statistics and R Programming paper

Discuss two or more of the following questions, in your own words. You may choose to address

any two, three, or even all questions but should target 3-4 pages of text in total (not

counting figures, tables, and references). Upload your answers to the final section of the class

Moodle page as a single narrative document in pdf format. You may, and are encouraged to,

illustrate your answers using R, but that's no substitute for lucid natural language explanations.

To preserve the natural flow of the narrative, figures and tables should be embedded into the

document near their first mention. Any supplementary files like code or data should be

referenced in the text and separately uploaded. You may use books, articles, notes, search

engines, or computers, but may not solicit or receive direct assistance from other human beings.

Cite sources if you use them. For the first three questions you may want to illustrate technical

detail using R, discuss practical aspects that are important for applications, and theoretical

aspects of the subject.

Question 1. Construct a dataset with at least 8 observations and 3 variables (y, x1, and x2) such

that least squares linear regression of y versus x1 produces y = 2x1 + e1 and regressing y versus

x1 and x2 produces y = -2x1 + x2 + e2. How might you interpret the relationship between y and

x1? Show your work in R.

Question 2. Write a short essay explaining the p-value and show to calculate it on a dataset of

your choice. Show your work in R.

Question 3. Write a short essay explaining the four assumptions of linear regression and show

how to test them on a dataset of your choice. Show your work in R.

Question 4. Write a short essay on the subject of Bayes theorem and illustrate its use in an

application of your making.