Description

Download Rdata files from Piazza or Coursera
The assignment is related to the Boston Housing data. The original data is from the R library “mlbench”, which has 506 observations on 19 variables.
crim zn indus chas nox rm
age dis rad tax ptratio b
lstat
medv cmedv town
tract lon lat per capita crime rate by town proportion of residential land zoned for lots over 25,000 sq.ft proportion of non-retail business acres per town
Charles River dummy variable (= 1 if tract bounds river; 0 otherwise) nitric oxides concentration (parts per 10 million) average number of rooms per dwelling proportion of owner-occupied units built prior to 1940 weighted distances to five Boston employment centres index of accessibility to radial highways full-value property-tax rate per USD 10,000 pupil-teacher ratio by town
1000(B − 0.63)2 where B is the proportion of blacks by town percentage of lower status of the population median value of owner-occupied homes in USD 1000’s corrected median value of owner-occupied homes in USD 1000’s name of town census tract longitude of census tract latitude of census tract
First, we apply some suggested transformations on the data, then remove three variables medv, town, and tract, and use cmedv as the response variable Y.
Consider following 10 procedures:
• Full: run a linear regression model using all features,
• AIC.F and AIC.B: Forward/backward selection with AIC,
• BIC.F and BIC.B: Forward/backward selection with BIC,
• R.min and R.1se: Ridge regression using lambda.min or lambda.1se,
• L.min and L.1se: Lasso using lambda.min or lambda.1se,
• L.Refit: Refit the model selected by Lasso using lambda.1se.
1. Load BostonHousing1.Rdata, which has 16 variables including the response variable Y. The data has been pre-processed, so no need to apply any transformation.
a) Repeat the following simulation 50 times. In each iteration, randomly split the data into two parts, 75% for training and 25% for testing. fit the model based on the training data and obtain a prediction on the test data, record the mean squared prediction error (MSPE) on the test set, the selected model-size or effect dimension (for Ridge), and the computation time for each procedure.
Exclude intercept in computing model-size or effect dimension.

b) Summarize your results on MSPE and model size graphically, e.g., using boxplot or stripchart.
2. Load BostonHousing2.Rdata, which has 135 variables including the response variable Y. In addition to the original 15 predictors, the data contains their quadratic and all pairwise interaction terms.
Repeat (a-b) above for only five methods: R.min, R.1se, L.min L.1se, and
L.Refit.
3. Load BostonHousing3.Rdata, which has 635 variables including the response variable Y. In addition to BostonHousing2.Rdata, the data contains 500 noise features.
Repeat (a-b) above for only five methods: R.min, R.1se, L.min L.1se, and
L.Refit.
(Continue on the next page −→)
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What you need to submit?
A PDF file (maximum two-page) and the R/Python code that produces the PDF file. Your code will be run in a directory that has the three data files.
• The PDF file should contain three sets of figures (one for each data set) which provide graphical summary of MSPE and model size.
• The PDF file should contain the computation time for each procedure for each data set. Students can display the computation time graphically or just provide the numbers.
• Students are allowed to use R/Python code to generate Markdown file in PDF. Since the file size is restricted to be two pages, suggest to hide your code and only display the results.
• Name your R/Python file (Rmd files are allowed) starting with
For example, the submission for Max Y. Chen with UID 672757127 and netID mychen12 would be named
Assignment 2 7127 mychen12 MaxChen.R.
You can add whatever characters after your netID.
• Name the PDF file similarly, starting with
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