statistic midterm sarup sood, Cheat Sheet of Law

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Typology: Cheat Sheet

2017/2018

Uploaded on 04/01/2024

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Assumptions
1.
Past
into
Error
measurements
2.
Quantified
form
of
data
Trend s
3.
continued
pattern
1.
Qualitative
:
xmathax
historical
data
.
a
biased
1.
Trend
¢
m
nemanh-ajts.tn#.nlAt-Ftty
improved
2.
Quantitative
:
2.
seasonal
e'
die
L
penalize
Erin
's
3.
Cyclical
table
Eh
her
rat
'
'
Y¥¥aEge
=
In
¥
.
,
lAt
large
error
Explanatory
-
relationships
Ex
.
Regression
analysis
4.
Random
disasters
At
time
series
-
historical
patterns
so
.pl?o,.mneasnEsauared=fIFAt-FtT
"
s
'D
'
*
StationaryMod
:
steady
constant
meant
random
variation
-
j
penance
n
n
around
'
n'
intr
models
Description
Formulas
Tren d
Analysis
rise
=
In
,
lat
-
ft
)
'
n
.
,
an
-
e
-
simple
-1
flexible
Future
I
=
a
tbt
'
frnecdnatem
a
variance
adjusted
NAIVE
-
baseline
Etty
=
At
L
projected
value
<
actual
present
be
Eta
-
lEt)(E#
x
stationary
simple
iaiiiiiiiiaiiiiaiaiiaiiiiiiiim
"
.
Eat
.
"
sis
.int?a..:..::::i
:i÷:÷:÷÷÷÷:÷÷
:
:
Moving
AV
"
responsive
,
,
i
:O
a
=
A-
-
BE
÷i
.
Seasonal
Ty
-
a.
of
cycle
annual
)
'
factor
'
easy
a
Stable
no
.
of
periods
L
factor
in
an
seasons
-
X
trend
seasonality
v
,
agg
trend
,
ignore
complex
used
to
forecast
E
'
Ent
A-
'
-
EA
behind
relationship
n
use
yea
tbf
n
-
I
d.
n'
in
int
www.NMNWW
:
total
demand
forecast
in
yr
it
Is
÷±÷÷i÷÷÷±÷÷÷÷
:/
!
!
:÷÷÷÷÷÷÷÷÷:÷i÷÷÷::i
:÷÷÷÷÷:÷÷÷÷÷÷÷÷÷
:
"
:
:
:
"
"
"
"
'
iii.
sun
.
Smoothing
-
recent
data
>
old
1
(
previous
determined
'
forecast
-
-
lags
a
trend
Ifn
:
A
,
)
Smoothing
constant
'
nib
for
PRESENT
period
0
AM
X
stable
inn
trend
(
Trio
)
at
Stable
Si
'
-
121=0.28
9:40
.tt#teigeeasrg;gn
Adjusted
trend
expo
smoothed
51.9
trend
factor
predict
season
n
in
ft
:S
)
Exponential
+
seasonality
Aff
-
-
Ft
-11
+
Ttt
,
y
:
40.7
-14.4Gt
-
-
40.7+4.46157=63
Forecast
SMOOTHING
t
t
for
period
season
1
:
Snfs
=
0.281631
i
17.64
darth
-
d)
Fe
/
Bette
,
-
ft
)
-111
-
B)
Tt
Ho
benttereminden.fm
stable
)
Hq
Hypothesissteps
}
Goodness
of
fit
tests
1)
observed
Test
stats
-
Check
distribution
2)
Expected
critical
region
(
find
)
pi
is
given
:
Multinomial
/
Emstaiieiffff
conclusion
inborn
observed
/
k
outcomes
-
Normal
VS
Homogeneity
tests
\
Ii
:
!
!
!
;e'
as
:
'
:p
!
!
"pi
.
.fi?9iii9iydf=K-rU-XnOfindprobpoow:iPooanoior.uao=
'
to
:
indiscrete
ru
Binomial
Geo
-
metric
Bernoulli
't
(
Xi
)
=
Mpi
find
E
y
category
W
j
category
\
Pi
's
are
functions
iunieopmflinosmi.fi?yphergeoiinr
.
L
,
arraign
'
em
.
ioii
column
noii
columns
R
i
Enn
Aliunde
Formula
Pex
:#
a-
et
nigra
rrwoiosvr.mn#-1
pig
!
!
Caution
hp
;
75
if
not
,
you
column
Ho
:
pm
=
Pmi
Pr
,
=
pay
for
each
j
-
-
1943,4
Distribution
is
continuous
Ha
:
Ho
is
not
true
Kw
:
K2
p
n
Nog
=
14
i
0.25
normal
Eiinpio
area
"
!
'
estimate
ftp.r
.
,
=
E
(
Observed
-
E
)
'
Test
Statistics
Distribution
Ex
.
8
intervals
aniioo
,
E
'
100×18=125
Eas
-
D
.
#
XZ
=
10
df
:
3
*
E
25
,
if
not
merge
columns
!
n
'
as
Lor
more
-1
=
E
(
hi
-
hp
;)
'
0.07
Cp
-
value
C
0.025
contingency
Idf
:
re
-
no
-
i
)
i
:
'
Tpi
critical
Region
qnorosiwjwprob.li#
1)
Homogeneity
Ho
:
Pij
:
Rj
=
.
.
.
-
-
Pij
X
!
.gg
,
,
=
9.384
-
Voy
>
E'
o.osasn.ndgpyq.mg
ow
@
going
"g
for
each
jink
.
.
.aJ
:
.
Reject
at
95%
Confidence
(
I
fixed
mainly
population
divided
into
j
categories
E
:
row
total
x
Col
total
iiioaume
"
-
f
mann
.
routed
a
j
column
totals
are
random
IUVO
@
Nosed
)
n
Independence
ftp.iiiimgni
)
find
relationship
of
factors
2
factors
in
-
nails
independent
TWIN
Ho
:
Pij
=p
,
-
*
pj
for
i.
Ig
.
.
.gI
j
.
-
ra
.
.
.aJ
1
population
2
factors
frow
in
column
j
)
total
sample
fixed
a
row
-1
column
totals
are
random
Et
.
X
:
NO
-
Of
defects
,
Xv
poison
in
:
go
)
Hou
Poison
laid
Han
Does
not
follow
poisoner
)
space
:{
Salalah
)
y
'
:
13111.83
't
.
.
.
.
PIKA
:e°
:
0.368
22.08
0
!
Pirin
:
e-
'
In
'
'
-
0.368
=
7.23 6
i.
Rejection
Xhosa
4
-
o
-
i
pay
-
-
e
"
'
'
0.184
:
as
,
PIX
-
-
3)
-
e-}
'
-
0.061
:
Do
not
Reject
Ho
Prx
?
3)
i
black
Amarna
up
25
Ho
:
Pij
=
Pit
Pj
for
i
:...
-
I j
=
...
]
89787
-
L
X
eijing
p
!
Not
reject
Her
Mel
zo
e
pf2

