Svim Lnuar Kegessnm and (melalim

dk helatmtheps betreen tm
let'ry
a nalyvs S lat1ktas techn

Tabk shes t dy oxyn fded

Chemicad datlatun o l t

obseryalen Hydsoterbrn fundy

Lel |
numben
o19-
89.05
2
2
15
-9143
3 3 74
4 2
5 46
4 5
36
6
o 84

123
1942
93.65
lo 13 54

12 252

3
89.s4
-81.85

0 3
20 13.2S
1-26
32 3 41
11 |3 94 13
20
81 33
 ue Shos the Stallt odojan

6
( ) 14
2

J.s
 Linta Kegs
ha qsunmed thd

whun My u (t) d

V)V(el a
eat imatd

wthedf Leo s tuanes

at Sumes etimaks Th ntaui f

slope Junan
mel ns
- 6z

(2
,

ectimetd essoh Jnu 3

R has fttd e
ne thet J:b»tXe+
Siuas.
Po- and S3
S
 S
6)

Vz

laot table
mede) n the
unean run
Simp
&F
3 2 13s 2,
20

2.2892 ni 22/4.sf6
1 , 44.S321 (21

23.2892(23) o-6gog
- 20

3iJ22
ai4.6ss6 -g3)(a5)
S o1774y

Jo17791- 19-147Y
0 68 08K

6(19.19718) ( 1) =74.2933
P - T
Jlmansjttaen mecle
u
stted Simhle
74.83 +19.197x
 The AC1dual - a 1d fo egtimat

f 1 SS, 0. 7.)

Unb asrd SSE

itimada
n
hm th fnmul
be Cemputad
E Can a/

SSE SS- SJ 2
Cale)

r -3)
Vaabe
aal
umf8tuares tk Aupo nse
totod
n th last Lle
altulate

113

eertus th le»t Spuns Ltimaes

Ca) E CE)P Ie E, an mbixd eatimalet the

u sle .

Cb) V():
S

EC f): P, k unbrád eshimader o

0 an

( V(&) ( SL
 -(K,R): -, Ss k
ACan d m plat
R fhmbd ralut ses
simde l tand and
The
stadard en
se()- Ahimatad

Si
ettimatud Jtondad f

Se(f) Si

knas ktgmn
K Aeri1n
1u n imle
Hyhothuns aso
also lndeperdent ly
ldepepdeAly distnbts
distnbit.s

dittu
ditta bited yOnd
bthdPOnd
be nmaly
OLt
- 2 ) depes Aulo.

Tot the sleke p,°

() 7

hs tdstnbatn with
o ith

TP- P,o ( 2 ) deyus fudan.

Test statutit

-Fe se6)

vejet

inor wpt
Tat t
(6)o

T2st Statutic Fr,s

se(
 (

h%t he elate

olatonah tu Ad

ltm ma
(rAm tha
alttheh olnuud orhy. 1
tuld
betfn t sull
ddalon d olrameal sm "

B 1411, : 20, SA06%»8k, M

14991 135

00059 18
288

Sinu
 46.62

S
po=o jetid-
cluy l toos18
J tut siynatame kpamin
tnalys vasante oteath
S
Is
hAnaly u Vastante dentuty
ST SSR+ SSE

en um u
(-
wh
2 nen Sum Sfuaes.

SSg
Sum Suares
(esected
tofal
SST

$egscefedm SST (n-1)

SS
SSt I (n-a)

ESSoa)), E(S] S
S
 SS n
ndependent andon
vakiales wth In)anddasas haudn

3 n th
u , th
MS dutnbd
MSE

vyest
Ht MS SS

MSe SSe(»a)
n tae fo tehin fi(ante
asanin
Vanuane
Mean Fo
Andys
Andyis
Swm
Soueo sedn
MSg MSME
SSRS
Er SSSS- (-) MSE

Total SST Cn-)

wete MSg

aphse ah t tet fo
Use the analys r a n e
$iCana ema.

4.191, S lo/7711, n: do
S SST7338, :

6i Say = I5a. 13
SSg =

1as
SSE SST -

SSR =
 f Mg 15 13 28 86
MSE 21-25 18

.01,18 82
,n-a

Sin 7,-
Ryet o

(frdent Jntnvnls A leo -A)* Conkidenu Lntenras

S
Y Sz

(ii) Fe t7taupt

Sx

(is) about t h mean tpernse at kh valu

Sxx Szs

w une yh 6t ,

K h e tnral wuath s muni mmm fv2 n, and

win o T n a n s .
 xmpesom k (12
sedd
ulue ohsesrnier
Plee( -a) sedchon Jnteral n a

rlue i

n-
n|%ée )) 4 Y+i+Ena +))
Sxx

whu +
minimum idth at
at
k
M h d l t i n Intural
tnueass
And widens
s |
hndon
wda than th
Than tenh dent
th Conhdent
d c e n Jntrd
15 alys
brth th e
th Th ee

decte lintnr daberds on

Linmts beCa dsstiatud
wh
7twh

ond uet
fittdplel
the
tbremotne
k t
ull lvok
leok
ea
J tuanftu haan
model
Hdeuae he iAtsn
Rpamn med) unes
Sema) ssunptins

gshes a nomally diobnbutd (-n tesd yketke

Ard tntevd estimat h)
n med mttt

to the adejuory I k mode) Atmdual

amalns 6 done.
 Kenlad Analy ss
Redea e - J l'z12, -- ,n,hWhent
nr

an autua bsenvat And tthe (meh

tnepenb
T Chrk te
nmality londduan a fupueny hustoyram
fthe hsndusts (but Siyi Sara s
snall, Juteran
ds net har
hare
mtenry)GE ahemal probslt
let emduls tan k Comductadt Aheady dane n the

toprelott tobre)
we may also Stardandsze th enduals 6
Cmputin d t : 11, -yn . If ees ane neimalty

stibulel, affheuinately 15 f the shandad1zi serduals

sheal fal tn2,). The outess nay k
distandad
bu Smetims onde tfeamalien abra unusal Ce Unst,

nd She uld not be discasded.

