36-226 Introduction to Statistical Inference
Final Solutions
May 8th, 2012
You must show all of your work and/or explain your steps in order to get full credit or be considered
for partial credit. This is a closed book/closed notes exam. You may use the f

Unix
The statistical package Splus is only available on campus for Unix machines (excluding
Linux machines). You will nd a large number of Sun computers in Wean 5201, 5202,
and 5204, and possibly other locations on campus. From the main entrance to Wean

36-401 Class Notes and Exercise for 9/18/01
Simple Linear Regression
Model:
Design or covariate space
Estimate/Prediction:
Residual error:
N
Estimation method: Least Squares
RSS
Minimization of RSS gives
Residual Variance
RSS
estimated by
is residual stan

36-463/663: Multilevel & Hierarchical Models
Fall 2012
HW09 Due Tue 11 Nov 2014
Announcements
Please submit this hw as a pdf le on blackboard
Reading:
Lynch: Chapter 9 is worth reading/skimming on your own, since it has a lot of examples of setting up

36-401 Class Notes and Exercise
Regression Criticism I: Checking the Assumptions
The regression model is
We check assumptions by thinking about the experimental design, viewing plots, and sometimes
by performing special statistical tests.
Checking the ass

36-463/663: Multilevel & Hierarchical Models
Fall 2014
HW10 Due Wed 26 Nov 2014
Announcements
The datasets we will we will use for this assignment are already installed in the lme package. For
example, to use the Pastes data set, after getting the lme pa

36-401 Class Notes
Data Reduction II: Principal Components and Factor Analysis
Some Technical Background on Principal Components
Recall that the principal problem with collinearity in the regression problem
(1)
is a technical one: The least-squares estima

21-256 Exam 2: Partial Dierentiation (sample)
Wednesday 18th June, 10:3011:20am
Instructions (please read carefully)
This test is split into three sections of four questions each:
Section A: Partial dierentiation and the chain rule
Section B: Tangent pl

18-447 Intro to Computer Architecture, Spring 2012
Midterm Exam I
Instructor: Onur Mutlu
Teaching Assistants: Chris Fallin, Lavanya Subramanian, Abeer Agrawal
Date: March 7, 2012
Name:
SOLUTION
Problem I (50 Points)
:
Problem II (50 Points)
:
Problem III

36-226 Introduction to Statistical Inference
Midterm 1 Solutions
February 19th, 2015
1. Let Xi , i = 1, 2, ., n be i.i.d. N (0, 1).
For the below, can cite known properties unless otherwise indicated.
Can also cite results from previous parts. Always incl

36-226 HOMEWORK 3
Due: Friday 2/5/16 at 9:30am in class
Remember to show all work; just writing down the answer will not receive credit.
1. Sometimes we re-write distributions as functions of other random variables to simplify
the problem. One situation w

36-401 Homework #2 Due Thursday Sept 20
1. (10 pts) The data set Prestige.dat (available from the data section of the 401 website;
see also Prestige.cbk) is extracted from the 1971 Census of Canada, and reports various
attributes (average income, educatio

1. Determine if the following statements are true or false. Circle your response.
(a) (2 pts) The condence interval for ,u. is narrower for larger sample size n. @or False)
(b) (2 pts) The condence interval for n is narrower for larger condence level C. (

36-226 Introduction to Statistical Inference
Spring 2015
Instructor: Rebecca Nugent
Baker Hall 232C
rnugent@stat.cmu.edu
http:/www.stat.cmu.edu/rnugent
Ofce Hours: TBA
Teaching Assistants:
Alex Reinhart (Head), Francesca Matano, Brendan McVeigh, Jerzy Wie

Homework 10
Problem One - Crossed Random Eects
The Penicillin data set in library(lme4) is derived from Table 6.6, page 144, of Davies and Goldsmith
(1972), where it is described as coming from an investigation to
assess the variability between samples of

Homework 7
3
x2
1.
1 x2 dx
x
dx
36 x2
2.
x
dx
1 + x2
0
3.
t2
1
t5
dt
+2
4.
0
6.
x
dx
1 + x2
5.
/2
7.
0
cos(t)
2
1 + sin (t)
dt
x2 9
dx
x3
8.
dt
t2 t2 16
9. Find the volume of the solid of revolution obtained by rotating about the line x = 1 the region und

Homework 8
Part I.
0.6
0
3.
x2
dx
9 25x2
2.
5 + 4x x2 dx
x
dx
2+x+1
x
4.
x2 + 1
dx
(x2 2x + 2)2
1.
Part II. In this part, we will review polynomial division. For each of the following, write the rational
function f (x)/g(x) as d(x) + r(x)/g(x) where the d

Exam 3 review sheet
Exam 3 will cover sections 5.1,5.2, and 5.3 of Walker, and sections 12.6, 14.1,
14.2, 14.3, 14.4, 14.5, 14.6 of Stewart. Only those topics that I covered in
lecture will be included on the exam - consult your class notes. I may also
in

36-309/749
Lecture 7: Power
10/21/2014
1) Introduction to Power (12.1)
a) Common mistaken impression: After seeing the p-value, and choosing retain vs.
reject based on =0.05, we know the chance that we have made a mistake.
b) What the omniscient see:
c) R

36-309/749
Lecture 9: Repeated Measures I
11/4/2014
1) Overview of Repeated Measures
a) Definition: more than one measurement is made on the same subject either over time
with one treatment or with different treatments. One synonym is within-subjects (stu

36-309/749
Lecture 11: Mixed Models
11/18/2014
1) Independent Errors Assumption
a) Errors are deviations of individual observed outcomes from the population mean of all
observed outcomes that have the same levels of all of the explanatory variables. They

36-309/749
Lecture 8: Contrasts
10/28/2014
1) Contrasts (in general) (13.1)
a) Context: An ANOVA rejects the overall null hypothesis that all k (>2) means of some
factor are not equal. Contrasts let us ask which are significantly different?
b) Terminology

36-226 Introduction to Statistical Inference
Midterm 1
February 19th, 2015
You must show all of your work and/or explain your steps in order to get full credit or be considered
for partial credit. This is a closed book/closed notes exam. You may use the f