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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.
Problem: A survey usually originates when an individual or an institution is confronted with an information need and the existing data are insufficient. Planning the questionn
Rank Correlation Sometimes the characteristics whose possible correlation is being investigated, cannot be measured but individuals can only be ranked on the basis of the chara
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
Importance of official statistic
Cartogram or Mapograph: Statistical maps are also used to represent data like density of population indifferent states in the country or different countries in the world or th
differance b/w big M mathod and two phase mathod
Is the random vector (Trunk Space, Length, Turning diameter) of US car normally distributed? Why? If yes, find the unbiased estimators for the mean and variance matrix of (Trunk Sp
Grouped Data In order to find the median, the median class is to be first located and then interpolation is to be used by assuming that items are evenly spaced over the entire
Ask question #MinimumA wedge is small piece of material having two of their opposite faces not parallel. To lift block of weight W, it is pushed by horizontal force P which lifts t
Q. Find the inverse Laplace transform of Y (s) = s-4/s 2 + 4s + 13 +3s+5/s 2 - 2s -3. Q. Use the Laplace transform to solve the initial value problem y''+ y = cos(3t), y(0) =
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