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As one of the oldest multivariate statistical methods of data reduction, Principal Component Analysis (PCA)simplifies a dataset by producing a small number of derived variables that are uncorrelated and that account for most of the variation in the original data set. Eventually, the derived variables are combinations of the original variables. For example, it might be ?hat students take 10 examinations and some students do well in one exam whilst other students do better in another. It is difficult to compare one student with another when we have marks from 10 examinations to consider. One obvious way of comparing students is to calculate tlie mean score. This is a constructed combination of the existing variables,. However. we may get a more useful comparison of overall performances by considering other constructed combinations of the 10 exam marks. The PCA is one way of constructing such combinations, doing so in such ewakas to account for as much as possible of the variation in the original data. One can then compare students' performance by considering this much sn~aller number of variables.
The first step in this case is to ensure that you are adequately clear on the General Linear Model and its relationship to both ANOVA and regression. The distinction is approxim
According to a recent study, when shopping online for luxury goods, men spend a mean of $2,401, whereas women spend a mean of $1,527. Suppose that the study was based on a sample o
For a distribution of scores with = 82 and standard deviation = 2.5, find the following: (Don't forget to sketch the normal curve to help you visualize what you are trying to fi
Consider a Cournot duopoly with two firms (firm 1 and firm 2) operating in a market with linear inverse Demand P(Q) = x Q where Q is the sum of the quantities produced by both
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Consider the following linear regression model: a) What does y and x 1 , x 2 , . . . . x k represent? b) What does β o , β 1 , β 2 , . . . . β k represent?
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Simple Linear Regression One calculate of the risk or volatility of an individual stock is the standard deviation of the total return (capital appreciation plus dividends) over
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
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