STAT5002 Introduction to Statistics – Semester 2, 2019 Assignment Notes and Instructions: • This assignment is structure assessed. It carries a weight of 8% towards your final mark for STAT5002. • You may discuss the questions with others but you must submit your own individual reports with your own working and words. • Presentation of your assignment is marked. • Show all R code or calculation used to answer the questions in your report. • Do NOT include your name in the assignment. • The report has to be submitted via Turnitin (Canvas) by Sunday 3rd November at 23:59pm. • If you have issues submitting your report, send your report to
[email protected]. • You may discuss the questions with others but you must submit your own individual reports with your own working and words. Written Report The written report is based on the Ames Housing data set (AmesHousing.txt, uploaded to Canvas in the folder AssignmentData along with the description file, DataDocumentation.txt) and should answer the 2 questions below. Show all R code or calculation used to answer the questions in your report. Your report should be no longer than 5 pages. Presentation of the report is marked. PLEASE SUBMIT A PDF VERSION OF YOUR REPORT ONLINE. Problem Suppose that the Ames Housing data is a representative sample of the houses in Ames. 1. If I select a random household from Ames, estimate the probability that (a) the selected household has a basement? (b) the selected household has a pool? (c) the selected household has a pool and a basement? 2. In this question consider the four variables SalePrice (Y ), Lot.Area (x1), Overall.Qual (x2) and MS.SubClass (x3). 1 (a) Consider the four simple linear regression model: Yij = 0 + 1x1i + ✏ij (1) log(Yij) = 0 + 1x1i + ✏ij (2) Yij = 0 + 1 log(x1i) + ✏ij (3) log(Yij) = 0 + 1 log(x1i) + ✏ij (4) where ✏ij ⇠ N(0, 2). By considering some diagnostic plots and the coe cient of determination, r2, explain which of the four model is the best. (b) Using only Y , x1, x2 and x3, what is the best (parsimonious) regression model that fits the data? Explain your conclusion. (c) Regardless of your answer in (b), consider the following model log(Yij) = 0 + 1x1i + 2x2i + ✏ij (5) assuming ✏ij ⇠ N(0, 2). i. Write the fitted model for (5). ii. Are there any outliers under model (5)? iii. You inspect a property with a lot area of 10000 feet2 with and an overall quality rated as “Excellent” using the same standard of rating in the Ames Housing data. What is your expected sales price under model (5)? 2