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Assumptions 1. 2.^ PastQuantified^ into^ form of data Error measurements

Trends 3. continued pattern

  1. Qualitative^ :^ xmathax^ historical^ data.^ a^ biased^ 1.^ Trend^ ① ¢ ③^ m nemanh-ajts.tn#.nlAt-Ftty improved
  2. Quantitative : (^) Erin's 2.3. seasonalCyclical tablee'^ die^ ① L^ penalize Eh ④ her rat'' Y¥¥aEge = → (^) Explanatory - relationships Ex^. Regression analysis (^) 4. Random disasters In^ ¥.^ ,^ lAtAt^ large^ error → (^) time series - historical (^) patterns (^) so .pl?o,.mneasnEsauared=fIFAt-FtT " (^) s 'D ' * StationaryMod :^ steady constant^ meant^ random^ variation^ - n j penance n around^ '^ n'^ intr models (^) Description Formulas Trend^ Analysis (^) rise = In .§,^ lat^
  • ft ) ' n. (^) , (^) an - e
  • simple -1 flexible Future (^) I = (^) a tbt ' frnecdnatem a variance (^) adjusted ① NAIVE -^ baseline^ Etty = At L^ projected value < (^) actual (^) present be Eta - lEt)(E# (^) x stationary ⑦ simple^ iaiiiiiiiiaiiiiaiaiiaiiiiiiiim (^) ". Eat. " sis.int?a..:..::::i:i÷:÷:÷÷÷÷:÷÷:: Moving AV^ " → responsive, (^) , i :O (^) a = A- - BE (^) ÷i. Seasonal Ty - a. of cycle annual) 'factor^ '
  • X trend (^) seasonality ✓^ easy^ a^ Stable^ no^.^ of^ periods^ L^ factor^ in^ an^ seasons v ,^ agg trend^ ,^ ignore^ complex^ used^ to^ forecast^ E^ ' Ent A-^ ' - EA behind relationship n^ use^ yea tbf n -^ I^ d. n'^ in^ int^ www.NMNWW^ :^ total^ demand^ forecast^ in^ yr^ it Is

