STAT331 Lecture Notes - Lecture 1: Simple Linear Regression, Bias Of An Estimator, Independent And Identically Distributed Random Variables
1 Oct 2016
School
Department
Course
Professor
Document Summary
Stat 331/syde 334 applied linear models exercise 1. Let x be the distance to a galaxy, in millions of light years, and let y be its velocity, in thousands of miles per second. The astronomer hubble noted that y is approximately proportional to x. The constant of proportionality is hub- ble"s constant, which has to be estimated from empirical data. Hubble"s constant is used to estimate the age of the universe and determine whether the universe will continue expanding or eventually contract. Hubble proposed to consider a no-intercept relationship: yi = 1xi + i, where i iid. , n. (a) derive 1, the least squares estimator of 1. (1) (b) show that 1 is an unbiased estimator of 1. (c) let ri = yi yi = yi 1xi denote the estimated residual. Does the relationship look approximately linear? (e) fit a simple linear regression model yi = 0 + 1xi + i, N (0, 2), i = 1, .
