Reference no: EM132371330

Assignment -

Answer all questions specified on the problem and include a discussion on how your results answered/addressed the question.

Submit your .rmd file with the knitted PDF (or knitted Word Document saved as a PDF). If you are having trouble with .rmd, let us know and we will help you, but both the .rmd and the PDF are required.

This file can be used as a skeleton document for your code/write up. Please follow the instructions found under Content for Formatting and Guidelines. No code should be in your PDF write-up unless stated otherwise.

For any question asking for plots/graphs, please do as the question asks as well as do the same but using the respective commands in the GGPLOT2 library. (So if the question asks for one plot, your results should have two plots. One produced using the given R-function and one produced from the GGPLOT2 equivalent).

This doesn't apply to questions that don't specifically ask for a plot, however I still would encourage you to produce both.

You do not need to include the above statements.

Please do the following problems from the text book R Handbook and stated.

1. Use the bladder-cancer data from the HSAUR3 library to answer the following questions

a) Construct graphical and numerical summaries that will show the relationship between tumor size and the number of recurrent tumors. Discuss your discovery. (Hint: mosaic plot may be a great way to assess this)

b) Build a Poisson regression that estimates the effect of size of tumor on the number of recurrent tumors. Discuss your results.

2. The following data is the number of new AIDS cases in Belgium between the years 1981-1993. Let t denote time

y = c(12, 14, 33, 50, 67, 74, 123, 141, 165, 204, 253, 246, 240)

t = 1:13

Do the following

a) Plot the relationship between AIDS cases against time. Comment on the plot

b) Fit a Poisson regression model log(µ_i) = β₀ + β₁t_i. Comment on the model parameters and residuals (deviance) vs Fitted plot.

c) Now add a quadratic term in time (i.e., log(µ_i) = β₀ + β₁t_i + β₂t²_i) and fit the model. Comment on the model parameters and assess the residual plots.

d) Compare the two models using AIC. Which model is better?

e) Use anova()-function to perform χ² test for model selection. Did adding the quadratic term improve model?

3. Load the Default dataset from ISLR library. The dataset contains information on ten thousand customers. The aim here is to predict which customers will default on their credit card debt. It is a 4 dimensional dataset with 10000 observations. You had developed a logistic regression model. Now consider the following two models

• Model1 → Default = Student + balance
• Model2 → Default = Balance

For the two competing models do the following

a) With the whole data compare the two models (Use AIC and/or error rate).

b) Use validation set approach and choose the best model. Be aware that we have few people who defaulted in the data.

c) Use LOOCV approach and choose the best model.

d) Use 10-fold cross-validation approach and choose the best model.

Report validation misclassification (error) rate for both models in each of the three assessment methods. Discuss your results.

4. In the ISLR library load the Smarket dataset. This contains Daily percentage returns for the S&P 500 stock index between 2001 and 2005. There are 1250 observations and 9 variables. The variable of interest is Direction which is a factor with levels Down and Up indicating whether the market had a positive or negative return on a given day. Since the goal is to predict the direction of the stock market in the future, here it would make sense to use the data from years 2001 - 2004 as training and 2005 as validation. According to this, create a training set and testing set. Perform logistic regression and assess the error rate.

Attachment:- Assignment Files.rar