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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.
Arithmetic Average or Mean The arithmetic mean is the most widely and the most generally understandable of all the averages. This is clear from the reason that when the term
Q. Find the inverse Laplace transform of Y (s) = s-4/s 2 + 4s + 13 +3s+5/s 2 - 2s -3. Q. Use the Laplace transform to solve the initial value problem y''+ y = cos(3t), y(0) =
Estimate the standard deviation of the process: Draw the X (bar) and R charts for the data given and give your comments about the process under study. Estimate the standard de
There are situations where none of the three averages is fully satisfactory. For example, if the number of items in a series is very small, none of these av
You want to know the thoughts of air travelers in fields such as tickets, comffort, safety, securuty, services and economic growth. You are given a database and 20 questions to ask
Correspondence Analysis (CA) is a generalization of PCA to contingency tables. The factors of correspondence analysis give an orthogonal decomposi:ion of the Chi- square associated
Lifts usually have signs indicating their maximum capacity. Consider a sign in a lift that reads "maximum capacity 1400kg or 20 persons". Suppose that the weights of lift-users are
HOW WOULD YOU INTERPRET THIS PROBABILITY:P(a)=1.05
Test the following claim. Identify the null hypothesis, alternative hypothesis, test statistic, critical value(s), conclusion about the null hypothesis, and final conclusion that
The cornlnunalities h j represent the fraction of the total variance' 'accounted for of variabie j. Ry calculating the communalities we can keep track of how much of-the orig
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