x
( t x )1 x t y
b0
b1 =B=
bk
()
For multiple regression:
= a + bx = b0 + b1x1 +b2x2 + + bkxk
*
XB =
x
1 t
x ( t x) x y=
Hat Matrix =
HY =
x
x ( t x)1 x t
*
()( )( )
e1
y1
1
e 2 = y 2 2 = y = yHY
en
yn
n
( y )2
S y=
=measures the spred of the yvalues .
ECON 337 Assignment 1
Fall 2007
Consider the following data set:
x1 2 5 5 7 10
x2 28 23 27 18 11
x3 23 45 12 54 37
y 123 150 164 205 214
1
If y is regressed on x1, find the following using the matrix method. Feel free to use EXCEL to help wit
ECON 337
Introductory Econometrics I
Instructor:
K.MacKenzie, Leacock 435, 514-398-4400, local 00017
[email protected]
Hours: See post on WEB-CT or office door
Textbook:
Some material will be on WEB CT. Introduction to Econometrics by Stock and
Soci709 (formerly 209) Module 4 Matrix Representation of Regression Model
Franois Nielsen March 22, 2006
1 Introduction
Module 4 covers the following topics
properties of, and operations on, matrices and vectors matrix representation of the linear regre
a)
b)
c)
d)
Q- NcR how to use thisss?
RULE=right hand left hand
Can have negetives
If they are not all stationary, then keep going, till the 3rd difference which will be the same
number.this is when we can fit an exact poly through the data
e) If the data
1.
a)
b)
c)
2.
Find polynomial functions that give the following sequences of numbers:
i)
ii)
Here is a table of finite differences. Most of the numbers have mysteriously
changed to asterisks. What is the 12th number in the original sequence?
Find the pol
1.
Since the residuals must add to 0, the final residual is , and the sum of the squares of the
residuals is
2.
so the table is
ANOVA
df
SS
Regressn
Residual
Total
MS
F
pvalue
3 275.2126 91.73754 8.294267
0.109
2 22.12071 11.06036
5 297.3333
3.
Since the
1
Abstract
Operations Management and Statistics textbooks consider various models to deal with
seasonal variation in time series. In this paper two common models are examined :
multiplicative models and multiple-regression models .
In multiplicative model
1.
Data for the multiple-regression of Y on X1, X2, and X3 are given below, together with some sets
of residuals. The residuals have headings of the form ABC. The heading ABC indicates that the
residuals are for the multiple regression of A on B and C. Fo
1.
The Eurelian Bureau of Mines produces data on the price of minerals.
Shown here are prices for minerals over some randomly-selected months.
The Eurelian Secrecy Act does not allow complete data sets to be made
public, so only the first 8 lines of data
FACULTY OF ARTS
FINAL EXAMINATION
ECON 337 sec 001
Introductory Econometrics I
Examiner: Prof. K. MacKenzie
Friday April 22, 2005
Associate Examiner: Prof.
J. Kurien 9 a.m. 12 p.m.
INS TRUCT IONS :
Answer in exam book.
Calculators are allowed.
No notes or
MC Gill DECEMBER 11*, 2013
Final Examination
INTRODUCTORY ECONOMETRICS I
ECON 337
DECEMBER 11th
18:00 to 21:00
Examiner: K.MacKenzie Associate Examiner: J.Kurien
INSTRUCTIONS:
. This is a CLOSED BOOK examination
. One legal-sized CRIB SHEET permitted
ECON 337
l.
:5; eves.
as.
A study is to be undertaken to determine factors in the success of a
programme to help smokers quit. The preliminary data set given
below has been used to check the logistic-regression method. The
variables are: age in years, wei
1
Abstract
Operations Management and Statistics textbooks consider various models to deal with
seasonal variation in time series. In this paper two common models are examined :
multiplicative models and multiple-regression models .
In multiplicative model
1.
The Eurelian Bureau of Mines produces data on the price of minerals.
Shown here are prices for minerals over some randomly-selected months.
The Eurelian Secrecy Act does not allow complete data sets to be made
public, so only the first 8 lines of data
The highlighted questions deal with material not done in Fall 2013
ECON 337
1.
A study is to be undertaken to determine factors in the success of a
programme to help smokers quit. The preliminary data set given
below has been used to check the logistic-re
ECON 326 REVIEW
Energy- ability to do work
Energy can be stored or transferred from place to place, or object to object in different ways.
Kinetic Energy- energy possessed by an object due to its motion or movement.
Mechanical Energy
Work- is done when a
1. For the data set
x
2
0
1
1
y
20
24
24
40
a)
Obtain the equation of the least-squares line of best fit using the
appropriate matrix method.
b)
Why is the line called a least-squares line?
c)
Find the sum of the squares of the residuals.
d)
2.
Consider t
1.
In November 2001 a popular chain of coffee shops launched its prepaid debit
card. The card, which can be for any amount from $5 to $500, can be used at any
of the locations of the chain. The card was so popular when it was first released
that many stor
1.
For the data set
x
y
2
0
1
20
24
24
1
40
a)
Obtain the equation of the least-squares line of best fit using the
appropriate matrix method.
b)
Why is the line called a least-squares line?
c)
Find the sum of the squares of the residuals.
d)
2.
Consider t
1.
669
845 , and the sum of the squares of
Since the residuals must add to 0, the final residual is
the
residuals is
2.
15794740
22.1207 .
714025
SSTOTAL=2314
1102
=297.3 3,
so the table is
6
ANOVA
Regressn
Residual
Total
2
3.
R=
df
3
2
5
SS
MS
F
275.212
Consider the following data set:
x1
2
5
5
7
10
1
x2
28
23
27
18
11
x3
23
45
12
54
37
y
123
150
164
205
214
If y is regressed on x1, find the following using the matrix method. Feel free to
use EXCEL to help with the matrix manipulations, but make sure you
1.
The lifetimes of anabolic gyrogizmos are to be analysed as if they
followed a Weibull distribution. The initial number of gyrogizmos was
2500, and after five hours of operation, 2400 were still operating, but 38
were on the verge of failure.
a)
How man