% Rapport package team
% Principal Component Analysis
% 2011-04-26 20:25 CET
## Description
In this template Rapporter will present you Principal Component Analysis.
### Introduction
[Principal Component Analysis](https://en.wikipedia.org/wiki/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.png)](plots/PCA.tpl-1-hires.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
We can say that none of these impacts are negative.
## Description
In this template Rapporter will present you Principal Component Analysis.
### Introduction
[Principal Component Analysis](https://en.wikipedia.org/wiki/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.png)](plots/PCA.tpl-1-hires.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
We can say that none of these impacts are negative.
-------
This report was generated with [R](http://www.r-project.org/) (3.0.1) and [rapport](https://rapporter.github.io/rapport/) (0.51) in _0.891_ sec on x86_64-unknown-linux-gnu platform.
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