#+TITLE: Rapport package team
#+AUTHOR: Factor Analysis
#+DATE: 2011-04-26 20:25 CET
** Description
In this template Rapporter will present you Factor Analysis.
*** Introduction
[[http://en.wikipedia.org/wiki/Factor_analysis][Factor Analysis]] is
applied as a data reduction or structure detection method. There are two
main applications of it: reducing the number of variables and detecting
structure in the relationships between variables, thus explore latent
structure behind the data, classify variables.
****** Determining the number of the factors
[[plots/FactorAnalysis.tpl-1-hires.png][[[plots/FactorAnalysis.tpl-1.png]]]]
****** Eigenvalues
You can find the eigenvalues of the possible factors in the following
table (/2/ factors were produced as you set):
| Factor Number | Eigenvalues |
|-----------------+---------------|
| *1* | *2.461* |
| *2* | *1.273* |
| 3 | 0.1485 |
| 4 | 0.1176 |
**** Factor loadings
At the next step let's check the factor loadings. They mean that how
deep the impact of a factor for the variables. We emphasized the cells
when the explained is higher than 30% of the whole variance.
| | ML1 | ML2 |
|----------+-------------+------------|
| *carb* | *0.8723* | *0.3756* |
| *gear* | -0.08811 | *0.9343* |
| *mpg* | *-0.8197* | *0.4368* |
| *cyl* | *0.7988* | *-0.452* |
So it can be said that
- ML1 is a latent factor of carb
- ML1 is a latent factor of mpg
- ML1 is a latent factor of cyl
- ML2 is a latent factor of carb
- ML2 is a latent factor of gear
- ML2 is a latent factor of mpg
- ML2 is a latent factor of cyl
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From them in the cases of the /ML1's impact on mpg/ and /ML2's impact on
cyl/, we can say they are negative effects.
**** Uniquenesses
At last but not least let us say some words about the not explained part
of the variables. There are two statistics which help us quantifying
this concept: Communality and Uniqueness. They are in a really strong
relationship, because Uniqueness is the variability of a variable minus
its Communality. The first table contains the Uniqunesses, the second
the Communalities of the variables:
| | Uniqunesses | Communalities |
|----------+---------------+-----------------|
| *carb* | 0.09805 | 0.902 |
| *gear* | 0.1193 | 0.8807 |
| *mpg* | 0.1374 | 0.8626 |
| *cyl* | 0.1576 | 0.8424 |
We can see from the table that variable cyl has the highest Uniqueness,
so could be explained the least by the factors and variable carb
variance's was explained the most, because it has the lowest Uniqueness.
From the communalities we can draw the same conclusion.
** Description
In this template Rapporter will present you Factor Analysis.
*** Introduction
[[http://en.wikipedia.org/wiki/Factor_analysis][Factor Analysis]] is
applied as a data reduction or structure detection method. There are two
main applications of it: reducing the number of variables and detecting
structure in the relationships between variables, thus explore latent
structure behind the data, classify variables.
****** Eigenvalues
You can find the eigenvalues of the possible factors in the following
table (/3/ factors were produced as you set):
| Factor Number | Eigenvalues |
|-----------------+---------------|
| *1* | *2.461* |
| *2* | *1.273* |
| *3* | *0.1485* |
| 4 | 0.1176 |
**** Factor loadings
At the next step let's check the factor loadings. They mean that how
deep the impact of a factor for the variables. We emphasized the cells
when the explained is higher than 30% of the whole variance.
| | ML1 | ML2 | ML3 |
|----------+-------------+-------------+-------------|
| *carb* | *0.8771* | *0.3502* | -0.001772 |
| *gear* | -0.0595 | *0.9317* | -0.005685 |
| *mpg* | *-0.8132* | *0.4641* | 0.0972 |
| *cyl* | *0.7917* | *-0.4774* | 0.1361 |
So it can be said that
- ML1 is a latent factor of carb
- ML1 is a latent factor of mpg
- ML1 is a latent factor of cyl
- ML2 is a latent factor of carb
- ML2 is a latent factor of gear
- ML2 is a latent factor of mpg
- ML2 is a latent factor of cyl
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#+END_HTML
From them in the cases of the /ML1's impact on mpg/ and /ML2's impact on
cyl/, we can say they are negative effects.
**** Uniquenesses
At last but not least let us say some words about the not explained part
of the variables. There are two statistics which help us quantifying
this concept: Communality and Uniqueness. They are in a really strong
relationship, because Uniqueness is the variability of a variable minus
its Communality. The first table contains the Uniqunesses, the second
the Communalities of the variables:
| | Uniqunesses | Communalities |
|----------+---------------+-----------------|
| *carb* | 0.1081 | 0.8919 |
| *gear* | 0.1283 | 0.8717 |
| *mpg* | 0.1138 | 0.8862 |
| *cyl* | 0.1268 | 0.8732 |
We can see from the table that variable gear has the highest Uniqueness,
so could be explained the least by the factors and variable carb
variance's was explained the most, because it has the lowest Uniqueness.
From the communalities we can draw the same conclusion.
** Description
In this template Rapporter will present you Factor Analysis.
Your request cannot be implemented, because there are the same number of
variables (/5/) like the number of the requested factors (/5/) . Please
set the number of the factors to maximum /4/ with the same number of the
variables or extend the number of those variables at least to /6/.
--------------
This report was generated with [[http://www.r-project.org/][R]] (3.0.1)
and [[https://rapporter.github.io/rapport/][rapport]] (0.51) in /1.479/ sec on
x86\_64-unknown-linux-gnu platform.
[[images/logo.png]]