Problem Set 1
Due in class on paper, Wednesday October 8, 2014
This problem set includes a gentle introduction to R. If you are new to
R, I recommend spending a few hours at rst going over the early parts of
Dalgaards book. R is easy to nd and download. T
STATS 305 Notes1
Art Owen2
Autumn 2013
1
The class notes were beautifully scribed by Eric Min. He has kindly allowed his notes to be placed online
for stat 305 students. Reading these at leasure, you will spot a few errors and omissions due to the hurried
36
APPENDIX
B
Probability review
c A. B. Owen 2006, 2008
We review some results from probability theory. The presentation avoids
measure theoretic complications, using terms like sets and functions where
measurable sets and measurable functions respective
2
Linear Least Squares
The linear model is the main technique in regression problems and the primary
tool for it is least squares tting. We minimize a sum of squared errors, or
equivalently the sample average of squared errors. That is a natural choice
wh
2
Two or more categorical predictors
Here we extend the ANOVA methods to handle multiple categorical predictors. The statistician has to watch carefully to see whether the effects being considered are properly treated as fixed or random. Just turning the
CHAPTER
1
Introduction
Stat 305 is the rst course in our applied statistics sequence. It focusses on
regression problems, especially the linear model. We will get a deep understanding of linear regression and, in learning the limits of linear regression,
1
One categorical predictor at k levels
Here we look at the regression model in the case where there are k 2 groups. We have a single predictor X cfw_1, 2, . . . , k. For observation we get X which tells us which group and response Y R. Instead of working