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The basic idea of PLSR is to build a regression prediction model between the observation variables X (independent variables) and the dependent variables Y [ 39– 42 ].
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The observation variables are interpreted through a desirability scale.
The biggest advantage of the model is that it allows the testing of the relationship between observation variable and latent, and the latent variables under the situation in which there are measurement errors.
The proposed heuristic optimisation approach relies on the rank of the cross-covariance matrix between the observations of the target variables and the observations of the sensor measurement variables obtained from simulations using the computational model of an experiment.
Observation variables have been described before [ 42- 44], but these were mainly variables from the doctor's own observations.
MFA was used in order to simultaneously analyse several tables of variables (three tables for instrumental data: volatiles, semi-volatiles and non-volatiles and one table for sensory data), thus facilitating a study of the relationship between the observations (different samples), the variables and the tables.
Bottom, residuals between the observation and the best fit.
A related paper [ 8] uses the latent variable modeling based on the hierarchical Bayes approach to incorporate the dependence between the observations.
The mean Pearson correlation for all variable was 0.932, and it ranged from 0.801 to 0.988, which implies a highly significant correlation between the observations (p = <0.01).
Furthermore it also can uncover the relationships between observations and variables and between the variables themselves [16],[16].
aThis number includes only the observations for the correlations between the proxy variables and the binary hedging variable.
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