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BMEN 5007/4007 Problem Set 7 11/16/2023 Due: 11/30/2023 by 4 PM in PDF form on Canvas 1. In Type 2 diabetes, there are three possible stages. Normal (non-diabetic), latent (asymptomatic chemical diabetes), and overt (symptomatic diabetes). You are attempting to index patients based on 5 variables. Relwt : relative weight, expressed as the ratio of actual weight to expected weight, given the person's height, a numeric vector glufast : fasting plasma glucose level, a numeric vector glutest : test plasma glucose level, a measure of glucose intolerance, a numeric vector instest : plasma insulin during test, a measure of insulin response to oral glucose, a numeric vector sspg : steady state plasma glucose, a measure of insulin resistance, a numeric vector group : diagnostic group, a factor. For a-c, use the dataset, “diabetesgrouping.xlsx”. a. Evaluate whether the collective of these parameters can separate patients (i.e.; run an a MANOVA). b. Evaluate which of these factors are different between the groups. c. Evaluate which groups are different for factors that are also different. 2. You wish to utilize this information to create a discriminate function analysis for categorizing patients a. How many DFA functions will be generated? (5 pts) b. Generate a DFA model using the dataset “diabetestraining.xlsx”. c. How much of the error is explained by each DFA function? d. Show the plots that demonstrate that the DFA function separates each group. e. Evaluate your model using the dataset “diabetestesting.xlsx”. How correctly are the patients classified. (5 pts) f. Using the dataset provided for unknown patients (“diabetescategorize.xlsx”). Classify each as Overt diabetic, chemically diabetic, or normal. 3. We are interested in reducing the number of variables in the data set using principal component analysis. You are evaluating breast tissue samples are possibly cancerous. The data set (breast_cancer.xlsx) contains the following variables scored from 1 to 10:  Clump Thickness  Uniformity of Cell Size  Uniformity of Cell Shape  Marginal Adhesion  Single Epithelial Cell Size  Bare Nuclei  Bland Chromatin  Normal Nucleoli  Mitoses a. Determine the number of component variables? b. Which of the variables are correlated with one another (use rotation as necessary to separate variables)? c. Plot the loading into the respective components.