STA 6326
EXAM I - SOLUTIONS
PROBLEM 1
Let
Ai i th question is answered correctly
and assume that A1 , A2 , , A10 are mutually independent. Furthermore, if the student is guessing,
then P Ai 0.20 . Define
X = # of questions answered correctly
Then
10
j
1
September 24, 2014
Last week of extra class covering for Dr. Maboudou
Last class in earnest:
One Intercept parameter and p-1 parameters related to
predictor variables gives p total parameters
Predictor variables can be well-defined, identifiable
character
September 22, 2014
One Intercept parameter and p-1 parameters related to
predictor variables gives p total parameters
Predictor variables should be well-defined, identifiable
characteristics possibly related to the response variable (to
be determinedlikel
October 13, 2014
Quiz on Wednesday J
Ground rules/Reminders: closed book, notes, calculators,
iphones, ipads, iwatches, google glasses, etc.
I will post the clock time occasionally
Must write neatly (cant read = 0 credit)
Typos or Clarification questions
Chapter 2
1
2.1: Inferences about 1
Test of interest throughout regression:
Need sampling distribution of the estimator b1.
Idea: If b1 can be written as a linear combination of the
responses (which are independent and normally
distributed), then from A.4
September 15, 2014
Moving into more than one predictor
variable
1
Chapter 5
Fast forward for those who are already
experts in matrix methods
Least squares estimates for multiple
regression, matrix representation of
ANOVA calculations
Feel free to look
Chapter 12
Autocorrelationnon-independence with time
Assume error term is normal with mean
zero, variance one, independent
For situations with time as a explanatory
variable or covariate, can check for
autocorrelation
Durbin-Watson test for one form of
October 6, 2014
Data sets other than the text?
Last time suggested you practice on the
various data sets in Chapter 8; On
Wednesday will likely look at many of
these;
Chapter 9: Model Selection and Validation
Quiz on October 17, 2014 (leaning to
makin
November 3, 2014
Collect model fits for 4 problems
Look at the Xs
Ys in order
1
Lets have a look
Y1 is easy
Guess from fits:
20 5 X2 + 2 X3 4 X7
+ normal (0, 1)
2
Y2 (X2, X7, X8 look promising)
Fit all models just with these
3
Y3
X6 and X6 squared an
STA 6327
STATISTICAL THEORY II
EXAM III
PROBLEM 1
Note that
n
n
L x exp ln xi n
exp ln xi
i 1 xi
xi i 1
n
i 1
while
: 0
and
0 : 1 .
Hence,
x
sup L x
o
sup L x
L 1 x
Lx
1
n
n
exp 1 ln xi
n
xi i1
i 1
n
n
ln x
i
i 1
n
exp n
n
n
xi
ln xi
STA 6327
STATISTICAL THEORY II
EXAM II
PROBLEM 1
Note that the likelihood function is given by
n
L | x 1 xi 1
n
i 1
n
x
i 1
i
Hence, the natural log of the likelihood is
n
ln L | x n ln 1 ln xi .
i 1
Consequently, taking a derivative with respect to , s
STA 6326
EXAM II - SOLUTIONS
PROBLEM 1
E Y E 2 X
n 1 5
2
x 0
x 6 6
x
n
x
n 2 5
x 0 x 6 6
x
n
2 5
6 6
7
6
n
n
PROBLEM 2
The mgf of X is given by
M X (t ) E (etX )
etx e x dx
ln
e 1t x dx
ln
1 t
1 t
1 t
e 1t x
e1t ln
1t
ln
n x
n x
2
STA 6327
STATISTICAL THEORY II
EXAM I - SOLUTIONS
PROBLEM 1
Note that
Fn
t P n 1 X n t
1 X
n
t
P 1 X n
n
t
1 P 1 X n
n
t
1 P X n 1
n
t
1 FX n 1
n
n
t
1 1 ,
n
if 0 1
t
1 0 t n . If we let 1 , then
n
n
t
Fn 1 X t 1 1 1 e t ,
n
n
n
if 0 t
Week One
Slides posted; new work item posted; videos for
sta6236 on line on you tube
Pep talk for regression, especially in light of
predicAve analyAcs
Reality check (informaAve quiz) reveals that
many of you ne