is defined as the th root of the product of numbers .It is obtained by multiplying all the values of a variable and then extracti
We want to investigate the income data. In the Excel file Midterm Data.xls there is a tab labeled "Income Data 2006". The data in the tab is the income reported by 400 people in
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