Description
1. Consider the wine data available on eLearning as wine.txt. The data come from a study of Pinot Noir
wine quality. The dataset contains 38 observations and 7 variables: Quality, Clarity, Aroma, Body,
Flavor, Oakiness, and Region. We will take Quality as the response variable and the remaining
variables (which represent features of the wine) as predictors. Be sure to treat Region as a qualitative
predictor. The goal is to develop a model that relates the quality of Pinot Noir with its features.
The model can potentially be used to predict the quality of the wine.
(a) Perform an exploratory analysis of data. Comment on findings that interest you.
(b) Is Quality appropriate as a response variable or a transformation is necessary? In case a
transformation is necessary, find a simple transformation and use it for the rest of this problem.
(c) Do part (a) of Exercise 15 in Chapter 3 for these data.
(d) Do part (b) of Exercise 15 in Chapter 3 for these data.
(e) Build a “reasonably good” multiple regression model for these data. Be sure to explore interactions of Region with other predictors. Carefully justify all the choices you make in building
the model and verify the model assumptions.
(f) Write the final model in equation form, being careful to handle the qualitative predictors and
interactions (if any) properly.
(g) Use the final model to predict the Quality of a wine from Region 1 with other predictors set
equal to their sample means. Also provide a 95% prediction interval for the response and a 95%
confidence interval for the mean response. Interpret the results.
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2. Consider the business school admission data available on eLearning as admission.csv. The admission
officer of a business school has used an “index” of undergraduate grade point average (GPA, X1) and
graduate management aptitude test (GMAT, X2) scores to help decide which applicants should be
admitted to the school’s graduate programs. This index is used categorize each applicant into one of
three groups — admit (group 1), do not admit (group 2), and borderline (group 3). We will take the
first five observations in each category as test data and the remaining observations as training data.
Read the handout regarding drawing multiclass decision boundaries before proceeding any further.
(a) Perform an exploratory analysis of the training data data by examining appropriate plots and
comment on how helpful these predictors may be in predicting response.
(b) Perform an LDA using the training data. Superimpose the decision boundary on an appropriate
display of the data. Does the decision boundary seem sensible? In addition, compute the
confusion matrix and overall misclassification rate based on both training and test data. What
do you observe?
(c) Repeat (b) using QDA.
(d) Compare the results in (b) and (c). Which classifier would you recommend? Justify your
conclusions.
3. Consider the diabetes dataset available on eLearning as diabetes.csv. These data are from https:
//www.kaggle.com/johndasilva/diabetes?select=diabetes.csv. You can read more about the
data, including a description of the variables, on this website. We will take Outcome as the response,
the other variables as predictors, and all the data as training data.
(a) Perform an exploratory analysis of the data. Comment on findings that interest you.
(b) Perform an LDA of the data. Compute the confusion matrix, sensitivity, specificity, and overall
misclassification rate based on 0.5 cutoff for the posterior probability. Plot the ROC curve.
What do you observe?
(c) Repeat (a) using QDA.
(d) Compare the results from (a) and (b). Which classifier would you recommend? For the recommended classifier what posterior probability cutoff would you suggest? Justify your answer.
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