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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.
a) List down several measures of central tendency and define the difference among them? b) What do you mean by confidence interval, and why it is useful? What is a confidence lev
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Melissa Bakery is preparing for the coming thanksgiving festival. The bakery plans to bake and sell its favourite cookies; butter cookies, chocolate cookies and almond cookies. A k
Grouped Data For calculating mode from a frequency distribution, the following formula Mode = L mo + x W where,
In reduced rank regression (RRR), the dependent variables are first submitted to a PCA and the scores of the units are then used as dependent variables in a series of
Type of Correlation 1. Positive and Negative Correlation: 2. Simple Partial and Multiple Correlations. 3. Linear and Non linear or Correlations
Empirical Mode Where mode is ill-defined, its value may be ascertained by the following formula based upon the empirical relationship between Mean, Median and Mode: Mode = 3
The prevalence of undetected diabetes in a population to be screened is approximately 1.5% and it is assumed that 10,000 persons will be screened. The screening test will measure
Let X 1 and X 2 be two independent populations with population means μ 1 and μ 2 respectively. Two samples are taken, one from each population, of sizes n 1 and n 2 re
What is an example of a real life situation when I would use each of these test
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