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PCA is a linear transformation that transforms the data to a new coordinate system such that the greatest variance by any projection of the data comes to lie on the first coordinate (called the first principal component), the second greatest variance on the second coordinate, and so on. The PCA can be used for dimensionality reduction in a dataset while retaining those characteristics of the dataset that contribute most to its variance, by keeping lower-order principal components and ignoring higher-order ones. Such low-order components often contain the "most important" aspects of the data. But this is not necessarily the case, depending on the application. Let p and tn denote respectively the original and reduced number of variables. The original variables are denoted X. In the simplest case our measure of accuracy of reconstruction is the sum ofp squared multiple correlations between X-variables and the predictions of X made froin the factors. In the more general case we can weight each squared multiple correlation by the variance of the corresponding X-variable.
Since we can set those variances ourselves by multiplying scores on each variable,by any constant we choose, this amounts to the ability to assign any weights we choose to the different variables.
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
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PCA is a linear transformation that transforms the data to a new coordinate system such that the greatest variance by any projection of the data comes to lie on the first coordinat
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Admixture in human populations The inter-breeding amongst the two or more populations which were previously isolated from each other for the geographical or the cultural reason
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Chi-square analysis can be used with both Goodness-of-Fit Tests and with Tests for Independence. There are specific instances when each test should be used based on the information
Introduction to Probability A student is considering whether she should enroll in an MBA educational program offered by a well-known college. Among othe
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