STAT 3A03 Applied Regression With SAS
Fall 2013
Assignment 2 Solution Set
Q. 1 Let the data be (x11 , . . . , x1n ), (x21 , . . . , x2n ) and (y1 , . . . , yn ). To avoid confusion, I will use the
following notation in this question
n
(x1i x1 )2
S11 =
i=1
STAT 3A03 Applied Regression With SAS
Fall 2013
Term Test 1 Solution Set
Q. 1
a) The sum of squared errors is
n
(yi 2 1 xi )2
S(1 ) =
i=1
[3 marks]
To minimize this we take the derivative with respect to 1
dS(1 )
= 2
d1
n
xi (yi 2 1 xi )
i=1
Now we set th
STAT 3A03 Applied Regression With SAS
Assignment 3
Due at 12:30pm on Monday November 4, 2013
N.B. Late assignments will not be accepted
Q. 1 A survey was conducted in Britain to study teenage gambling. The data for 47 teenagers is
in the dataset teengambl
STAT 3A03 Applied Regression With SAS
Fall 2013
Assignment 3 Solution Set
Q. 1
a) Here is the code and tted model. The code also produces the three major diagnostic plots
for part (b). I have also saved an output dataset which we will use in subsequent pa
STAT 3A03 Applied Regression With SAS
Assignment 5 Solution Set
Q. 1
a) The code that I used and the output is as follows
PROC GLM Data=Wool;
Class Amp Len Load;
Model Cycles=Amp Len Load;
Output Out=woolout
predicted=fitted
student=student;
run;
quit;
Th
STAT 3A03 Applied Regression With SAS
Fall 2012
Assignment 1 Solution Set
Q. 1
a) (i)
n
(xi x)2
Sxx =
i=1
n
(x2 2xi x + x2 )
i
=
i=1
n
n
x2
i
=
xi + nx2
2x
i=1
i=1
n
x2 2nx2 + nx2
i
=
i=1
n
x2 nx2
i
=
i=1
[5 marks]
(ii)
n
(xi x)(yi y )
Sxy =
i=1
n
(xi yi
STAT 3A03 Applied Regression Analysis With SAS
Fall 2013
Assignment 4 Solution Set
Q. 1
a) The assumptions for this model are that the error terms i are independently and normally
distributed with zero mean and equal variance for each level of the categor
STAT 3A03 Applied Regression With SAS
Assignment 1
Due at 12:30 on Thursday September 26, 2013
N.B. Late assignments will not be accepted
Q. 1
a) Prove the following equalities
(i) Sxx =
(ii) Sxy =
n
2
2
i=1 xi nx
n
i=1 xi yi nx
y
b) Suppose that 0 and 1
STAT 3A03 Applied Regression With SAS
Assignment 2
Due at 12:30am on Thursday October 10, 2013
N.B. Late assignments will not be accepted
Q. 1 Suppose we have a response variable Y and two predictors X1 and X2 and that the observed
values of X1 and X2 hav
STAT 3A03 Applied Regression With SAS
Fall 2013
Assignment 1 Solution Set
Q. 1
a) (i)
n
(xi x)2
Sxx =
i=1
n
(x2 2xi x + x2 )
i
=
i=1
n
n
x2
i
=
xi + nx2
2x
i=1
i=1
n
x2 2nx2 + nx2
i
=
i=1
n
x2 nx2
i
=
i=1
[5 marks]
(ii)
n
(xi x)(yi y )
Sxy =
i=1
n
(xi yi
Name:
ID #:
MATH 2FM3 Second Midterm
Instructor: Petar Jevtic
Date: November 15th, 2013, 10h30am-11h30am
Duration: 50 min
McMaster University Second Midterm
This test includes 6 pages containing instructions, questions and formula sheet, together
with 8 e
STATS 3A03 PROBLEM SETS 3 - SOLUTIONS
4.5) Use the bootstrap to estimate confidence intervals of the coefficients in the fuel data.
Answers:
FIRST PREPARE THE DATA BY IMPORTING THE EXCEL FILE TO SAS FILE CALLED Fuel.
Remember we defined new variables when
STATISTICS 3A03
Fall 2012
TERM TEST 2
Dr. Angelo Canty
November 22, 2012.
DAY CLASS
DURATION OF EXAMINATION: 50 Minutes
THIS EXAMINATION PAPER INCLUDES 5 PAGES AND 3 QUESTIONS. YOU ARE RESPONSIBLE
FOR ENSURING THAT YOU COPY OF THE PAPER IS COMPLETE. BRING
STAT 3A03 Applied Regression With SAS
Term Test 2 Solution Set
Q. 1
a) The model we shall t is of the form
Yi = 0 + 1 I1i + 2 I2i + i
if xi = A
0 + 1 + i
0 + 2 + i
if xi = B
=
0 + i
if xi = C
For any parameter values 0 , 1 , 2 we therefore need to minimi
STATS 2MB3 STATISTICAL METHODS
Assignment 2 Due during class on Monday February 13th.
