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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.
The displacement of a simply supported beam subject to a uniform load is given by the solution of the following differential equation (for small displacements); and q is th
Origin and Development of probability Theory: The credit for origin and development of probability goes to the European gamblers of 17 th century. They used to gamble on gam
The investor has constant wealth 1 and is o?ered to invest in shares of a project that either gains 3=2 or loses 1 with equal probabilities. Therefore, if the investor obtains sha
Assumptions in Regression To understand the properties underlying the regression line, let us go back to the example of model exam and main exam. Now we can find an estimate o
Consider the following linear regression model: a) What does y and x 1 , x 2 , . . . . x k represent? b) What does β o , β 1 , β 2 , . . . . β k represent?
The median, as the name suggests, is the middle value of a series arranged in any of the orders of magnitude i.e. ascending or descending order. As distinct from the arithmetic
Application of the chi Square Test
Regression Lines It has already been discussed that there are two regression lines and they show mutual relationship between two variable . The regression line Yon X gives th
Make a decision about the given claim. Use only the rare event rule, and make subjective estimates to determine whether events are likely. For example, if the claim is that a coi
The regression line should be drawn on the scatter diagram in such a way that when the squared values of the vertical distance from each plotted point to the line are added, the to
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