Customer Rating of Breakfast Cereals. The dataset Cereals.jmp Download Cereals.jmpincludes nutritional information, store display, and consumer ratings for $77$ breakfast cereals.

Data preprocessing. Note that some cereals are missing values. These will be automatically omitted from the analysis. Use the Cols$>$Columns Viewer to identify which variables are missing values and how many values are missing.

The variables

carbo, sugars, and potass

have

$4$

missing variables in total.

The Hierarchical platform dialog provides an option to standardize $($Standardize Data$).$ Should this be selected? Why?

The scales used for measurement

$[$ Select: are vastly OR are not significantly $]$

different, so the distance measure

$[$ Select: would OR would not be$]$

dominated by variables with larger values. Hence, Standardize Data option in Hierarchical platform

$[$ Select: should OR should not ne $]$

selected.

Apply hierarchical clustering to the data using single linkage and complete linkage $($use only continuous variables in Y$,$ Columns and cast the variable name to Label$).$ Look at the dendrograms and the parallel plots. Comment on the structure of the clusters and on their stability.

With

$[$ Select: complete linkage OR single linkage $]$

$,$ small changes in the distance cause large changes in the number of clusters. For example, the distance from $55$ to $30$ clusters is very narrow $$ clusters change very quickly over a short distance. So$,$

$[$ Select: single linkage OR complete linkage $]$

is more unstable. The change in clusters for

$[$ Select: single linkage OR complete linkage $]$

is more gradual.

Hence

$[$ Select : single linkage OR complete linkage$]$

method leads to the most insightful or meaningful clusters.

In Distance Graph there is a sharp upward bend at cluster number$=$

$[$ Select one: $3,2,$ OR $5]$

$.$ This gives an idea about the optimal number of clusters that will be used in clustering.

The public elementary schools would like to choose a set of cereals to include in their daily cafeterias. Every day a different cereal is offered, but all cereals should support a healthy diet. For this goal you are requested to find a cluster of $$healthy cereals.$$

Based on the variables at hand, how would you characterize $$healthy cereals$?$

$[$ Select high OR low$]$

calories,

$[$ Select high or low$]$

protein,

$[$ Select high or low$]$

fat,

$[$ Select high or low$]$

fiber,

$[$ Select high or low$]$

carbo,

$[$ Select high or low$]$

sugar,

$[$ Select high or low$]$

potass,

$[$ Select high or low$]$

vitamins.

Use the red triangle options Cluster Summary, Cluster Means, and Parallel Coord Plots to check cluster means across the variables. Which cluster of cereals is the most $$healthy$?$

$[$ Select cluster #$2,$ cluster #$1,$ or cluster #$4]$

is the healthiest, with high protein, fiber, and potass and low calories, fat, and carbs. But, this cluster contains the high bran and high fiber cereals that students might generally don$$t like. An alternative might be

$[$ Select cluster #$2,$ cluster #$4,$ or cluster #$5]$

$,$ which is moderately high in the $$good$$ characteristics $($protein$,$ vitamin, potassium$)$ and students would be more likely to eat.