If you want it back before the test, you must hand it in by Friday February 10th Late assignments will not be accepted
Derivations must be done by hand (naturally); howe
McMaster University
Stats 3A03- Midterm I Exam
Thursday, October 8, 2009
QUESTIONS & SOLUTIONS
Question 1 (30 points): Find , , R and write the regression equation for this data and
interpretate the coefficients of regression model and the coefficient of
STAT 3A03 Applied Regression With SAS
Assignment 1
Due at 9:30am on Thursday September 27, 2012 N.B. Late assignments will not be accepted
Q. 1
a) Prove the following equalities (i) Sxx = (ii) Sxy =
n 2 2 i=1 xi - nx n i=1 xi yi - nx
y
b) Suppose that (y1
STAT 3A03 Applied Regression With SAS
Term Test 2 Solution Set
Q. 1
a) An outlier is a point which deviates from the linear model. Such a point can usually be seen
from plots of the studentized residuals since it has a large studentized residual (in absol
STAT 3A03 Applied Regression Analysis With SAS
Assignment 4
Due at 12:30pm on Thursday November 14, 2013
N.B. Late assignments will not be accepted
Q. 1 Suppose that a we have a continuous response variable Y and a single categorical variable X with
value
STAT 3A03 Applied Regression With SAS
Assignment 3
Due at 9:30am on Thursday November 1, 2012 N.B. Late assignments will not be accepted
Q. 1 The Scottish Hill Races dataset describes the fastest times (in seconds) in 35 races in the Highlands of Scotland
Student Name
Student Number
STATISTICS 3A03
FALL 2011
DR. ANGELO CANTY
DAY CLASS
DURATION OF EXAMINATION: 3 Hours
MCMASTER UNIVERSITY FINAL EXAMINATION
December 10, 2011
THIS EXAMINATION PAPER INCLUDES 10 PAGES AND 8 QUESTIONS. YOU ARE RESPONSIBLE FOR
ENS
STAT 3A03 Applied Regression With SAS
Fall 2012
Assignment 2 Solution Set
Q. 1 Let the data be (x11 , . . . , x1n ), (x21 , . . . , x2n ) and (y1 , . . . , yn ). To avoid confusion, I will use the
following notation in this question
n
(x1i x1 )2
S11 =
i=1
STAT 3A03 Applied Regression With SAS
Assignment 5 Solution Set
Q. 1
a) The code that I used and the output is as follows
PROC GLM Data=Wool;
Class Amp Len Load;
Model Cycles=Amp Len Load;
Output Out=woolout
predicted=fitted
student=student;
run;
quit;
Th
STATISTICS 3A03
Fall 2012
Dr. Angelo Canty
TERM TEST 1
October 18, 2012.
DAY CLASS
DURATION OF EXAMINATION: 50 Minutes
THIS EXAMINATION PAPER INCLUDES 4 PAGES AND 3 QUESTIONS. YOU ARE RESPONSIBLE
FOR ENSURING THAT YOUR COPY OF THE PAPER IS COMPLETE. BRING
STAT 3A03 Applied Regression With SAS
Term Test 1 Solution Set
Q. 1
a) The sum of squared errors is
n
(yi 2 1 xi )2
S (1 ) =
i=1
[2 marks]
To minimize this we take the derivative with respect to 1
dS (1 )
= 2
d1
n
xi (yi 2 1 xi )
i=1
Now we set that equal
The Population Mode
The value which is most likely/probable to occur. This may or may not be unique.
Stats 2MB3 - Winter 2012
36
Discrete/Qualitative
0.07 0.00 0.01 0.02 0.03 0.04 0.05 0.06
15
Stats 2MB3 - Winter 2012
18
21
24
27
30
33
36
39
42
37
Continu
Question #1
a
If you keep every parameter in the full model, it is apparent that the following equations are
generated by the estimated value of D (beta2) shown in the table below:
When D = -1,
When D = 0,
When D = 1,
Where a D = 1, increases the value of
McMaster University
Department of Mathematics and Statistics
STATISTICS 3A03: Applied Regression Analysis with SAS
Fall 2016
Due at 2:00 pm, Wednesday, October 26, 2016.
Assignment 2
Note: Late assignments will not be accepted.
Qi:
546Lf(Q
-re(iM.,
\/
x=(
McMaster University
Department of Mathematics and Statistics
STATISTICS 3A03: Applied Regression Analysis with SAS
Fall 2016
Assignment 3
Due at 2:00 pm, Friday, November 18, 2016.
Note: Late assignments will not be accepted.
Q1: Question 4.5. at textbook
STATS 3A03: Part 2
Introduction to SAS and Regression
Justin Jia
Sept. ~ Dec., 2016
McMaster University
What is SAS ?
SAS stands for Statistical Analysis System
developed by SAS Institute.
Originated at North Carolina Univ. since 1966.
Strong in proces
McMaster University
Department of Mathematics and Statistics
STATISTICS 3A03: Applied Regression Analysis with SAS
Fall 2016
Assignment 1
Due at 2:00 pm, Friday, September 30, 2016.
Note: Late assignments will not be accepted.
Solution:
(1)
First compute