University of California, Los Angeles
Department of Statistics
Statistics 100C
Instructor: Nicolas Christou
Homework 1
Exercise 1
A new profit-sharing plan was introduced at an automobile parts manufacturing plant last year. Both
management and union repr
University of California, Los Angeles
Department of Statistics
Statistics 100C
Instructor: Nicolas Christou
Exam 1
26 April 2013
Name:
Problem 1 (25 points)
Consider the simple regression model
yi = 0 + 1 xi + i
with E(i ) = 0, var(i ) = 2 , and cov(i , j
University of California, Los Angeles
Department of Statistics
Statistics 100C
Instructor: Nicolas Christou
Homework 2
EXERCISE 1
Data have been
for 19 observations of two variables, y and x, in order to run a regression of y on x. You are given
Pcollecte
Stats 100C: HW2 Solution
Exercise 1
a. The scatter plot is
120
y
90 100
10
15
20
x
b.
14801.2 1 (133.9)(965)
Sxy
9
1 =
=
= 1.67.
Sxx
2258.73 1 (133.9)2
9
965
133.9
0 = y 1 x =
1.67
= 82.38.
9
9
Therefore the tted regression line is: y = 82.38 + 1.67x.
University of California, Los Angeles
Department of Statistics
Statistics 100C
Instructor: Nicolas Christou
Comparing regression equations
Using two dierent data sets on the same variables we build the following two regression models
y1
= X1 1 +
1
y2
= X2
University of California, Los Angeles
Department of Statistics
Statistics 1000 Instructor: Nicolas Christou
Exam 1
26 April 2013
Sou/("Tram
Name:
Problem 1 (25 points)
Consider the simple regression model
yi=o+m+ci
with E(e.-) = 0, var(e.-) - 0'2, and cov
University of California, Los Angeles
Department of Statistics
Statistics 100C
Instructor: Nicolas Christou
Homework 1
Exercise 1
Show that the error sum of squares SSE = e0 e, is equal to the following expressions:
0 X0 X
= Y0 Y
0 X0 Y = Y0 Y
0 X0 Y.
University of California, Los Angeles
Department of Statistics
Statistics 100C
Instructor: Nicolas Christou
Regression analysis in matrix form - summary
The model:
Y = X +
Where:
Y=
y1
y2
y3
.
.
yn
,
X=
1
1
1
.
.
1
x1
x2
x3
.
.
xn
,
=
0
1
,
=
1
2
3
.
.
University of California, Los Angeles
Department of Statistics
Statistics 100C
Instructor: Nicolas Christou
Homework 2
Exercise 1
Consider the regression model y = X + , with E() = 0, cov() = 2 I, and N (0, 2 I). Let
= (X0 X)1 X0 y, and y
= Hy. Show tha
University of California, Los Angeles
Department of Statistics
Statistics 100C
Instructor: Nicolas Christou
Homework 1
Exercise 1
Show that the error sum of squares SSE = e0 e, is equal to the following expressions:
0 X0 X
= Y0 Y
0 X0 Y = Y0 Y
0 X0 Y.
University of California, Los Angeles
Department of Statistics
Statistics 100C
Instructor: Nicolas Christou
Homework 4
Exercise 1
Answer the followig questions:
a. You are given the two multiple regressions:
y on x1 , x2 , x3 , x4 , x5 with R2 = 0.6991
y
University of California, Los Angeles
Department of Statistics
Statistics 100C
Instructor: Nicolas Christou
The fitted values and their variance-covariance matrix
The variance-covarince matrix of the fitted values can be expressed as follows:
= Xcov()X
University of California, Los Angeles
Department of Statistics
Statistics 100C
Instructor: Nicolas Christou
Homework 2
EXERCISE 1
Data have been
for 19 observations of two variables, y and x, in order to run a regression of y on x. You are given
Pcollecte
University of California, Los Angeles
Department of Statistics
Statistics 100C
Instructor: Nicolas Christou
Homework 7
Exercise 1
Consider the models
Y = X + , and Y = X + ,
where E() = 0, cov() = 2 I, Y = Y, X = X, = , and is a known n n orthogonal matri
Chapter 4 Model Adequacy Checking
Ray-Bing Chen
Institute of Statistics
National University of Kaohsiung
1
4.1 Introduction
The major assumptions:
1. The relationship between y and xs is linear.
2. The error term has zero mean.
3. The error term has const
Ordinary Least Squares Regression
PO7001: Quantitative Methods I
Kenneth Benoit
24 November 2010
Independent and Dependent variables
I
I
A dependent variable represents the quantity we wish to
explain variation in, or the thing we are trying to explain
Ty
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,
COPYRIGHT
Abraham, B. and Ledolter, J.
Introduction to Regression Modeling
Belmont, CA: Duxbury Press, 2006
Abraham
AbrahamC01
November 8, 2004
1
0:33
Introduction to
Regression Models
1.1 INTRODUCTION
Regression modeling is an activity that leads to a ma
Chapter 2 Discussion Section
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.
Wh
University of California, Los Angeles
Department of Statistics
Statistics 100C
Instructor: Nicolas Christou
Homework 1 - Solutions
Exercise 1
0 (Y X).
This can be written as:
We begin with SSE = e0 e = (Y X)
0
0 (Y X)
= (Y0
X0 )(Y X)
=
SSE = e0 e =
Statistics 1000
Exercise 1
Consider the regression model
Iii = 50 + [31111; + 5213214 5333i + .3427 + 55555; + 5636: + in i= 1, - - - a 71-
Also, E(e.-) = 0, E(6iJ-) = 0 for i 7.- j, and var(e.-) 2 0'2. Dene the matrix C and the vector 7 using the
notatio
University of California, Los Angeles
Department of Statistics
Statistics 100C
Instructor: Nicolas Christou
Homework 1
Exercise 1
Show that the error sum of squares SSE = e0 e, is equal to the following expressions:
SSE = Y0 Y
0 X0 X = Y0 Y
0 X0 Y = Y0 Y
University of California, Los Angeles
Department of Statistics
Statistics 100C
Instructor: Nicolas Christou
Homework 2
Exercise 1
Consider the regression model y = X + , with E() = 0, cov() = 2 I, and N (0,
= (X0 X) 1 X0 y, and y
= Hy. Show that y
and
University of California, Los Angeles
Department of Statistics
Statistics 100C
Instructor: Nicolas Christou
Homework 5
Exercise 1
Consider the models
Y = X + , and Y = X + ,
where E() = 0, cov() = 2 I, Y = Y, X =
Here orthogonal means 0 = I. Show that:
a.
University of California, Los Angeles
Department of Statistics
Statistics 100C
Instructor: Nicolas Christou
Homework 4
Exercise 1
Answer the followig questions:
a. You are given the two multiple regressions:
y on x1 , x2 , x3 , x4 , x5 with R2 = 0.6991
y