:÷÷:÷±÷÷i÷÷÷±÷÷÷÷:/^

!!:÷÷÷÷÷÷÷÷÷:÷i÷÷÷::i :÷÷÷÷÷:÷÷÷÷÷÷÷÷÷ : " :::^ """"^ '^ iii.^ sun^. Smoothing - -^ recent^ data^ >^ old^1 (^ previous^ determined^ '^ forecast^ -

lags a^ trend^ Ifn ( Trio^ :^ A ), )^ SmoothingAM X stable^ constant inn trend'^ nib^ for^ PRESENT^ period^0

at ✓^ Stable^ Si^ '^ -^ 121=0.28^9 :^40 .tt#teigeeasrg;gn ⑤ Adjusted ✓^ trend^ expo^ smoothed trend factor predict51.9 season n in (^) ft :S ) Exponential +^ seasonality^ Aff -^ -^ Ft-11^ +^ Ttt,^ Forecasty :^ 40.7^ -14.4Gt^ -^ -^ 40.7+4.46157= SMOOTHING t^ t^ for^ period^ season^ 1 :^ Snfs =^ 0.281631 i^ 17. darth-^ d)^ Fe / Bette,^ -^ ft^ )^ -111^ - B) Tt ① Ho benttereminden.fm stable ) ②^ Hq^ Hypothesissteps} ① Goodness^ of^ fit^ tests^ 1)^ observed^ ③ Test stats

  • Check distribution 2)^ Expected( find )^ ④ critical (^) region pi is^ given :^ Multinomial^ /^ Emstaiieiffff^ ⑤^ conclusion^ inborn observed

/ k outcomes - Normal VS Homogeneity tests


Ii:! (^) !! (^) ;e'as:' :p! !"pi (^).^ .fi?9iii9iydf=K-rU-XnOfindprobpoow:iPooanoior.uao=^ ' to : (^) indiscrete ru Binomial^ Geo^ -^ metric^ Bernoulli^ 't^ (Xi) = Mpi (^) ③ find E (^) y category W (^) j category

\

Pi 's are functions iunieopmflinosmi.fi?yphergeoiinr.^ L, arraign^ ' em. R i^ ①^ ioii^ column^ noii^ columns Enn Aliunde^ Formula Pex :# a- et nigra rrwoiosvr.mn#-1 (^) pig !! Caution hp; 75 if not (^) , (^) you column^ ①^ Ho^ :^ pm^ =^ Pmi^ Pr^ ,^ =^ pay^ for^ each^ j^ -^ -^ 1943, Distribution is^ continuous^ ⑦ Ha^ :^ Ho^ is^ not^ true Kw : K2^ p^ n^ Nog^ = normal Eiinpio^ area"^ !'^ estimate^14 i^ 0. ftp.r. ,^ =^ E^ ( (^) Observed - E) ' ③ Test Statistics Distribution (^) Ex. 8 intervals aniioo , E^ ' 100 ×18=125 Eas - D (^). # XZ = (^10) df : 3

* E^25 ' as , if→ notLor^ moremerge columns^!^ n

  • = (^) E ( hi - hp;) ' 0.07 Cp - value C^ 0. ⑦ contingency Idf qnorosiwjwprob.li# :^ re^ -^ no^ -^ i^ )^ i^ :^ '^ Tpi ④critical^ Region
  1. (^) Homogeneity Ho^ : Pij : Rj =^.^.^.^ -^ - Pij X!.gg (^) , ,^ =^ 9.384-^ Voy^ >^ E' o.osasn.ndgpyq.mgow @ (^) going"g for^ each^ jink.^.^ .aJ^ : (^). Reject at (^) 95% Confidence ( (^) I fixed iiioaume^ mainly "^ population^ divided^ into^ j^ categories^ E^ :^ - row^ total^ x^ Col^ totalf mann^.^ routed^ a^ j^ column^ totals^ are^ random^ IUVO^ @^ Nosed^ )^ n Independence (^) find relationship of factors ftp.iiiimgni^ )

