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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.
If the sample size is less than 30, then we need to make the assumption that X (the volume of liquid in any cup) is normally distributed. This forces (the mean volume in the sam
A. Do the correlation matrix table. B. Which variable (s) has the largest correlation coeffieient which is not a perfect correlation? C. Which variable (s) has the s
Median Median is a position average. It is the value of middle item of a variable when the items are arranged according to their values either in ascending or descending order.
Assume that the pulley at A is a small frictionless pulley. The cord AB is only allowed to support a maximum tension in Newtons as given in P4, and the cord supporting the block ca
a. How can break-even analysis be used in selecting a new plant site? b. What are potential advantages and disadvantage of locating a production facility in foreign country i
calculate variance and standard deviation of the following sample 12,22,32,13,12,23,34,52,56,23,44,32,11,11
Asymmetric proximity matrices Immediacy matrices in which the off-diagonal elements which are, in the i th row and j th column and the j th row and i th column, are not essent
Importance of official statistic
Regression Coefficient While analysing regression in two related series, we calculate their regression coefficients also. There are two regression coefficients like two regress
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