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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

The most basic measure determining whether there is a linear correlation between parameters

where

This formula can be simplified to

where

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

Correlation type:

rs ${r}_{s}$> 0 positive correlation – when the value of X increases, so does Yrs ${r}_{s}$= 0 no correlation – when X increases, Y sometimes increases and sometimes decreasesrs ${r}_{s}$< 0 negative correlation – when X increases, Y decreases

Correlation strength:

|rs|<0.2 $|{r}_{s}|<0.2$– no linear relationship0.2≤|rs|<0.4 $0.2\le |{r}_{s}|<0.4$- weak dependence0.4≤|rs|<0.7 $0.4\le |{r}_{s}|<0.7$– moderate dependency0.7≤|rs|<0.9 $0.7\le |{r}_{s}|<0.9$- quite a strong relationship|rs|≥0.9 $|{r}_{s}|\ge 0.9$- very strong dependence

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

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 $p\le \alpha $we reject itH0 ${H}_{0}$acceptingH1 ${H}_{1}$ - if
p>α $p>\alpha $there is no reason to reject itH0 ${H}_{0}$

Typically, a significance level is selected

The same is done for the other correlation coefficients instead

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All the best!

Thank you 2022, I thank you for all the good and bad memories of 2022. All of them has made me wiser and more mature. And I welcome the 2023! With all the best in everything!

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:

**Correlation coefficients** are used to measure how strong a relationship is between two variables. There are several types of correlation coefficient, but the most popular is Pearson’s. **Pearson’s correlation** (also called Pearson’s *R*) is a **correlation coefficient** commonly used in linear regression. If you’re starting out in statistics, you’ll probably learn about Pearson’s *R* first. In fact, when anyone refers to **the **correlation coefficient, they are usually talking about Pearson’s.

SVAR model example can be found in literature of macroeconomic.

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