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University of Toronto St. George

Statistical Sciences

STA302H1

Sotirios Damouras

Fall

Description

ession Antal
STA 207.
where tes:
af
www. utstat utorovuta
each
Stoc 202 leet
SAS
/SAs
Atmosp
ro carbon
b to
reflects
Cre
the atom Splues
Ct
xown the Ozone layer
Autarctt
Pruntu
hare out CFC
production
NO
Pata
ber
Cart
measure une
una Loa
Last Class
row
measureur
Montreal
bespre Jan lato
Pret
Moutr
MP
Impose.
it ts deta
model.
The
straight
vs nst alw
statistician
data were
de
13st.
Some are
useful
ored CHR.
data w
nust real
but
ession Antal STA 207. where tes: af www. utstat utorovuta each Stoc 202 leet SAS /SAs Atmosp ro carbon b to reflects Cre the atom Splues Ct xown the Ozone layer Autarctt Pruntu hare out CFC production NO Pata ber Cart measure une una Loa Last Class row measureur Montreal bespre Jan lato Pret Moutr MP Impose. it ts deta model. The straight vs nst alw statistician data were de 13st. Some are useful ored CHR. data w nust real butstatistical uotele,
round
Jal and
f tted ual
obser
res
Simple
linear Regress
Asn svmple sue -t
r near
in RS
dependent Janabe.
modell ed as
variab
round
ve dict
various
be chose
by Hne person
Study
serve.
cou taunts
in
ran meters
t know
Estima Woo, b.
NOTES
randusm se
variation mrea une we can't
Ele.
Kwant esti mede and e.
observations c-xi, i 1.2, ...n
each
value.
Deviat
frsm line
predict value
measure
have
do they
olev at
Same
measure verhede
dewiatu ers in r
fr
duct
as to
variable
dependent
Dev at
statistical uotele, round Jal and f tted ual obser res Simple linear Regress Asn svmple sue -t r near in RS dependent Janabe. modell ed as variab round ve dict various be chose by Hne person Study serve. cou taunts in ran meters t know Estima Woo, b. NOTES randusm se variation mrea une we can't Ele. Kwant esti mede and e. observations c-xi, i 1.2, ...n each value. Deviat frsm line predict value measure have do they olev at Same measure verhede dewiatu ers in r fr duct as to variable dependent Dev atNOTES
total
all
Auethod least squares
sf the
A 2
Squares
RSS
b, to
be bi
Minimize RSS
the b
neadu
vote,
Une puts he appl Eat
ssion
raudowna.
Mathem
a
varalo
on a non
Su
Tina
the bet
approximatum
the ba. b. minimize RSS.
Calculus
RSS
2 X
2 Yi
2.X
NOTES total all Auethod least squares sf the A 2 Squares RSS b, to be bi Minimize RSS the b neadu vote, Une puts he appl Eat ssion raudowna. Mathem a varalo on a non Su Tina the bet approximatum the ba. b. minimize RSS. Calculus RSS 2 X 2 Yi 2.XNOTES
Back board ms read.
Reminder
Thur-day SAS lecture
hour
2:00
1 estimates.
Simde linear
2
eserved ualuee of
s i 2,... n
uri
Data
Method least
5 uanu finca LA
Cresuduol s
Suares
class
vent
they hann
deviatism do
NOTES
NOTES Back board ms read. Reminder Thur-day SAS lecture hour 2:00 1 estimates. Simde linear 2 eserved ualuee of s i 2,... n uri Data Method least 5 uanu finca LA Cresuduol s Suares class vent they hann deviatism do NOTESNOTES
ad ba, b
aRSS
br
3b
RSS
bv.
ba, b
b X
Can Shun
Exercise z shN a minu
for CFC.
Befo
Mr
b 933
befo
th
when
bt gs. CFCs were
fist manu factured
Darre d data
tercept
Cis o in r
the data
any bo y
residuals
S CO
fitted
X +b,
