Extrapolation: The file swim.dat contains data on the amount of time, in seconds, it takes each of
Question:
Extrapolation: The file swim.dat contains data on the amount of time, in seconds, it takes each of four high school swimmers to swim 50 yards. Each swimmer has six times, taken on a biweekly basis.
a) Perform the following data analysis for each swimmer separately:
Fit a linear regression model of swimming time as the response and week as the explanatory variable. To formulate your prior, use the information that competitive times for this age group generally range from 22 to 24 seconds.
For each swimmer j, obtain a posterior predictive distribution
for Yj∗, their time if they were to swim two weeks from the last
recorded time.
swim.dat
23.1 23.2 22.9 22.9 22.8 22.7 23.2 23.1 23.4 23.5 23.5 23.4 22.7 22.6 22.8 22.8 22.9 22.8 23.7 23.6 23.7 23.5 23.5 23.4
b) The coach of the team has to decide which of the four swimmers will
compete in a swimming meet in two weeks. Using your predictive dis- tributions,computePr(Yj∗ =max{Y1∗,...,Y4∗}|Y))foreachswimmer j, and based on this make a recommendation to the coach.
Business Analytics Data Analysis and Decision Making
ISBN: 978-1305947542
6th edition
Authors: S. Christian Albright, Wayne L. Winston