#+TITLE: Rapport package team
#+AUTHOR: Correlations
#+DATE: 2011-04-26 20:25 CET
** Description
This template will return the correlation matrix of supplied numerical
variables.
*** Introduction
[[http://en.wikipedia.org/wiki/Correlation_and_dependence][Correlation]]
is one of the most commonly used statistical tool. With the help of that
we can get information about a possible
[[http://en.wikipedia.org/wiki/Linear_independence][linear relation]]
between two variables. According to the definition of the correlation,
one can call it also as the standardized
[[http://en.wikipedia.org/wiki/Covariance][covariance]].
The maximum possible value of the correlation (the so-called
[[http://en.wikipedia.org/wiki/Correlation_coefficient][correlation
coefficient]]) could be 1, the minimum could be -1. In the first case
there is a perfect positive (thus in the second case there is a perfect
negative) linear relationship between the two variables, though perfect
relationships, especially in the social sciences, are quite rare. If two
variables are independent from each other, the correlation between them
is 0, but 0 correlation coefficient only means certainly a
[[http://en.wikipedia.org/wiki/Correlation_and_dependence#Correlation_and_linearity][linear
independency]].
Because extreme values occur seldom we have rule of thumbs for the
coefficients, like other fields of statistics:
- we call two variables highly correlated if the absolute value of the
correlation coefficient between them is higher than 0.7 and
- we call them uncorrelated if that is smaller than 0.2.
Please note that
[[http://en.wikipedia.org/wiki/Correlation_does_not_imply_causation][correlation
has nothing to do with causal models]], it only shows association but
not effects.
*** Variable description
/709/ variables with /2/ cases provided.
There are no highly correlated (r < -0.7 or r > 0.7) variables.
There are no uncorrelated correlated (r < -0.2 or r > 0.2) variables.
*** Correlation matrix
| | age | edu |
|---------+----------------+----------------|
| *age* | | 0.2185 * * * |
| *edu* | 0.2185 * * * | |
#+CAPTION: Correlation matrix
Where the stars represent the
[[http://en.wikipedia.org/wiki/Statistical_significance][significance
levels]] of the bivariate correlation coefficients: one star for a
[[http://en.wikipedia.org/wiki/P-value][p value]] below =0.05=, two for
below =0.01= and three for below =0.001=.
On the plot one can see the correlation in two forms: below the
[[http://en.wikipedia.org/wiki/Main_diagonal][diagonal]] visually, above
that one can find the coefficient(s).
[[plots/Correlation-1-hires.png][[[plots/Correlation-1.png]]]]
** Description
This template will return the correlation matrix of supplied numerical
variables.
*** Introduction
[[http://en.wikipedia.org/wiki/Correlation_and_dependence][Correlation]]
is one of the most commonly used statistical tool. With the help of that
we can get information about a possible
[[http://en.wikipedia.org/wiki/Linear_independence][linear relation]]
between two variables. According to the definition of the correlation,
one can call it also as the standardized
[[http://en.wikipedia.org/wiki/Covariance][covariance]].
The maximum possible value of the correlation (the so-called
[[http://en.wikipedia.org/wiki/Correlation_coefficient][correlation
coefficient]]) could be 1, the minimum could be -1. In the first case
there is a perfect positive (thus in the second case there is a perfect
negative) linear relationship between the two variables, though perfect
relationships, especially in the social sciences, are quite rare. If two
variables are independent from each other, the correlation between them
is 0, but 0 correlation coefficient only means certainly a
[[http://en.wikipedia.org/wiki/Correlation_and_dependence#Correlation_and_linearity][linear
independency]].
Because extreme values occur seldom we have rule of thumbs for the
coefficients, like other fields of statistics:
- we call two variables highly correlated if the absolute value of the
correlation coefficient between them is higher than 0.7 and
- we call them uncorrelated if that is smaller than 0.2.
Please note that
[[http://en.wikipedia.org/wiki/Correlation_does_not_imply_causation][correlation
has nothing to do with causal models]], it only shows association but
not effects.
*** Variable description
/709/ variables with /3/ cases provided.
The highest correlation coefficient (/0.2273/) is between /edu/ and
/age/ and the lowest (/-0.03377/) is between /leisure/ and /age/. It
seems that the strongest association (r=/0.2273/) is between /edu/ and
/age/.
There are no highly correlated (r < -0.7 or r > 0.7) variables.
