367
• A multivariate regression model in which more dependent variables occur, which
is why it consists of several regression equations
In addition to enabling the assessment of the degree of correlation of phenomena,
regression analysis also gives the probability of occurrence of the calculated correlation. It is used to test hypotheses in studies and experiments but also to predict the
future movement of the observed phenomenon. The concept of regression is easy to
understand and is implemented in almost every statistical package and allows the
examination of the functional dependence between variables, so as such it is the
basis of many modern statistical techniques.
12.4.3 Cluster Analysis
Cluster analysis is a statistical technique for determining relatively homogeneous
groups of objects. It is used in various branches of science to categorize or classify
individual units of analysis (objects or respondents) with regard to their similarity or
difference according to some of their measured characteristics. Although both discriminant analysis and cluster analysis relate to the problem of classifying objects or
respondents into categories, discriminant analysis requires knowledge of group affiliation for the units we use to determine classification rules. For example, if we try to
distinguish subjects who fall into three diagnostic categories, we must know the diagnosis (group affiliation) for each subject. In the cluster analysis, the group affiliation
of the objects is not known, nor is the final number of groups. The goal of cluster
analysis is to identify homogeneous groups or clusters.
12.5 Case Study of Isotopic Ratio Measurements
The aim of this case study was to evaluate lead composition of red goji berry
(Lycium barbarum L.) cultivated in the Republic of North Macedonia compared to
the same species obtained in market in China. Several metrics have been applied for
authenticity testing of the samples: total lead content, multi-elements’ characterization with clustering and lead isotopic ratios.
12.5.1 Instrumental Conditions for Isotopic Measurement
To confirm that Pb does not undergo a charge-transfer reaction (and to check if any
cluster ions are formed), 20 μg/L Pb solution was aspirated, and a mass scan was
performed. The sum of the signal for these clusters amounted to <0.5% of the total
Pb signal (the sum of the unreacted precursor and reacted product Pb ions); at this
level the product ions can be considered negligible and ignored (Fig. 12.1). Pb did
12 Characterization of Multi-element Profiles and Multi-isotope Ratio Records as…
• A multivariate regression model in which more dependent variables occur, which
is why it consists of several regression equations
In addition to enabling the assessment of the degree of correlation of phenomena,
regression analysis also gives the probability of occurrence of the calculated correlation. It is used to test hypotheses in studies and experiments but also to predict the
future movement of the observed phenomenon. The concept of regression is easy to
understand and is implemented in almost every statistical package and allows the
examination of the functional dependence between variables, so as such it is the
basis of many modern statistical techniques.
12.4.3 Cluster Analysis
Cluster analysis is a statistical technique for determining relatively homogeneous
groups of objects. It is used in various branches of science to categorize or classify
individual units of analysis (objects or respondents) with regard to their similarity or
difference according to some of their measured characteristics. Although both discriminant analysis and cluster analysis relate to the problem of classifying objects or
respondents into categories, discriminant analysis requires knowledge of group affiliation for the units we use to determine classification rules. For example, if we try to
distinguish subjects who fall into three diagnostic categories, we must know the diagnosis (group affiliation) for each subject. In the cluster analysis, the group affiliation
of the objects is not known, nor is the final number of groups. The goal of cluster
analysis is to identify homogeneous groups or clusters.
12.5 Case Study of Isotopic Ratio Measurements
The aim of this case study was to evaluate lead composition of red goji berry
(Lycium barbarum L.) cultivated in the Republic of North Macedonia compared to
the same species obtained in market in China. Several metrics have been applied for
authenticity testing of the samples: total lead content, multi-elements’ characterization with clustering and lead isotopic ratios.
12.5.1 Instrumental Conditions for Isotopic Measurement
To confirm that Pb does not undergo a charge-transfer reaction (and to check if any
cluster ions are formed), 20 μg/L Pb solution was aspirated, and a mass scan was
performed. The sum of the signal for these clusters amounted to <0.5% of the total
Pb signal (the sum of the unreacted precursor and reacted product Pb ions); at this
level the product ions can be considered negligible and ignored (Fig. 12.1). Pb did
12 Characterization of Multi-element Profiles and Multi-isotope Ratio Records as…