365
variable and predict or explain possible outcomes. All multivariate statistical techniques can be divided into two groups:
• Techniques that analyse addiction
• Techniques that analyse interdependence
In dependency analysis techniques, the goal is to explain one dependent variable
and predict its variation based on other independent variables.
There is often a need for a combination of techniques from the two groups. All
multivariate techniques have been developed based on research by experts from
various scientific disciplines. As a result, multivariate statistical analysis is interdisciplinary both in its origin and in its application. The techniques presented in this
book are those that are currently most used in research. Many of these techniques
have a strict mathematical derivation and basis and belong to ‘classical’ statistical
models. Other techniques include various approximation methods and solutions that
have proven to be sufficiently accurate and usable through practice.
Rank correlation is when the original values of a feature are replaced by ranks. If
it is necessary to observe the correlation of phenomena whose characteristics cannot
be measured numerically or if it is necessary to quickly reach at least the approximate value of the correlation coefficient, Spearman’s (for two phenomena) and
Kendall’s rank correlation coefficient (for more than two phenomena) are most
commonly used.
Multiple linear regression predicts the dependence of one phenomenon on two or
more independent phenomena and is examined; then we are talking about multiple
or multiple regression. The task of regression is to discover as many factors as possible. The starting point is the assumption: the more independent phenomena in the
model, the smaller the latent influence variables (random errors).
12.4.2 Correlations and Regression Analysis
Correlation is the interrelationship between different phenomena that are represented by values in two or more random variables. In this case, the connection
means that based on the knowledge of the value of one variable, with a certain probability, it is possible to predict the value of another variable, since these values
appear in a certain ratio. The degree to which two values coincide can be represented graphically on a scatter plot or by a correlation coefficient.
Regression analysis is an extension of correlation analysis and is one of the most
commonly used statistical techniques today. Regression analysis is a set of analytical techniques used to better understand the interrelationship between the phenomena observed, expressed in the form of collected data. As an end result, the analysis
produces a regression equation, but all the results obtained in this process can provide valuable information about the observed phenomena and their environment.
Basically, regression analysis involves two or more variables that are related to each
other in some way. One of the variables is of special interest, because the purpose of
12 Characterization of Multi-element Profiles and Multi-isotope Ratio Records as…
variable and predict or explain possible outcomes. All multivariate statistical techniques can be divided into two groups:
• Techniques that analyse addiction
• Techniques that analyse interdependence
In dependency analysis techniques, the goal is to explain one dependent variable
and predict its variation based on other independent variables.
There is often a need for a combination of techniques from the two groups. All
multivariate techniques have been developed based on research by experts from
various scientific disciplines. As a result, multivariate statistical analysis is interdisciplinary both in its origin and in its application. The techniques presented in this
book are those that are currently most used in research. Many of these techniques
have a strict mathematical derivation and basis and belong to ‘classical’ statistical
models. Other techniques include various approximation methods and solutions that
have proven to be sufficiently accurate and usable through practice.
Rank correlation is when the original values of a feature are replaced by ranks. If
it is necessary to observe the correlation of phenomena whose characteristics cannot
be measured numerically or if it is necessary to quickly reach at least the approximate value of the correlation coefficient, Spearman’s (for two phenomena) and
Kendall’s rank correlation coefficient (for more than two phenomena) are most
commonly used.
Multiple linear regression predicts the dependence of one phenomenon on two or
more independent phenomena and is examined; then we are talking about multiple
or multiple regression. The task of regression is to discover as many factors as possible. The starting point is the assumption: the more independent phenomena in the
model, the smaller the latent influence variables (random errors).
12.4.2 Correlations and Regression Analysis
Correlation is the interrelationship between different phenomena that are represented by values in two or more random variables. In this case, the connection
means that based on the knowledge of the value of one variable, with a certain probability, it is possible to predict the value of another variable, since these values
appear in a certain ratio. The degree to which two values coincide can be represented graphically on a scatter plot or by a correlation coefficient.
Regression analysis is an extension of correlation analysis and is one of the most
commonly used statistical techniques today. Regression analysis is a set of analytical techniques used to better understand the interrelationship between the phenomena observed, expressed in the form of collected data. As an end result, the analysis
produces a regression equation, but all the results obtained in this process can provide valuable information about the observed phenomena and their environment.
Basically, regression analysis involves two or more variables that are related to each
other in some way. One of the variables is of special interest, because the purpose of
12 Characterization of Multi-element Profiles and Multi-isotope Ratio Records as…