Uncorrelated (-0.2 < r < 0.2) variables:
- /leisure/ and /age/ (-0.03)
- /leisure/ and /edu/ (0.17)
#+BEGIN_HTML
#+END_HTML
*** Correlation matrix
| | age | edu | leisure |
|-------------+----------------+----------------+----------------|
| *age* | | 0.2273 * * * | -0.0338 |
| *edu* | 0.2273 * * * | | 0.1732 * * * |
| *leisure* | -0.0338 | 0.1732 * * * | |
#+CAPTION: Correlation matrix
Where the stars represent the
[[http://en.wikipedia.org/wiki/Statistical_significance][significance
levels]] of the bivariate correlation coefficients: one star for a
[[http://en.wikipedia.org/wiki/P-value][p value]] below =0.05=, two for
below =0.01= and three for below =0.001=.
On the plot one can see the correlation in two forms: below the
[[http://en.wikipedia.org/wiki/Main_diagonal][diagonal]] visually, above
that one can find the coefficient(s).
[[plots/Correlation-2-hires.png][[[plots/Correlation-2.png]]]]
** Description
This template will return the correlation matrix of supplied numerical
variables.
*** Introduction
[[http://en.wikipedia.org/wiki/Correlation_and_dependence][Correlation]]
is one of the most commonly used statistical tool. With the help of that
we can get information about a possible
[[http://en.wikipedia.org/wiki/Linear_independence][linear relation]]
between two variables. According to the definition of the correlation,
one can call it also as the standardized
[[http://en.wikipedia.org/wiki/Covariance][covariance]].
The maximum possible value of the correlation (the so-called
[[http://en.wikipedia.org/wiki/Correlation_coefficient][correlation
coefficient]]) could be 1, the minimum could be -1. In the first case
there is a perfect positive (thus in the second case there is a perfect
negative) linear relationship between the two variables, though perfect
relationships, especially in the social sciences, are quite rare. If two
variables are independent from each other, the correlation between them
is 0, but 0 correlation coefficient only means certainly a
[[http://en.wikipedia.org/wiki/Correlation_and_dependence#Correlation_and_linearity][linear
independency]].
Because extreme values occur seldom we have rule of thumbs for the
coefficients, like other fields of statistics:
- we call two variables highly correlated if the absolute value of the
correlation coefficient between them is higher than 0.7 and
- we call them uncorrelated if that is smaller than 0.2.
Please note that
[[http://en.wikipedia.org/wiki/Correlation_does_not_imply_causation][correlation
has nothing to do with causal models]], it only shows association but
not effects.
*** Variable description
/32/ variables with /11/ cases provided.
The highest correlation coefficient (/0.902/) is between /disp/ and
/cyl/ and the lowest (/-0.8677/) is between /wt/ and /mpg/. It seems
that the strongest association (r=/0.902/) is between /disp/ and /cyl/.
Highly correlated (r < -0.7 or r > 0.7) variables:
- /cyl/ and /mpg/ (-0.85)
- /disp/ and /mpg/ (-0.85)
- /hp/ and /mpg/ (-0.78)
- /wt/ and /mpg/ (-0.87)
- /disp/ and /cyl/ (0.9)
- /hp/ and /cyl/ (0.83)
- /wt/ and /cyl/ (0.78)
- /vs/ and /cyl/ (-0.81)
- /hp/ and /disp/ (0.79)
- /drat/ and /disp/ (-0.71)
- /wt/ and /disp/ (0.89)
- /vs/ and /disp/ (-0.71)
- /qsec/ and /hp/ (-0.71)
- /vs/ and /hp/ (-0.72)
- /carb/ and /hp/ (0.75)
- /wt/ and /drat/ (-0.71)
- /am/ and /drat/ (0.71)
- /vs/ and /qsec/ (0.74)
- /gear/ and /am/ (0.79)
#+BEGIN_HTML