NOTES ad ba, b aRSS br 3b RSS bv. ba, b b X Can Shun Exercise z shN a minu for CFC. Befo Mr b 933 befo th when bt gs. CFCs were fist manu factured Darre d data tercept Cis o in r the data any bo y residuals S CO fitted X +b,NOTES
exercises.
S far, we have a sumes in evan made
add some
ML del
aauss Markov Conditions
te
eis o tandem Jara,
Var (ei) cans
Marks/ Theorem
e thee least uare esti
un bloused (wal do
C, a funct
3L U
Per minimum
varuamee
estimate e
st under
estimat
A. A
epten uvedl
estimoudu
Leaf squares Estimaturs
MAK
2.X
n X
Varian
E
X
2 x
NOTES exercises. S far, we have a sumes in evan made add some ML del aauss Markov Conditions te eis o tandem Jara, Var (ei) cans Marks/ Theorem e thee least uare esti un bloused (wal do C, a funct 3L U Per minimum varuamee estimate e st under estimat A. A epten uvedl estimoudu Leaf squares Estimaturs MAK 2.X n X Varian E X 2 xNOTES
(ATA
2 X
2X
Var (u
are
Var
2
e Nan (3
SXX
constru wer value
mare spread out que
Not
Sos.
parameters GWTu near
Need
2 e
Var(2)
est. 202
n-1 is the
degrzes.
freed
NOTES (ATA 2 X 2X Var (u are Var 2 e Nan (3 SXX constru wer value mare spread out que Not Sos. parameters GWTu near Need 2 e Var(2) est. 202 n-1 is the degrzes. freed12
Oct 5
linear
Leash
sti nafte
unbiased
esilinechr f
only
NO
2
MSET
s notes
Root MSE
SSL estimate of s d of e
MSE
variat.
(A)
r est
S for S
clare error
Se
MSE
1788
CA
2,82
Tb see data
12 Oct 5 linear Leash sti nafte unbiased esilinechr f only NO 2 MSET s notes Root MSE SSL estimate of s d of e MSE variat. (A) r est S for S clare error Se MSE 1788 CA 2,82 Tb see dataNormal
Model
Cons
Mark v c
www-
have
Add.
Since ei's are uncorrelated
diet
under the
aastrih Errors
the least stares
mark munn likeliha estimates
The results in te estimates ha
nice
MLE
Charter
mav Maria noR biased estinaton
t- clist
and a
norm
NOT
tsr.
x are inde
yin
MG windows
tware.
www. cs. Caltech ..edu/ cara k il
Normal Model Cons Mark v c www- have Add. Since ei's are uncorrelated diet under the aastrih Errors the least stares mark munn likeliha estimates The results in te estimates ha nice MLE Charter mav Maria noR biased estinaton t- clist and a norm NOT tsr. x are inde yin MG windows tware. www. cs. Caltech ..edu/ cara k ilNOT
(S) Amy
AM ear Cambi
mally cha tributed
rourda vario hles
Confidence
for t
in
is a f a cont de mer
est. pa
size n
true (un
will
f the
that
C-T
NO
Mae CDs pre a range of P
we values
The P
Common values
made
Normal error SLR model
NC
Var (B) by
elf. Arrest
Jana
C-T
by t
NOT (S) Amy AM ear Cambi mally cha tributed rourda vario hles Confidence for t in is a f a cont de mer est. pa size n true (un will f the that C-T NO Mae CDs pre a range of P we values The P Common values made Normal error SLR model NC Var (B) by elf. Arrest Jana C-T by tSAS
re AMP ctce, clata
Test
hyp thes
of interest
Calculate a test tia whe
known
Linder the null hy the
estimate
a p -value Assemeng thet H. aneet
the
test statistic or
a
b. of th
the P
mag extreme
Gives
curaende against
reat
a test stars
d the
has
or Ho incorrect Tto smaller p-value
evide
stronger
large P
value indicates data are consisteier
no endeu.
weak
Guden, a
rate
TT 6
133 used
3
SSL
MSE-
Root
R-square
SECb
Thursday /2 ou ou
Andry
