(Solved): Jay Gatsby categorizes wines into one of three clusters. The centroids of these clusters, describi ...

Jay Gatsby categorizes wines into one of three clusters. The centroids of these clusters, describing the average characteristics of a wine in each cluster, are listed in the following table. Jay has recently discovered a new wine from the Piedmont region of Italy with the following characteristics. In which cluster of wines should he place this new wine? Justify your choice with appropriate calculations. Characteristic \( \begin{array}{lr}\text { Alcohol } & -1.023 \\ \text { MalicAcid } & -0.480 \\ \text { Ash } & 0.049 \\ \text { Alcalinity } & 0.600 \\ \text { Magnesium } & -1.242 \\ \text { Phenols } & 1.094 \\ \text { Flavanoids } & 0.001 \\ \text { Nonflavanoids } & 0.548 \\ \text { Proanthocyanins } & -0.229 \\ \text { Colorlntensity } & -0.797 \\ \text { Hue } & 0.711 \\ \text { Dilution } & -0.425\end{array} \) If required, round your answers to three decimal places. Do not round intermediate calculations. Distance from new wine and Cluster 1: Distance from new wine and Cluster 2: Distance from new wine and Cluster 3: is the most appropriate for the new wine observation.