ISyE 6414: Regression Analysis
HW#2 (due in class at the beginning of class on Friday, May 24, 2013)
There are 3 questions, and please look at both sides. Total points = 20 + 20 + 40 = 80 pts.
(It is OK to use R or other statistical softwares for this hom
ISyE 7401
Advanced Statistical Modeling
Spring 2013
HW #3 (due in class on February 6, Wednesday)
(There are 4 questions, and please look at both sides)
Problem 1. Suppose that each setting xi of the independent variable in a simple least squares
problem
ISyE 7401
Advanced Statistical Modeling
Spring 2013
HW #5 (due in class on March 06, Wednesday)
(There are four questions, and please look at both sides)
Problem 1. The dataset wbca (in the library(faraway) in R) comes from a study of breast cancer in Wis
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Ne
ISYE 7401A
Homework 5 Solutions
Spring 2016
Problem 1
a) Shorts data
If we consider A and B as factor variables and fit a logit GLM model
considering main effects, interactions and quadratic effects for variables
C-H, we get the following:
Call:
glm(formu
ISYE 7401A
Homework 2 Solutions
Spring 2016
Problem 1
The key idea is the write our models together as y = X + , where:
y
y= 1
y2
X1 0
X=
0 X2
= 1
2
= 1
2
and follow the derivations provided in the class for the generalized likelihood
ratio test. Fr
ISYE 7401A
Homework 6 Solutions
Spring 2016
Problem 1
In this split-plot problem we have two factors, recipe and temperature, where
recipe was applied to the whole plot and temperature was applied to the splitplot. Fit a linear mixed model with batch as a
ISYE 7401A
Homework 4 Solutions
Spring 2016
Problem 1
After taking the log transformation, note that
y
log( ) = x.
x
Thus we can fit a linear regression model using the R code
> lm(log(y/x)~x-1)
and use the estimated slope as an initial guess for .
Proble
ISYE 7401A
Homework 1 Solutions
Spring 2016
Problem 1
From the problem specification:
1 x1 x
.
X = .
.
1 xn x
Therefore:
P
y
n P 0
i
0
i
XX=
and X y = P
)yi
0
)2
i (xi x
i (xi x
0
From this it follows:
y
= (X 0 X)1 X 0 y =
P
!
x)(yi
y)
i (x
Pi
x)
i (x
ISYE 7401A
Homework 1
Due February 2, 2016
= (X 0 X)1 X 0 y,
1. Let yi = 0 + 1 (xi x) + i for i = 1, , n. Using the formula
show that
0 = y
Pn
(x x)(yi y)
i=1
Pn i
1 =
.
)2
i=1 (xi x
= 2 (X 0 X)1 , show that
Now using the formula var()
var(0 ) =
2
n
2
ISYE 7401A
Homework 4
Due March 29, 2016
1. Suppose you want to fit the following nonlinear regression model to the data: y =
xex + . Explain how linear regression can be used for approximately estimating the
unknown parameter . Answer using R commands.
2
ISyE 7400
Homework 2
Due October 6, 2016
1. Show that
R(x) = ekxk +
2
1
, x Rd ,
1 + kxk2
is a strictly positive definite radial basis function for > 0.
2. Consider the model
s(x)(Y (x) ) = Z(x),
where s(x) = r(x)0 R1 1, and Z(x) GP (0, 2 R(). Find the po
ISYE 7401A
Homework 3
Due March 15, 2016
1. Using ozone data (in faraway library), fit a model with O3 as the response and temp,
humidity, and ibh as predictors. Use the Box-Cox method to detrmine the best transformation on the response.
2. For the prosta
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