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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.
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
Simulation When decisions are to be taken under conditions of uncertainty, simulation can be used. Simulation as a quantitative method requires the setting up of a mathematical
1. Use the concepts of sampling error and z-scores to explain the concept of distribution of sample means. 2. Describe the distribution of sample means shape for samples of n=36
The box plot displays the diversity of data for the totexp; the data ranges from 30 being the minimum value and 390 being the maximum value. The box plot is positively skewed at 1.
Investigate the use of fixed and percentile meshes when applying chi squared goodness-of-t hypothesis tests. Apply the oversmoothing procedure to the LRL data. Compare the res
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Pattie-Lynn's utility function for total assets is, in which A represents total assets in thousands of dollars. (a) Graph Pattie-Lynn's utility function. How would y
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Advantages It is especially useful in case of open-end classes since only the position and not the values of items must be known. The median is also recommended if th
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