Instructions:
There are a total of four (4) multi-part questions, with point values noted for each question.
Please show your calculations, or the details of your program(s) for each problem. You must supply the SAS program, and the program should be commented so that each step is clearly explained.
Combine all your answers/files into a single zipped file and post the zipped file to “HW_Final_new” in CANVAS.
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Problem 1 – (25 points)
Normalize and perform PCA analysis on the “PCA_data” dataset on CANVAS. Perform the following:
· Create an output dataset “out_PCA” containing the results of your PCA transformation for X1 to X6
· What is the sum of the variances of the normalized data?
· What is the sum of the eigenvalues?
· If you wanted to reduce the number of dimensions, how many principal components would you choose? Why?
· What would be the number of principal components you would choose if you want to capture around 90% of the variabilities?
· What would be the first principal component for a record with the normalized values of X1=.5, X2=.5 X3=.5 X4=.5 X5=.5 X6=.5?
Problem 2 – (25 points)
Use the “out_PCA” dataset above to establish a regression model using y as the dependent variable and Prin1 to Prin6 as independent variables. Use the following selection models and answer the corresponding questions:
1) Selection=Stepwise. What is the final model? Is it a good model?
2) Selection=MaxR. What is the best model for two predictors? Is that a good model? Why
The following two questions use the SAS dataset “Admission” on CANVAS. The dataset shows whether an applicant has been admitted to a college (admit=1), or not (admit=0). There are three predictors. The variables gre and gpa are continuous. The variable rank is categorical and takes on the values 1 through 4.
Problem 3 – (25 points)
· Establish a logistic regression model to predict admission (admit=1) using rank as a predictor. Using rank=1 as your base answer the following questions:
· Is this a good model?
Assuming the model is a good model
· What are the odds of admission for rank=1
· What is the P(admit=1/rank=1)
· What is P(admit=1/rank=2)
· What is the odds ratio of rank=2 over rank=1?
Problem 4 – (25 points)
· Use hierarchical (method=average) and kmeans clustering methods to create two clusters for the Admission dataset using gre and gpa as clustering variables.
· Do Applicant 1008 and 1009 belong to the same clusters? Please explain.
Datasets: PCA_data, Admission
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