#+TITLE: Rapport package team
#+AUTHOR: Principal Component Analysis
#+DATE: 2011-04-26 20:25 CET
** Description
In this template Rapporter will present you Principal Component
Analysis.
*** Introduction
[[https://en.wikipedia.org/wiki/Principal_component_analysis][Principal
Component Analysis]] is a dimension reduction method. It produces
linearly independent principal components using the variances of the
observations in a set of variables.
*** Results
| | PC1 | PC2 | PC3 |
|----------------------------+----------+-----------+-----------|
| *Standard deviation* | 6.298 | 1.35 | 0.9088 |
| *Proportion of Variance* | 0.9354 | 0.04298 | 0.01947 |
| *Cumulative Proportion* | 0.9354 | 0.9783 | 0.9978 |
From the table above one can see that the first /3/ Principal Components
contains the /93.535 %/, /4.298 %/ and /1.947 %/ of the variances, so
together the 99.78 % of that.
***** Visual representation
It could be informative to see visually how the observations lies on
these components. On that two dimensional plot below, where the axes are
the components which contains the two most variances, you can see (the
red vectors) the effect of the variables as well.
[[plots/PCA.tpl-1-hires.png][[[plots/PCA.tpl-1.png]]]]
**** Rotation
As you wanted to check the Rotation matrix let us present that for you:
| | PC1 | PC2 | PC3 |
|----------+------------+------------+------------|
| *carb* | -0.1486 | *0.9728* | -0.08587 |
| *mpg* | *0.9557* | 0.1614 | 0.2433 |
| *cyl* | -0.2476 | 0.07389 | *0.9502* |
| *drat* | 0.05777 | 0.1488 | -0.1745 |
The cells written in bold shows which components explain the most
variances of the variables, with the help of them we can draw the
following conclusion:
- PC1 is a principal component of mpg
- PC2 is a principal component of carb
- PC3 is a principal component of cyl
#+BEGIN_HTML
#+END_HTML
We can say that none of these impacts are negative.
** Description
In this template Rapporter will present you Principal Component
Analysis.
*** Introduction
[[https://en.wikipedia.org/wiki/Principal_component_analysis][Principal
Component Analysis]] is a dimension reduction method. It produces
linearly independent principal components using the variances of the
observations in a set of variables.
*** Results
| | PC1 | PC2 | PC3 |
|----------------------------+----------+-----------+-----------|
| *Standard deviation* | 6.298 | 1.35 | 0.9088 |
| *Proportion of Variance* | 0.9354 | 0.04298 | 0.01947 |
| *Cumulative Proportion* | 0.9354 | 0.9783 | 0.9978 |
From the table above one can see that the first /3/ Principal Components
contains the /93.535 %/, /4.298 %/ and /1.947 %/ of the variances, so
together the 99.78 % of that.
***** Visual representation
It could be informative to see visually how the observations lies on
these components. On that two dimensional plot below, where the axes are
the components which contains the two most variances, you can see (the
red vectors) the effect of the variables as well.
[[plots/PCA.tpl-1-hires.png][[[plots/PCA.tpl-1.png]]]]
**** Rotation
As you wanted to check the Rotation matrix let us present that for you:
| | PC1 | PC2 | PC3 |
|----------+------------+------------+------------|
| *carb* | -0.1486 | *0.9728* | -0.08587 |
| *mpg* | *0.9557* | 0.1614 | 0.2433 |
| *cyl* | -0.2476 | 0.07389 | *0.9502* |
| *drat* | 0.05777 | 0.1488 | -0.1745 |
The cells written in bold shows which components explain the most
variances of the variables, with the help of them we can draw the
following conclusion:
- PC1 is a principal component of mpg
- PC2 is a principal component of carb
- PC3 is a principal component of cyl
#+BEGIN_HTML
#+END_HTML
We can say that none of these impacts are negative.
--------------
This report was generated with [[http://www.r-project.org/][R]] (3.0.1)
and [[http://rapport-package.info/][rapport]] (0.51) in /0.891/ sec on
x86\_64-unknown-linux-gnu platform.
[[images/logo.png]]