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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.
Show how the Normal bin width rule can be modied if f is skewed or kurtotic. Examine the effect of bimodality. Compare your rules to Doane's (1976) extensions of Sturges' rule.
In a three-cornered paint ball duel, A, B, and C successively take shots at each other until only one of them remains paint free. Once hit, a player is out of the game and gets no
Origin and Development of probability Theory: The credit for origin and development of probability goes to the European gamblers of 17 th century. They used to gamble on gam
Sampling A Population is a collection of all the data points being studied. For example, if we are studying the annual incomes of all the people in India, then the population
There may be two values which occur with the same maximum frequency. The distribution is then called bimodal. In a bimodal distribution, the value of mode cannot be determined with
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Other Measures of Dispersion In this section, we look at relatively less used measures of dispersion like fractiles, deciles, percentiles, quartiles, interquartile range and f
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
The PCA is amongst the oldest of the multivariate statistical methods of data reduction. It is a technique for simplifying a dataset, by reducing multidimensional datasets to lower
What would be the cutoff score to indicate a score that is in the top 15% of the scores on a test with a mean of 100 and a standard deviation of 15? This question has multiple p
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