#+END_HTML
Uncorrelated (-0.2 < r < 0.2) variables:
- /gear/ and /hp/ (-0.13)
- /qsec/ and /drat/ (0.09)
- /carb/ and /drat/ (-0.09)
- /qsec/ and /wt/ (-0.17)
- /am/ and /vs/ (0.17)
- /carb/ and /am/ (0.06)
#+BEGIN_HTML
#+END_HTML
*** Correlation matrix
| | mpg | cyl | disp |
|----------+-----------------+-----------------+-----------------|
| *mpg* | | -0.8522 * * * | -0.8476 * * * |
| *cyl* | -0.8522 * * * | | 0.9020 * * * |
| *disp* | -0.8476 * * * | 0.9020 * * * | |
| *hp* | -0.7762 * * * | 0.8324 * * * | 0.7909 * * * |
| *drat* | 0.6812 * * * | -0.6999 * * * | -0.7102 * * * |
| *wt* | -0.8677 * * * | 0.7825 * * * | 0.8880 * * * |
| *qsec* | 0.4187 * | -0.5912 * * * | -0.4337 * |
| *vs* | 0.6640 * * * | -0.8108 * * * | -0.7104 * * * |
| *am* | 0.5998 * * * | -0.5226 * * | -0.5912 * * * |
| *gear* | 0.4803 * * | -0.4927 * * | -0.5556 * * * |
| *carb* | -0.5509 * * | 0.5270 * * | 0.3950 * |
#+CAPTION: Correlation matrix (continued below)
| | hp | drat | wt |
|----------+-----------------+-----------------+-----------------|
| *mpg* | -0.7762 * * * | 0.6812 * * * | -0.8677 * * * |
| *cyl* | 0.8324 * * * | -0.6999 * * * | 0.7825 * * * |
| *disp* | 0.7909 * * * | -0.7102 * * * | 0.8880 * * * |
| *hp* | | -0.4488 * * | 0.6587 * * * |
| *drat* | -0.4488 * * | | -0.7124 * * * |
| *wt* | 0.6587 * * * | -0.7124 * * * | |
| *qsec* | -0.7082 * * * | 0.0912 | -0.1747 |
| *vs* | -0.7231 * * * | 0.4403 * | -0.5549 * * * |
| *am* | -0.2432 | 0.7127 * * * | -0.6925 * * * |
| *gear* | -0.1257 | 0.6996 * * * | -0.5833 * * * |
| *carb* | 0.7498 * * * | -0.0908 | 0.4276 * |
#+CAPTION: Table continues below
| | qsec | vs | am |
|----------+-----------------+-----------------+-----------------|
| *mpg* | 0.4187 * | 0.6640 * * * | 0.5998 * * * |
| *cyl* | -0.5912 * * * | -0.8108 * * * | -0.5226 * * |
| *disp* | -0.4337 * | -0.7104 * * * | -0.5912 * * * |
| *hp* | -0.7082 * * * | -0.7231 * * * | -0.2432 |
| *drat* | 0.0912 | 0.4403 * | 0.7127 * * * |
| *wt* | -0.1747 | -0.5549 * * * | -0.6925 * * * |
| *qsec* | | 0.7445 * * * | -0.2299 |
| *vs* | 0.7445 * * * | | 0.1683 |
| *am* | -0.2299 | 0.1683 | |
| *gear* | -0.2127 | 0.2060 | 0.7941 * * * |
| *carb* | -0.6562 * * * | -0.5696 * * * | 0.0575 |
#+CAPTION: Table continues below
| | gear | carb |
|----------+-----------------+-----------------|
| *mpg* | 0.4803 * * | -0.5509 * * |
| *cyl* | -0.4927 * * | 0.5270 * * |
| *disp* | -0.5556 * * * | 0.3950 * |
| *hp* | -0.1257 | 0.7498 * * * |
| *drat* | 0.6996 * * * | -0.0908 |
| *wt* | -0.5833 * * * | 0.4276 * |
| *qsec* | -0.2127 | -0.6562 * * * |
| *vs* | 0.2060 | -0.5696 * * * |
| *am* | 0.7941 * * * | 0.0575 |
| *gear* | | 0.2741 |
| *carb* | 0.2741 | |
Where the stars represent the
[[http://en.wikipedia.org/wiki/Statistical_significance][significance
levels]] of the bivariate correlation coefficients: one star for a
[[http://en.wikipedia.org/wiki/P-value][p value]] below =0.05=, two for
below =0.01= and three for below =0.001=.
On the plot one can see the correlation in two forms: below the
[[http://en.wikipedia.org/wiki/Main_diagonal][diagonal]] visually, above
that one can find the coefficient(s).
[[plots/Correlation-3-hires.png][[[plots/Correlation-3.png]]]]
--------------
This report was generated with [[http://www.r-project.org/][R]] (3.0.1)
and [[http://rapport-package.info/][rapport]] (0.51) in /4.769/ sec on
x86\_64-unknown-linux-gnu platform.
[[images/logo.png]]