How to calcualte pearson correlation
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Analysis of correlation and significance of parameters
Correlation
The study of the significance of the impact of input parameters on output parameters should begin with the analysis of the correlation of individual parameters. Three basic dependencies can be checked:
- monotonic linear
- monotonic non-linear
- square
Pearson's correlation coefficient (monotonic linear relationship)
The most basic measure determining whether there is a linear correlation between parameters
where
This formula can be simplified to
where
Spearman's correlation coefficient (monotonic non-linear relationship)
Spearman's rank correlation coefficient is more universal because it allows to determine the strength of monotonic correlation, which may be non-linear and is expressed by the relation:
where
Interpretation of the correlation coefficient value
Correlation type:
rs > 0 positive correlation – when the value of X increases, so does Yrs = 0 no correlation – when X increases, Y sometimes increases and sometimes decreasesrs < 0 negative correlation – when X increases, Y decreases
Correlation strength:
|rs|<0.2 – no linear relationship0.2≤|rs|<0.4 - weak dependence0.4≤|rs|<0.7 – moderate dependency0.7≤|rs|<0.9 - quite a strong relationship|rs|≥0.9 - very strong dependence
Quadratic correlation coefficient
The quadratic correlation coefficient is determined on the basis of regression analysis.
Error sum of squares
After performing the approximation with a polynomial of the second degree (i.e. determining the coefficients
total sum of squares
The correlation coefficient is determined from the relationship
Statistical testing of the significance of the correlation coefficient
To determine whether the determined correlation coefficient is statistically significant, it is necessary to make a null hypothesis
meaning that there is no correlation between the parameters. The alternative hypothesis has the form
It is assumed that the statistic takes the Student's t-distribution o
The value of the test statistic cannot be determined when
In other cases, the value determined on its basis
- if
p≤α we reject itH0 acceptingH1 - if
p>α there is no reason to reject itH0
Typically, a significance level is selected
The same is done for the other correlation coefficients instead
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