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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.
In an agricultural experiment, we wish to compare the yields of three different varieties of wheat. Call these varieties A, B and C. We have a ?eld that has been marked into a 3 *
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
Mathematical Properties The sum of deviations of the items from the arithmetic mean (taking signs into account) is always zero, i.e. = 0. The sum of
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Rank Correlation Sometimes the characteristics whose possible correlation is being investigated, cannot be measured but individuals can only be ranked on the basis of the chara
Ten balls are put in 6 slots at random.Then expected total number of balls in the two extreme slots
A researcher is interested in comparing the effectiveness of three different parts of therapy for anger problems. 8 participants are randomly assigned to 3 treatment conditions: Co
Coefficient of Determination The coefficient of determination is given by r 2 i.e., the square of the correlation coefficient. It explains to what extent the variation
Each question, by default, should be solved INDIVIDUALLY, unless marked as \collaborative". Questions marked as \collaborative" implies that for those questions you are encourage
Frequency distribution A frequency distribution is a series where a number of items with similar values are put in separate groups or bunches. In other words a frequency distri
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