software for data presentation, statistical analysis, marketing and prediction.
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LeoStatistic.zip
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LeoStatistic.exe
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Correlation between parameters.
Let's presume that there is a task to analyze a table of data - are there a mutual dependences between parameters or not? In general responsible answers could be only "Yes" - we found one, or "Maybe" - we didn't find it yet but who knows. Practically imposable definitely to rule out virtual opportunity that some undiscovered dependence exist in the spite all efforts to find them with available statistical schemes.
Saying this, let's see how to apply "correlation" statistical method incorporated in LeoStatistic to find existing dependences.
Go to "Statistics" tab of control panel and check up a "Correlation" control. The correlations matrix for all existing parameters will be calculated and presented in working and result areas of the LeoStatistic. In result area the matrix of standard correlations coefficients are given in numerical presentation. For more theoretical foundation about meaning of correlation coefficient do check for example the link Correlation, and regression analysis for curve fitting For simple practical goals important to know that value of correlation coefficient close to 1.0 or -1.0 witness a strong linear dependence between two parameters. The value near 0 means that there are no linear dependence. It's not really evidence of absence of any other dependences. They could exist, even very strong, although not a linear.
For example the data that could be imported from text file correlation are producing this correlation matrix:
|
|
x |
y |
z |
r |
|
x |
1 |
0.0031 |
0.45 |
-0.005 |
|
y |
0.0031 |
1 |
0.89 |
0.01 |
|
z |
0.45 |
0.89 |
1 |
0.0068 |
|
r |
-0.005 |
0.01 |
0.0068 |
1 |
If limit ourselves with only numerical presentations of coefficient of correlation it's quite possible to come to blunder conclusion that there is no dependence between parameters y versus z or r versus x. Nevertheless if take a look at the graphical presentation of correlation matrix in working area of LeoStatistic:
one can see that there are very strong dependence between y vs. x and practically none one between r vs. x. Furthermore dependence y(x) and z(y) are practically of the same order but second has very strong correlation coefficient and first near to 0. That emphasize the importance to be very cautious in statements about nonexistence of the correlations inside analyzing data.
click on picture to enlarge
Distribution of two variables.
Approximation
(constructor style interface).
