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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.
10. If a set of scores has a sample mean of 25 and a sample variance of 4, find the following: a. the z-score for a raw score of 31 b. the z-score for a raw score of 18 c. the raw
To determine the proportion of people in your town who are smokers, it has been decided to poll people at one of the following local spots: (a) the pool hall; (b) the bowling alley
Example of discrete random variable: 1. What is a discrete random variable? Give three examples from the field of business. 2. Of 1000 items produced in a day at XYZ Manufa
Circles or Pie Diagram: Circles or pie diagrams are alternative to squares. These are used for the same purpose i.e. when the values are differing widely in their magnitude
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
Consider the following game: (a) If (top, left) is a Weakly Dominant Strategy Equilibrium, then what inequalities must hold among (a, ..., h)? (b) If (top, left) is a Na
how to determine GRR?
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A marketing research firm was engaged by an automobile manufacturer to conduct a pilot study to examine the feasibility of using logistic regression for ascertaining the likelihood
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