Author:
Christine Farr

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Homework 2 - STAT 462Fall 2015Please bring a hard copy of your homework to class and submit it at the beginning of the class or submit it via ANGEL before class. You could eithertype or write down your answers. Attach your code used to obtain your results. This is should be as neat as possible. Make sure your name is on it. .Deadline: 09/18/2015.Exercise 1 (20 points)Consider the Simple Linear Regression (SLR) model, Yi = β0 + β1 Xi + i .1. Suppose that the parameter values are β0 = 200, β1 = 5 and σ = 4.(a) Plot the regression line. Show the distribution of Y for X =10, 20, 40.(b) Explain the meaning of the parameters β0 and β1 . Assume thatthe scope of the model includes X = 0.(c) What is the implication for the SLR model if β1 = 0 so that themodel is Yi = β0 + i .2. Let be β0 = 3, β1 = −2 and σ = 1.25. Set the seed for random numbergeneration in R: before your code, type set.seed(123).(a) Create in R the observations for the predictor X: generate 100observation from a normal distribution with µ = 0 and σ 2 = 1.1(b) Generate the response values, Yi , using the SLR model Yi = β0 +β1 Xi + i .(c) Create a scatterplot of Y vs X and compute the correlation coefﬁcient of Y and X. Comment on your results.Exercise 2 (20 points)A substance used in biological and medical research is shipped by airfreightto users in cartons of 1000 ampules.Table 1: Airfreight breakagei Xi Yi11 1620932 1740 1253 2261 1370881 1592 1910 0 11

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