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

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 k=n−2$k=n-2$degrees of freedom and hence, for example, for the Pearson correlation coefficient, the value of the statistics is

The value of the test statistic cannot be determined whenrp=1$r_p=1$ therp=−1$r_p=-1$or whenn<3$n<3$.

In other cases, the value determined on its basisp$p$ (read from the Student's t-distribution) is compared with the assumed significance levelα$\alpha$

• ifp≤α$p\le \alpha$we reject itH0$H_0$accepting H1$H_1$
• ifp>α$p>\alpha$there is no reason to reject itH0$H_0$

Typically, a significance level is selectedα=0.05$\alpha =0.05$, agreeing that in 5% of situations we will reject the null hypothesis when it is true.

The same is done for the other correlation coefficients insteadrp$r_p$substitutingrs$r_s$therq$r_q$.