STAT 100C
UCLA Department of Statistics
Midterm
Name: _KEY_
April , 28, 2016
SID:_
Start with the show your work part first.
Part A: 18 Multiple Choice Questions (Each worth 2 point) Total of 30 points
4. In the context of simple linear regression, the po
STAT 100C
HW #6
Due (In-Class) Tuesday May 31, 2016
Q1) Consider the following Regression model:
Spring 2016
Q2) We have data on IQ scores of identical twins, one raised in a foster home and the other raised by
natural parents. The social class of the par
STAT 100C
HW #4 Hints
Due (In-Class) Tuesday May 10, 2016
Q1) 1.- Consider the following set of hypothetical data
Y
X1
X2
-10
1
1
-8
2
3
-6
3
5
-4
4
7
-2
5
9
0
6
11
2
7
13
4
8
15
6
9
17
8
10
19
10
11
21
Suppose you want to fit the model
yi 0 1x1i 2 x2i i
University of California, Los Angeles
Department of Statistics
Statistics 100C
Instructor: Nicolas Christou
Uncorrelated predictors - example
The table below contains data for a small scale experiment on the eect of work crew size (x1 ) and level of
bonus
University of California, Los Angeles
Department of Statistics
Statistics 100C
Instructor: Nicolas Christou
Inclusion/exclusion of a predictor in multiple regression
Consider the usual multiple regression model in matrix form
Y = X +
Suppose that X is par
University of California, Los Angeles
Department of Statistics
Statistics 100C
Instructor: Nicolas Christou
Centering and scaling
Let k be the number of predictors. The usual multiple regression model is
yi =
0
+
1 xi1
+
2 xi2
+ . +
k xik
+ i .
After we a
University of California, Los Angeles
Department of Statistics
Statistics 100C
Instructor: Nicolas Christou
Multicollinearity
Using the centered and scaled model we showed that the variance covariance matrix of (0) is equal to
2 1
2
var(0) ) = R . We want
University of California, Los Angeles
Department of Statistics
Statistics 100C
Instructor: Nicolas Christou
Centering and scaling
Let k be the number of predictors. The usual multiple regression model is
yi =
0
+
1 xi1
+
2 xi2
+ . +
k xik
+ i .
After we a
(
(
(
University of California, Los Angeles
Department of Statistics
Statistics lOOC
cov(13) = ,2(X'X)-1 = ,'
Instructor: Nicolas Christou
Homework 4 - Solutions
Of course
Exercise 1
. (fJo)
13,
(nE'=lXi
=
",2
(t
is unknown and needs to be estimated by
d.
(
University of Califurnia, Los Angeles
Department of Statistics
data. from homework 5, exercise 4:
a <- read. table('http:/wl,l. stat.ucla,edu/ nchristo!statisticsl00C/restaurant. txt", l1eacier"'TRUE)
P
Statistics lOOC
Instructor: Nicola. Christou
Homew
STAT 100C
HW #4
Due (In-Class) Tuesday May 10, 2016
Q1) 1.- Consider the following set of hypothetical data
Y
X1
X2
-10
1
1
-8
2
3
-6
3
5
-4
4
7
-2
5
9
0
6
11
2
7
13
4
8
15
6
9
17
8
10
19
10
11
21
Spring 2016
Suppose you want to fit the model
yi 0 1x1i 2
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 #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
Stat100C
Chapter 5
Comparison of several treatments
What are indicator or dummy independent variables
Categorical variables tell us what type of group an observation belongs to. For example, the
categorical variable sex tells us whether an observation bel
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=
Chapter 1
Introduction to Regression Models
Regression modeling is an activity that leads to a mathematical
description of a process in terms of a set of associated variables.
The values of one variable frequently depend on the levels of several
others.
T
Chapter Two
Simple Linear Regression
The Model
Simple Linear Regression:
y Where
0 1 x
Important Assumptions:
Minimize means taking derivatives or partial
derivatives with respect to the parameters of
interest (in this case the slope and the yintercept).
Chapter 4:
Multiple Linear Regression
Multiple Regression Model
A regression model that contains more than one
regressor variable.
Multiple Linear Regression Model
A multiple regression model that is a linear function of
the unknown parameters b0, b1,
STAT 100C
HW #3 KEY
Due (In-Class) Tuesday April 26, 2016
Spring 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
STAT 100C
HW #1
Spring 2016
Q1) Given the following scenario and short data with a ready calculated sums:
Q2) Basic Mathematical proofs:
Q3) Consider the matrix below. Just show your work by hand -no R codes here-. How would you
write an R code to solve t
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
University of California, Los Angeles
Department of Statistics
Statistics lOOC
Instructor: Nicolas Christou
Homework 7 - Solutions
Exercise 1
We are given:
Y
Xf3+e, and Y*
where E(e) = 0, cov(ti)
orthogonal means r'r I.
X*f3+e*,
(/21,
Y*
= rY,x* = rX,e* =
University of California, Los Angeles
Department of Statistics
Statistics lOOC
Nicolas Christou
Homework 3 - SolutiGns
EXERCISE 1
We are given
8y
= 10,
'V
.
C;:;,
"
1
E:!l (Yi - Yi)2 = 180.
a. The proportion of the variation in Y that can be explained by
(
\
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.
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
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
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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.