AMS 545/CSE 555 (Spring, 2016)
Joe Mitchell
COMPUTATIONAL GEOMETRY
Homework Problem # 1 Solution Notes
(1). We defined a set Q to be convex if for any two points p and q in Q the line segment pq also
lies in Q.
Let us define the notion of rectangle-convex
AMS 573
HW2 Solution
2.4 a. (i) 1085/56708; (ii) 703/441942.
b. (i) 703/1788; (ii)441239/496864.
c. Choose injury status as the response variable. Difference of proportions =
"#$%
%&'#$
*",)+
#.#"+
'#)
*"+*,
=
0.019 0.00159 = 0.01741. =
= 12.01. Odd r
AMS 573 HW5 Solution
5.15,5.17,5.19,5.25,5.30, 5.32,5.35, 5.36
5.15
a. Black defendants with white victims had estimated probability
5.17
a. For = 2, = 2 = 2, we have = 1
! ",.*
! "#.%&'()*.+,+
-.! "#.%&'()*.+,+
= 0.23
= 5.26 + 0.17 + 0.91 + 3.98 =
0.2,
1
CATEGORICAL DATA ANALYSIS, 3rd edition
Solutions to Selected Exercises
Alan Agresti
c
Version August 3, 2012, Alan
Agresti 2012
This file contains solutions and hints to solutions for some of the exercises in Categorical
Data Analysis, third edition, by
HW6 Solution
5.17, 5.19, 5.35, 6.22, 6.23, 6.31, 6.32
)2
(1
32. Since 2 = (1
=
)
1
2
or 2 = (1
=
)
,
1
so when nears 1 it is either small
positive or large negative, and
when nears 0, it is either small negative or large positive.
2.2
a. |
b. We use B to denote black, and W to denote white. Then,
( = | = ) =
( = | = )( = )
( = | = )( = ) + ( = | = )( = )
where ( = ) = 1 ( = ). So we may need ( = ) or ( = ), which can be
estimated by the ratio of race of victim.
1710
200
1710+200
45
0'61
3 3 (a) log(9)= 111;(5M ) = 10941.59 = 3.728
(1060099): +=0.746
711211211122
(c) 95% CI. for 1095 is 1099 i 2260090), so CI. for 0 is [5 Ir exp (256(log), 5 t
2 2
exp (2560093) = [10.222, 169.223]. Since the number of person whose political party I
Chapter2: Describing two-way contingency tables
A contingency table displays frequencies for a cross classification of
categorical random variables. Ex: A general social survey
Belief in after life
Yes
No
Female
435
147
Male
375
134
Notations for general
Chapter4: Generalized Linear Models (GLM)
Components
[
1. Random component: identify response variable y. Assume (1 , , ) are
independent from a distribution that is natural exponential family.
( | )=a( )b( )exp[ ( )]
( ) is called the natural parameter
2
Practice Exam 1
AMS 573
Categorical Data Analysis
Name: _
SBU- ID: _
On my honor, I have neither given nor received unauthorized aid on this examination.
Signature: _ Date: _
Instruction: There are 5 problems with 50 total points. You must show your work
Chapter 8: Log-linear Model
Two-way contingency tables IxJ
X and Y independent
= + + all i,j
= = + +
log = log + log + + log + = + + all i,j
This is a log-linear model for
The general log-linear model is
log = + + +
Add constraints to make model ident
Chapter 6: Building and Applying Logistic
Regression
Strategies for model selection:
Compare models to answer questions posed by study (confirmatory)
Exploratory to get information about which predictors may be useful. e.g.
using forward selection or ba
HW7 Solution
8.1, 8.31, 8.32, 8.37, 8.38, 9.1, 9.18
8.1
a.
1
2
=
1
3
2
3
= 1 + 1 1 + 1 2 2 2 1 2 2
= 0.23 + 0.791 + 0.812
b. for 1 is 1.044 1.960.259 = [0.536,1.552]
for exp(1 ) is [exp(0.536) , exp(1.552)], which is [1.71,4.72]
The odds ratio does n
Chapter2: Describing two-way contingency tables
A contingency table displays frequencies for a cross classification of
categorical random variables. Ex: A general social survey
Belief in after life
Yes
No
Female
435
147
Male
375
134
Notations for general
AMS 573
Categorical Data Analysis
Spring 2015
1. For a 2x2 contingency table below:
(a) Show that its odds ratio 6 - 1 corresponds to the independence of 1ts row and column variables. (5
PointS) L 7:] 5.07941? WWW? (1M, WARAIA?
><1T=) C, 7711 EJ,W:Z-'i-
AMS 573
HW1 Solution
1.1 a. Nominal; b. Ordinal; c. Interval; d. Nominal; e. Ordinal; f. Nominal.
1.3 =
+
= (1 )
1.7 a. = 01 , (0 < < 1)
b. The estimate of is = 1.0 . Wald test statistic is 7 =
898:
8(;98)/=
= , it follows a
standard normal distributi
Chapter 6: Building and Applying Logistic
Regression
Strategies for model selection:
Compare models to answer questions posed by study (confirmatory)
Exploratory to get information about which predictors may be useful. e.g.
using forward selection or ba
AMS573 Categorical Data
Analysis
Instructor: Prof. Song Wu
Chapter 1: Introduction
Methods for response (dependent) variable Y having scale that
is a set of categories
Explanatory variables may be categorical or continuous or
both
Categorical: Continge
Chapter2: Describing two-way contingency tables
A contingency table displays frequencies for a cross classification of
categorical random variables. Ex: A general social survey
Belief in after life
Yes
No
Female
435
147
Male
375
134
Notations for general