Simple Linear
Regression
Relationship Between Two
Quantitative Variables
If we can model the relationship between
two quantitative variables, we can use one
variable, X, to predict another variable, Y.
Use height to predict weight.
Use percentage of har
Normal Distributions
Normal
Normal Distribution
f(y)
y
f(y) =
E[Y] =
E[Y]
1
( y ) 2 / 2 2
e
, < y <
2
and Var[Y] = 2
and
G. Baker, Department of Statistics
G.
University of South Carolina; Slide 2
Normal Distribution
Characteristics
Characteristics
B
Multiple Regression
Slide 1
Multiple Regression
Consider situations involving two or more
independent variables.
This subject area, called multiple regression
analysis, enables us to consider more factors and
thus obtain better estimates than are possible
NAME (Please Print): Score: /20
Are you a graduate student ? Yes No
c ,1: an
HONOR PLEDGE (Please Sign):
Statistics 509: Fall 2013
Midterm H
You may use your calculator and one page of notes.
You may use the attached table of the cumulative distrib
Inferences on Population
Proportions
Proportions
Use Calculation from Sample to
Use
Estimate Population Parameter
Estimate
Population
(select)
Sample
(calculate)
(describes)
Parameter
p=?
(estimate)
Statistic
p = 63%
G. baker, Department of Statistics
G.
Inference on a Single
Inference
Mean
Mean
G. Baker, Department of Statistics
G.
University of South Carolina
Use Calculation from Sample to
Use
Estimate Population Parameter
Estimate
Population
(select)
Sample
(calculate)
(describes)
Parameter
p=?
(estima
NAME (Please Print):
Score:
/20
HONOR PLEDGE (Please Sign):
Statistics 509: Fall 2010
Midterm I
You may use your calculator and one page of notes.
Report all numerical answers to four correct significant figures.
You may use the attached table of the cumu
Inferences on Two
Populations
Populations
Two Samples from Independent Populations
An independent consumer group tested
radial tires from two major brands to
determine whether there was any difference
in the average tread life (thousands of
miles). The su
Longitudinal Data Analysis
Spring 2011
Monday/Wednesday 2:303:45 in LeConte College 210A
Instructor: Prof. Tim Hanson
Oce: LeConte 219C (777-3859)
email: hansont@stat.sc.edu
Website: http:/www.stat.sc.edu/hansont/stat771/
Oce hours: Monday & Wednesday 1:
Random vectors
X
1
X2
Recall that a random vector X = . is made up of, say, k
.
.
Xk
random variables.
A random vector has a joint distribution, e.g. a density f (x), that
gives probabilities
P (X A) =
f (x)dx.
A
Just as a random variable X has a mean E
Matrices and vectors
A matrix is a rectangular array of numbers. Heres an example:
2.3
1.4 17
A=
.
22.5
0
2
This matrix has dimensions 2 3. The number of rows is rst, then
the number of columns.
We can write the n p matrix X
x11 x12
x21 x22
X = x31 x32
Chapter 12: Population-averaged models for Bernoulli
repeated measurements
Example of repeated measures:
Data are comprised of several repeated measurements on the
same individual over time, e.g. Yij = 1 indicates acne outbreak
for patient i in month j ;
Stat 771 Homework 5, due Monday, April 25
We will consider data from a longitudinal study at Harvard of eects of air pollution on
respiratory illness in children. The children were examined annually at ages 7 through 10
and classied according to the prese
Stat 771 Homework 4, due Monday, April 18
We will consider data from an AIDS trial comparing two drugs, ddI and ddC (Abrams
et al., 1995). This was a multicenter, randomized, open label trial to compare ddI to ddC in
HIV-infected patients who were intoler
Stat 771, Fall 2011: Homework 3
Due Wednesday, March 23
The le insulin.dat contains longitudinal data from a study on m = 36 rabbits; 12 rabbits were
randomly assigned to each of 3 groups: group 1 rabbits received the standard insulin mixture, group 2
rab
Stat 771, Fall 2011: Homework 2
Due Wednesday, February 23
1. The le insulin.dat contains longitudinal data from a study on m = 36 rabbits; 12 rabbits were
randomly assigned to each of 3 groups: group 1 rabbits received the standard insulin mixture, group
Stat 771, Fall 2011: Homework 1
Due Wednesday, February 6
1. Let
A=
2
1
1
2
,B =
2
1
1
2
, and c =
1
3
.
(a) Find 3B.
(b) Find A B.
(c) Find AB.
(d) Find |A|.
(e) Find A1 .
(f) Is A full rank? Why or why not?
(g) Let x =
x1
x2
. Show
x Ax = 2(x2 + x1 x2 +
Section 13.2: Generalized Linear Mixed Models
Observations often occur in related clusters. Phrases like repeated
measures and longitudinal data get at the same thing: theres
correlation among observations in a cluster.
Chapter 12 dealt with an estimati