2 factors^ in

  • nails (^) independent TWIN (^) Ho : Pij =p^ ,^ -^ * pj for^ i.^ Ig^.^.^ .gI

1 j^.^ -^ ra^.^.^ .aJ

population 2 factors

frow in column j )

total sample fixed a row -1^ column totals are random

Et. X :^ NO^ -^ Of^ defects^ , Xv^ poison^ in^ :^ go^ )^ Hou Han^ PoisonDoes not^ laid follow poisoner )

space :{^ Salalah) (^) y' : (^) 13111.83't.... PIKA :e° :^ 0.368^ 22. 0!

Pirin :^ e-^ ' In'^ '^ -^ 0.368^ =^ 7.

i. Rejection^ Xhosa 4 - o - i pay -^ -^ e "'^ '^ 0.184^ : (^) as , PIX Prx -^ -? 3) 3) - e-} '^ -^ 0.061^ : Do (^) not Reject Ho i black Amarna up 25 Ho : Pij =^ Pit (^) Pj for i^ :... - I j=^ ... ]

L

eijing X p!Not (^) rejectHer Melzoe

( factor →^ ①^ finders 2 X^ Replicate^ ②^ SSAASSBGSSIAB^ ) Factor I^ 2.^ NoteHoa^ Ha^ all^3 ① completely^ Randomized^ Design^ lone^

  • WAY ANOVA ! neawariedsrv^ Reff'sfate③ 3.^ ③^ iii.gig " 2 Factor^ =^ IDV Independent sample^ t-^ test^ lever. fan. ④ Randomized Block (^) Design Total SS =^ SST^ + nk-xeatnent.am#oroivomreaanndVoh2oio^ SSE^ main^ N'- response → var (^) measure k treatments each Of b blocks (^) a no. Of observations n - - bk by experimenter f-NYVA → (^) upper tail always! oh^ Farid^ And ate^ block-^ to^ -^ block^ variability .^ F^ Test^ ritical^ Region^ :^ Faadfiadfi^ Total SS^ SST^ t^ SSB t^ SSE F Test ① Ho^ :^ Mr^ =μz=μz=.^.^.^ '^ Mk ④ axb^ Factorial^ Experiment^ ① Ha :^ at least onedimffanenis a levels^ of^ factor^ A y investigate interaction^ ③ Test^ statistic^ :^ F^ '^ -^ Mst b levels^ of^ factor^ B^ between^ A^ and^ B^ Ho^ :^ +^ interact^ MSE replicated r^ times^ test for Interaction! (^) Ha : vintner (^) ④ rejection Region : (^) Fob > (^) Fagdf Total SS^ =^ SS^ At^ SSB^ 1- (^) SS IAB) 1-^ SSE ② ② ① I. (^) Best of estimate 62 ③ Inference^ f.Penne.^ raging^2 Population^ variances ⑦ serious^ test^ gigs, n^ brien^ F^ critical ① (^) Test +^ CI for difference (^) between (^2) population means Large sample^ r^ >^301 x, ax, independent (^) egg df (^) , adf, = 1-baton^ equal a^ UNEQUAL ( (^2) Sample 2- test t (^) CI /

P """ "^ ""^ ""^ "^ "^ "

" "%^ """"^ "" "" " "" " d " " " ¥¥ """

z q^ X^ S^.^ E^. → Experimentalobmienonsawnitnanmenasure^ unit.

→ S (^). 't. Experimental Design small Sample^ +^ Of^961 are unknown →^ observational^ study^ -^ i^ observe^ existing^ data 11 : 17 : (^) ie: (^) :÷÷ . ...ie . ::.. is:÷e÷÷¥÷÷÷i÷÷÷÷:÷en÷: nation. ( (^) Unequal VAV (^) iaestoasriuzob INV dads paired (^) Data (^) sroioriuasa Indi (^) airman x. ax.^ -^ sample^ is^ dependent

into Foster^ matched^ -^ pairs

→ boom ret ) -^ eliminate di =^ unwanted^ variability tri - Xzi

  • paired^ tortona'nuumY^ FEI ' nn- I ② (^) Estimating Differences^ between^ (^2) Proportions ( i¥ Of success

sit.^ =

¥n9I (^) z ; se^. TB G So C

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