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Unformatted text preview: STAT 231 Fall 2009 - Assignment 1 SOLUTION This assignment is out of 60 marks, each mark is denoted by  in the following mark scheme. Only give marks for the parts of the questions indicated. Please mark in RED INK and give a brief indication to the student of why you have taken off marks when you do. The solutions are in BOLD, everything else was on the question sheet. Please put your initials on top of each solution you mark so that we can trace back if the student has questions. This assignment is to be handed in at the start of the lecture of Tuesday 6 October . Some of these questions use R and so it is recommended that you work though the tutorial at http://www.stats.uwaterloo.ca/stats_navigation/StatSoftware/R/ You will need to cut and paste graphics from the R session into Word, which can then be edited, commented on and handed in. Do not hand in R code, or a print out of the R session unless asked for. Note that working with unfamiliar packages can take much longer than you might have planned for, so do not leave this work to the last minute. 1. Do not mark Do Question 1 of Section 1.6.1 in the Lecture Notes. 2. Do not mark Do Question 2 of Section 1.6.1 in the Lecture Notes. 3. [6 marks] Do Question 2 of Section 1.6.2 in the Lecture Notes. The plots for this question are -2 2 4 6 8 10 5 10 15 20 (a) Plot of raw data X Y 2 4 6 8 10 2 4 6 8 10 (b) Plot of ranks rank(X) rank(Y) Figure 1: Figures for Question 3 [4; 2 marks for each plot including labels. ] 1 The correlation in the first case is . 964 indicating a very strong linear relationship, but after taking ranks this drops to . 405  4. Do not mark Do Question 3 of Section 1.6.2 in the Lecture Notes. 5. [9 marks] The function logit( p ) = log p 1- p for p (0 , 1) will be used in this course. This question reviews some properties. [This is log base e ] (a) [5 marks] Show that logit( p ) is a monotonically increasing function Its is required to show that d dp logit( p ) > for all p (0 , 1)  the derivative is 1- p p 1- p- p (- 1) (1- p ) 2 = 1 p (1- p )  which is positive  for all p in range since p > and p < 1 [1; for explanation of positivity. (b) Do not mark Show that lim p logit( p ) =- and lim p 1 logit( p ) = + (c) Do not mark Using the above results sketch the function logit( p ) for 0 < p < 1....
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- Spring '08