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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.
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
Weighted Arithmetic Mean Another aspect to be considered is the importance we assign to each observation. The arithmetic mean as we calculated it so far gives equal
You are going to purchase a part from a specialty vendor. Your company needs a C p of at least 1.67 on a critical dimension of the part. The dimensional specification for this p
Year Production 2006 8 2007 6 2008 10 2009 12 2010 11 2011 15 2012 14 2013 16 Determine the trend from data given above?
The file Midterm Data.xls has a tab labeled "Income Data 2009". This data is collected income data from a sample of 400 people in 2009. Use a hypothesis test to see whether the av
Show that when h = h* for the histogram, the contribution to AMISE of the IV and ISB terms is asymptotically in the ratio 2:1. Compare the sensitivity of the AMISE(ch) in Equa
A medical researcher has 100 bone cancer patients in a study. Every patient's condition is one of six types, type \A" to type \F". The 100 patients split as follows: x There
Discriminant analysis (DA) helps to determine which variables discriminate between two or more naturally occurring groups. Mathematically equivalent to MANOVA, it ' is extensively
Use the information given below to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to
Calculation for Continuous Series or Grouped Data = where, m = mid-point of class =
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