Data reduction, Applied Statistics

Assignment Help:

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 dimensions for analysis. It produces a small number of derived variables that are uncorrelated and that account for most of the variation in the original data set.'By reducing the number of variables'in this way, we can understand the underlying structure of the data. 'The derived variables are combinations of the original variables. For example, it might be that students take I0 examinations and some students do well in one examination while other students do better in another. It is difficult to compare one student with another when we have 10 marks to consider. One obvious way of comparing students is to calculate the mean score.

This is a constructed combination of the existing variables. However, one might get a more useful comparison of overall performances by considering other constructed cwbinations of the 10 exam marks. The PCA is one way of constructing such combinations, doing so in such a way as to account fer the maximum possible variation in the original data. We can then compare students' performance by considering this much smaller number of variables.

PCA states and then solves a well-defined statistical problem, and except for special cases always gives a unique solution wi.th some very nice mathematical properties. We can even describe some very artificial practical problems for which PCA provides the exact solution. The difficulty comes in trying to relate PCA to real-life scientific problems; the match is simply not very good. Actually PCA often provides a good approximation to common factor analysis, but that feature is now unimportant since both methods are now easy enough.


Related Discussions:- Data reduction

Diversity of data , The box plot displays the diversity of data for the tot...

The box plot displays the diversity of data for the totexp; the data ranges from 30 being the minimum value and 390 being the maximum value. The box plot is positively skewed at 1.

Find the probability that a lift will weigh, Lifts usually have signs indic...

Lifts usually have signs indicating their maximum capacity. Consider a sign in a lift that reads "maximum capacity 1400kg or 20 persons". Suppose that the weights of lift-users are

Pie diagram, Circles or Pie Diagram: Circles or pie diagrams are alter...

Circles or Pie Diagram: Circles or pie diagrams are alternative to squares. These are used  for the same purpose i.e. when  the values are differing  widely in their magnitude

Team Collaboration: Business Decision Making Project, Collect data about th...

Collect data about the chosen business problem or opportunity at the company. Explain how you obtained a suitable sample of either qualitative or quantitative data. Review data f

Regression analysis, Meaning and Definitions of Regression The dictiona...

Meaning and Definitions of Regression The dictionary meaning of regression is just opposite the meaning of progression. Progression means to move forward while regression means

Data reduction, The PCA is amongst the oldest of the multivariate statistic...

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

Types of sampling, Given a certain population there are various ways in whi...

Given a certain population there are various ways in which a sample may be drawn from it. The chart below illustrates this point: Figure 1 In  Judgem

Find the mean and standard deviation, Problem : A company supplying ele...

Problem : A company supplying electrical products, places a rush order for electric wires. Consignments of wires are to be sent immediately when they are available. Previous

Redundancy analysis, In reduced rank regression (RRR), the dependent var...

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

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd