Answer Happy

11. (15 pts) Given the following data, a researcher wants to fit the model Y₁ =B X₁ + . The researcher hypothesizes from previous experiments that ẞ is either 3, 4, or 5 and desires to fit a robust regression using LAD (choose B that minimizes the sum of the absolute value of the residuals). i 1 2 X 2 2 2 3 4 5 5 5 6 5 Y 4 6 7 17 18 20 a. Find the LAD estimator for B keeping in mind the researcher's knowledge from past experiments. b. Researcher #2 is given the same data and the same model but has no previous experience regarding ß. Researcher #2 decides to perform a robust regression using a different technique. This researcher estimates ß by fitting the straight line connecting the median of the Y's at X=2 to the median of the Y's at X=5. Compute this researcher's estimate of B. c. Researcher #2 now wants to compute a 95% Confidence Interval on ß using bootstrapping with the number of bootstrapped samples (B) = 300. Compute (no need to graph) the empirical distribution function Fhat of the residuals from Researcher #2's fitted model to start the Bootstrapping in Regression process for Researcher #2. d. Researcher #2 continues the bootstrapping process by generating a sequence of 1800 (=300*6) random numbers between 1 and 6. Here are the first six random numbers generated: 3,1,1,4,6,2. Compute the first bootstrapped sample estimate of B for the researcher.