A testins, example
means
or S
S12R
n,, iid
Then A
random vanakles have the
sane variano
1-2
SAS re AMP ctce, clata Test hyp thes of interest Calculate a test tia whe known Linder the null hy the estimate a p -value Assemeng thet H. aneet the test statistic or a b. of th the P mag extreme Gives curaende against reat a test stars d the has or Ho incorrect Tto smaller p-value evide stronger large P value indicates data are consisteier no endeu. weak Guden, a rate TT 6 133 used 3 SSL MSE- Root R-square SECb Thursday /2 ou ou Andry A testins, example means or S S12R n,, iid Then A random vanakles have the sane variano 1-2NOTES
you dont assume
Common
test
Saffer wait
t-Test
de
sd
a dist
Calculate
value
with These
?value
Want f an CFC
Com
s the same
pre an
t Montreal
See output
d s
So use Gaffer warte frrmu a
OTES
re and pot
Refes in
Want to test
a linear relati
where 2e
Exx
ton test
o ace evidence
Values
NOTES you dont assume Common test Saffer wait t-Test de sd a dist Calculate value with These ?value Want f an CFC Com s the same pre an t Montreal See output d s So use Gaffer warte frrmu a OTES re and pot Refes in Want to test a linear relati where 2e Exx ton test o ace evidence Valuesme a SunR
ex tenue than
se ch)
stra
of O
7.3
Conclude
CP
est statistic
here Sie, (h
or- would be
half what
would be for
rest
2 Sided
test
statistic calculation
Me urauf to test
t sadist
2ecial
H the
can show (STAS) ,na
nals
correlat
Varc
can be shown that the cond nd of y
me a SunR ex tenue than se ch) stra of O 7.3 Conclude CP est statistic here Sie, (h or- would be half what would be for rest 2 Sided test statistic calculation Me urauf to test t sadist 2ecial H the can show (STAS) ,na nals correlat Varc can be shown that the cond nd of yNOTES
by
(xi
f dist
where b
Correlat
ke a
and y
relationshp X
measuro of the strenstt.
f the
he use matfer
which
and which
nat.
ob
Crea
This also ULE JF
Facts amuud r
the
linear
the dre
relation slip be an & N
NOT
Relationsh
2 (X
Unirs of b
Interpre
2 er Y
Cat
r linear
well das Izg
line summary Ara?
NOTES by (xi f dist where b Correlat ke a and y relationshp X measuro of the strenstt. f the he use matfer which and which nat. ob Crea This also ULE JF Facts amuud r the linear the dre relation slip be an & N NOT Relationsh 2 (X Unirs of b Interpre 2 er Y Cat r linear well das Izg line summary Ara?NOTES
of Suares
Total
ed SS
is subtrautel
i uncorrect
Residual
RSS
SS
Err
2
Model
of
the
show
207
ANOVA
Tebu
Mean
MS
Stuare
S5
SS
Se R
MS
n-2
Rss.
unde f
MSE
Var (e
to
Coe
named
time-
Almst all of the
var
plained
useful B
Correlation
No abs
nule.
Not resi tantr to outlier
Mot
meaningful for models with no utereit
only use for
ordinary leost stuary
Shaare o normally dir Nuo
Xin N
NOTES of Suares Total ed SS is subtrautel i uncorrect Residual RSS SS Err 2 Model of the show 207 ANOVA Tebu Mean MS Stuare S5 SS Se R MS n-2 Rss. unde f MSE Var (e to Coe named time- Almst all of the var plained useful B Correlation No abs nule. Not resi tantr to outlier Mot meaningful for models with no utereit only use for ordinary leost stuary Shaare o normally dir Nuo Xin NMASE
E(MSET)
US
So B.
Ha, P
then
Values
P-value
NOTES
with a fan has
r.
care
Reminder
tori
