UCLA
Department of Statistics
STAT 100C: Linear Models
Problem Set 5
Spring 2017
Due: Thursday, May 18
Problem 5.1
Exercise 4.6(d) from the textbook
Problem 5.2
A new profit-sharing plan was introduced at an automobile parts manufacturing
plant last year.
Chapter 3:
A Review of Matrix Algebra and Important Results
on Random Vectors
Second approach
Starting with the last system of equations
we can approach the solution of the
system using matrix algebra. Express
that system in matrix form
n
n
n
xi y i
i=
STATS 100C: Linear Models
Spring 2017
Lecture 1: April 4
Lecturer: Arash Amini
1.1
Scribes: Eric Chuu
Review of Linear Algebra
Some topics that we should be familiar with:
Fundamental subspaces with matrix X Rnp
Rank-Nullity Theorem: The image of X: [Im
STATS 100C, Spring 2017
Midterm Exam
Total 100 points; Thursday, May 11, 4-5:15pm
Last Name
First Name
UID
Scores
Discussion (circle one) (8am) or (9am)
Instruction: This is a closed-book exam. You can use a calculator and one sheet of notes.
Chapter 4: M
(
University of California, Los Angeles
Department of Statistics
Statistics lOOC
Finally we get:
Instructor: Nicolas Christou
Homework 1 - Solutions
We can use the above t'9 random variable to construct a 95% confidence interval for Ji.l
Exercise 1
S
a. W
University of California, Los Angeles
Department of Statistics
Statistics 100C
Instructor: Nicolas Christou
Homework 3
EXERCISE 1
Data have been collected for 19 observations of two variables, Y and x, in order to run a regression of y on x, You are given
University of California, Los Angeles
Department of Statistics
Statistics lOOC
Instructor: Nicolas Christou
Homework 2
EXERCISE 1
A new profit-sharing plan was iIi-traduced at an automobile parts manufacturiflg plant last year. Both management and union
r
University of California, Los Angeles
Department of Statistics
Statistics 100C
Instructor: Nicolas Christou
Homework 5
Exercise 1
Please refer to
a. Test the overall significance of the model. The easiest way to do this is to find first SSE and SST.
Then
University of California, Los Angeles
Department of Statistics
Statistics lOOC
Instructor: Nicolas Christou
Homework 1
Exercise 1
Suppose that we want to test the following two hypotheses;
Ho: /1-1 /1-2 = 0
Ha: /1-1- /1-2> 0
To perform this test a sample
University of California, Los Angeles
Department of Statistics
Statistics 100C
Instructor: Nicolas Christou
Homework 4
Exercise 1
Consider the following simple regression model Yi = f30 + f31xi + Ei, for which E(Ei)
i - j, and var( Ei)
u 2 . The normal eq
Stat100C
Heteroscedasticity, autocorrelation and generalized least squares. General Introduction
What is heteroscedasticity and autocorrelation?
The standard multiple regression model can be represented as
Yi 0 1 X i1 2 X i2 . 9 X i9 i
(1)
where each i is
Multiple Linear Regression
A regression with two or more explanatory variables is called a multiple
regression. Rather than modeling the mean response as a straight line, as in
simple regression, it is now modeled as a function of several explanatory
vari
Chapter Two Part of the Slides
Dr. Akram Almohalwas
April 6, 2016
This is an R Markdown document. Markdown is a simple formatting syntax for authoring
HTML, PDF, and MS Word documents. For more details on using R Markdown see
http:/rmarkdown.rstudio.com.
UCLA
Department of Statistics
STAT 100C: Linear Models
Problem Set 3
Spring 2017
Due: Tuesday, May 2
Problems 3.10, 3.11, 3.14, 4.5 from the book, and the following:
N (, ) denote a multivariate normal distribution (MVN).
Problem 3.1
Let x = (x1 , . . . ,
UCLA
Department of Statistics
STAT 100C: Linear Models
Problem Set 4
Spring 2017
Due: Thursday, May 11
Exercises 4.2, 4.6(a)-(c), and 4.14(a)-(c) from the textbook, and the following
problems:
Hint: You can read the data into R for exercise 4.14 using the
UCLA
Department of Statistics
STAT 100C: Linear Models
Problem Set 1
Spring 2017
Due: Thursday, April 13
Problems 3.12, 3.13 from the textbook. (See the next page if you dont have the
book yet.)
Also do the following:
Problem 1.1
Consider the matrices
A=
UCLA
Department of Statistics
STAT 100C: Linear Models
Problem Set 2
Spring 2017
Due: Tuesday, April 25
Problem 2.1
Let X1 , X2 , X3 be random variables with zero-mean and unit variance: E(Xi ) = 0
and var(Xi ) = 1. Assume that the covariance between any
1
Chapter 4:
Continuing with Heteroscedasticity and Weighted Least Squares
Outline
1) What is it?
2) What are the consequences for our Least Squares estimator when
we have heteroscedasticity
3) How do we test for heteroscedasticity?
4) How do we correct a
Chapter Two
Simple Linear Regression
The Model
Simple Linear Regression:
y
Where
0
Important Assumptions:
1
x
Minimize means taking derivatives or partial
derivatives with respect to the parameters of
interest (in this case the slope and the yintercept).
Bond Data Example
Dr. Akram Almohalwas
Thursday, October 15, 2015
This is an R Markdown document. Markdown is a simple formatting syntax for authoring HTML, PDF, and
MS Word documents. For more details on using R Markdown see http:/rmarkdown.rstudio.com.
One-Way, Two-Way Anova and Ancova
Akram Almohalwas
November 2, 2015
This is an R Markdown document. Markdown is a simple formatting syntax for authoring HTML, PDF, and
MS Word documents. For more details on using R Markdown see http:/rmarkdown.rstudio.com
wheat rain document
Dr. Akram Almohalwas
April 18, 2016
This is an R Markdown document. Markdown is a simple formatting syntax for authoring HTML, PDF, and
MS Word documents. For more details on using R Markdown see http:/rmarkdown.rstudio.com.
When you c
1
Chapter 7: Model Selection:
First steps in model building/checking
Scatterplot matrix: examine that predictors are
linear functions of each other and the response
variable.
Scatterplot matrix: use for educated first step
guess as to the shape of the m
University of California, Los Angeles
Department of Statistics
Statistics 100C
Instructor: Nicolas Christou
Homework 7
\
Exercise 1
, Consider the models
\
y
= X/3 + E,
X*/3 + E",
and Y*
where E(E) = 0, COV(E)
(j2I, y* = ry, X*
Here orthogonal means r'r I
(
\
University of California, Los Angeles
Department of Statistics
Statistics lOOC
c. The output from
Instructor: Nicolas Christou
R;
> q <- laCy x)
> fHllQlll3;['y(q)
call:
Y - x)
Homework 2 - Solutions
R&aldWll.lst
EXERCISEl
Min
lQ
Median
-6.7'5822 -a.
STAT 100C
HW #2
Due (In-Class) Tuesday April 19, 2016
Spring 2016
Q1) Suppose that grades on a midterm and a final have a correlation coefficient of 0.5 and both
exams have an average score of 75 and standard deviation of 10.
(a) If a students score on th
STAT 100C
HW #3
Spring 2016
Due (In-Class) Tuesday April 26, 2016
Q1) Use the results seen in class to show that the line fit by the method of least squares passes
through the point x, y .
Hint: From class notes, one of the ways to specify the least squ