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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.
Let X, Y, and Z refer to the three random variables. It is known that Var(X) = 4, Var(Y) = 9, and Var(Z) = 16. It is further known that E(X) = 1, E(Y) = 2, and E(Z) = 4. Furthermor
1. Recognize and explain the opportunities for statistical learning. 2. Describe how the use of statistics supports student learning. 3. Recognize appropriate data displays a
Sampling Error It is the difference between the value of the actual population parameter and the sample statistic. Samples are used to arrive at conclusions regarding the p
#regression line drawn as Y=C+1075x, when x was 2, and y was 239, given that y intercept was 11. calculate the residual
Regression line drawn as Y=C+1075x, when x was 2, and y was 239, given that y intercept was 11. calculate the residual
The box plot displays the diversity of data for the age; the data ranges from 19 being the minimum value and 60 being the maximum value. The box plot is positively skewed at 0.57 a
Question: (a) (i) Define the term multicollinearity. (ii) Explain why it is important to guard against multicollinearity. (b) (i) Sometimes we encounter missing values
Cluster Sampling Here the population is divided into clusters or groups and then Random Sampling is done for each cluster. Cluster Sampling differs from Stratified Sampl
Histogram: It is generally used for charting continuous frequency distribution. In histogram, data are plotted as a series of rectangle one over the other. Class intervals
(i) Plot the step responses of the following second order systems and state the nature of each system. For each case, find the poles and plot the location of the poles in the compl
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