rivere esaanple
r test
to lookout data.
a reas
throw
aeductiou and GT for th
Ceasar
ties f
and
slope
Esti
-b. Suppose
are
the
ngresiun lMe predicts
when
MASE E(MSET) US So B. Ha, P then Values P-value NOTES with a fan has r. care Reminder tori rivere esaanple r test to lookout data. a reas throw aeductiou and GT for th Ceasar ties f and slope Esti -b. Suppose are the ngresiun lMe predicts whenNOTES
ar
2 e
Eni sate value f regressin line a
I
made of mean value
y on 19
n X
nx
CI
confide limit
NOTES
Suppose. Ne an Interv
y hen
value
A
Want
r a new observation
prediction
reduction
Imhenu
Called a prediction Intervul ndden then
Confid
dene reserve
NOTES ar 2 e Eni sate value f regressin line a I made of mean value y on 19 n X nx CI confide limit NOTES Suppose. Ne an Interv y hen value A Want r a new observation prediction reduction Imhenu Called a prediction Intervul ndden then Confid dene reserveNOT
LAS cuss
C-1
Tntenval
Burfa intervals are wider
firms
variable
x also
n mally dist
India,
variable s
ndicad
Let
alt
Lan Test Lether mean f 's before/affon.
NO
n is called
the mean
D have taller chil
sh
test
situati
ffect hade
673 text
tert
24 on test
this
did
because
a
ski
extreme
be that
NOT LAS cuss C-1 Tntenval Burfa intervals are wider firms variable x also n mally dist India, variable s ndicad Let alt Lan Test Lether mean f 's before/affon. NO n is called the mean D have taller chil sh test situati ffect hade 673 text tert 24 on test this did because a ski extreme be thatNOTES
Chapter 3
DIAGN STC
ANP TRANSFORM ATnsNT
ap POP
the
aint
ster
than
and
Outleis
result in subs
c in the canine data
car all f the
the the
ref
vers t
Varah
to bo smaller
ito
that
the
Quanti Amis
leu erage
2 h
duda
verage
leverage pom
Avergr
and Thure is lan
befuzun
and th othr
NOTES Chapter 3 DIAGN STC ANP TRANSFORM ATnsNT ap POP the aint ster than and Outleis result in subs c in the canine data car all f the the the ref vers t Varah to bo smaller ito that the Quanti Amis leu erage 2 h duda verage leverage pom Avergr and Thure is lan befuzun and th othrLost na
HA U3
hours before. Test nep wed
Me.
lution, to thui parted
2.1%, 3.2.3, 3.2.
Calculator v D
Class
were h
of
data d
How un
3 dngin by
bserved. value
NOTES
bet.
ob
observotion has been deleted
frum data
hers been ref
DF BETAs ence
in
betas
pe calculated
Rule of thumb
lage data sut
between
Measure 2 influnce
diller
Lost na HA U3 hours before. Test nep wed Me. lution, to thui parted 2.1%, 3.2.3, 3.2. Calculator v D Class were h of data d How un 3 dngin by bserved. value NOTES bet. ob observotion has been deleted frum data hers been ref DF BETAs ence in betas pe calculated Rule of thumb lage data sut between Measure 2 influnce dillerNOTES
Carr
oli cat
Rule of
for
Measure
Cak
2 S
resi
hii
tureenco
Influence
SAS
End
NOTES
Test Thando No the lecture room
hours
today 3pm
Zeynep tomorrow
ss 2133
use sees
the condit
SLK
ei i-1,2.
une tata
pants
Least buar
Gauw) Mark
con din
ass m
errors have a normal
Dr
'Estimate
what do we know abad 2
NOTES Carr oli cat Rule of for Measure Cak 2 S resi hii tureenco Influence SAS End NOTES Test Thando No the lecture room hours today 3pm Ze

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