Rurduads Csn be lotd ( in hm sentme

i)auist
(h)adauns i

(b)
(a)

(C)
 ( ) threstnts Jht ndeal S1tuat ion

M, C),u tsed anemaluet.

n Ch, isdanls atpearan e hess Iha

uane may be

ate tsansfehnalin tn dhks n r Ied to timinate

t slem
h Ce), henduals afkasane shey tnuguality asianit
n Cc medel Inade yuacyje
rdes Tetms heuld be adlded t e medel.
hyher
E Thk uwun meld-fo 0njen pnity data is

7 2 8 3 + 11.944x, Table shors The obsenved ydur,

dickd r aun and th coapondeg Amduals.

Predicted Valkues, and Residuals

Table 11-4 Oxygen Purity Data from Example 11-1,
Residual Hydrocarbon Oxygen Predicted Residual
Oxygen Predicted
Hydrocarbon
Level, x Purity, y Value, ey- Level,J Purity., Value, e=y-j
89.069009 0.940991 L.19 93.54 92.063189 1476811
0.99 90.01
89.518136 -0.468136 12 1.15 92.52 91.614062 0.905938
1.02 89.05
I.15 91.43 91464353 -0.034353 13 0.98 90.56 88.919300 1.640700
14 1.01 89.54 89.368427 0.171573
1.29 93.74 93.560279 0.179721
15 89.85 90.865517 -1015517
96.105332 0.624668
1.46 96.72 92.212898 -1.822898
94.608242 -0.158242 16 1.20 90.39
36 94.45
0.317499 17 1.26 93.25 93.111152 0.138848
0.87 87.59 87.272501
92.662025-0.892025 18 1.32 93.41 94.009406 -0.599406
1.23 91.77
99.42 97.452713 1.967287 19 143 94.98 95.656205 -0.67620
1.55
93.65 95.2070781.557078 20 0.95 87.33 88.470173 -1.140173
10 I.40

A nma vebebilt let o he henduals Shekn tn (a)

A
tha veiduals falt at alana hagst lirne
Sin
hens sIduals felloy n ormal deshib ution

thoaph (b and () n duals

pheHtd nt J and X, bu bhen ptots de nit

indicate any Sehious medtd inada
Inade te
uay,
 99.9

99
2.5
95

80 .5

50 O.5

20
-0.5

1.5

0.1 2.5 87
19 -0.9 0.1 1.1 2.1 89 91 93 5 97 99
Residuals Predicted values. y

( 6)
AND CORRELATIKON
SIMPLE LINIEAR REGRESSION

2.1

1.T

0.1

-0.9

1 0.87 1.07 1.27 1.47 1.67

Hydrocarbon level (%)

(C)
Cotbitient dahnsten CR) t honds tfnel aboat
mlu t h
3fatitita euunes f ho
eodns f t fa molel. J
is
L apsoximato the
n
The Chbutrt ofdaotminatin
atu data
SS SSE
SST SST

kare.
E Fn 0 npuuby es an melt, we

R3S 52:15
45 38
0871 e he melel

dk v0tabelety in the dats.

acceunts fo 84 1 oh
Ymsen1atums to strakt dr

SOncdim
Jomtimas satt
suttu deajsam Shes a nm-unear Julatonshp

tn a
and y. JAt nm- intan funtim (on be epeed
as Stakt line b tina Suitabl ttanhnnmalhon

Calltel 1ttunsi cally lnan.

Can be wtten as »y- L»thxt Le

Po t (t)+t Y- Ps+Z+ s ng th ti ansbr

DMore than dre

ny* p»tfxt phens

tanshetmam
ttanshelmatim
orrelatim
as u m tht bolh A and
Y a andom
anialles y
kd (Mis ), i e l - n Jnt dit butd Y vs

kig rbetn fyg). Shear strenth pet-

elds to the weld duameler
t s sume that Joint distnbutim andand Y,
Yuale nemal dlkabulon. Man dd riunau

y nd Aopectie and oX ane

J Xy th (olaty (oelhuent Whn xy T

(ovii an & betren X and y.
 (mdtmal dttn bukn Y f t n X:

8r

wean

fmtt uYnn medel.Pko

An My a

Thnt is
no vheuun Yo X.
J: oo
dos net dst 1 n
tsedictin .
= Eneide fX
and o d and F. tepectiely
estomatadd rue
Th Jikeluhred estimatrs a

Ca Computrd e m ma4 mum

Y- Prand 2Y(M-
Sxx -)

TLeshimslt B
( x - S

that SSr
he
Sxx
SR Sxy
SST Sa
SST Sxx SS

SS
SST
 (

with (n-a)
a t-d stibutcon
S4atots ases fsudn

J:o yeitn
Jtel tapn-2, thp h:
lo tst
Jt arllnt

Jo
4Ttst H,: J ,
Jt u Tompicatad

M: SAS,

(n>2s)
menataly luje Jamples
s+atatic Z: dnctnahk n(tE_
th tut -R
duttribuld with mean z : auttarhf: 1h//t)
sa nemebly

and

atanhh - enctph b) (n-3)

lvera) cI
+
tapb (asc taph k
-

4/ SSstb/acts,h e
n-3 n-3
whuna tarhu e-e
ete

See smte fm th text bovk.