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Chemical & Biomolecular Engineering 154

ELEMENTARY ERROR ANALYSIS: ROA!ATION O" ERROR AN#

ESTIMATION O" ERROR "ROM LINEAR RE!RESSION

INTRO#$CTION:

Mo% o' he num(er% ha one re)or% a% he re%ul% o' one*% mea%uremen% an+

calculaion% are mean ,alue%- In or+er o a%%e%% he +egree o' heir ,ali+i./ an e%imae

o' heir %ai%ical relia(ili. calle+ he %an+ar+ error %houl+ (e calculae+- 0ere/ in ChE

154/ e u%e one o' he %im)le% concei,a(le a))roache% 'or hi% )ur)o%e/ rel.ing on he

conce) o' %an+ar+ +e,iaion- 2ere i )o%%i(le o u%e more a+,ance+

%ai%ical anal.%i%/ one oul+ (e re3ue%e+ o a))l. he %u+en*% e% a% a ne6 %e)-

San+ar+ error or %an+ar+ +e,iaion 7hiche,er i% a))ro)riae8 e%imae% o'

e6)erimenal +aa can (e o(aine+ (. re)eaing a rea+ing %e,eral ime%- In %ome ca%e%

here hi% i% no )o%%i(le/ one ill nee+ o gue%% he e%imae u%ing common %en%e-

9uaniie% ha are calculae+ (a%e+ on he%e e6)erimenal +aa al%o ha,e uncerainie%

a%%ociae+ ih hem +ue o he )ro)agaion o' error%/ an+ e u%e a meho+ rel.ing on he

in+e)en+ence o' muli)le conri(uing uncerainie% o e%imae he uncerain. in a re%ul

ha i% (a%e+ on e6)erimenall. mea%ure+ +aa- "or %ome e6)erimen%/ i i% nece%%ar. o

'i +aa u%ing linear regre%%ion (a%e+ on lea%%3uare%- In hi% cour%e/ a commercial

com)uer )rogram/ %uch a% E6cel/ ill (e u%e+ o calculae he error a%%ociae+ ih a

linear regre%%ion anal.%i% a% +eaile+ (elo- A% a general noe/ a%%ume ha error%

a%%ociae+ ih lieraure ,alue% or han+(oo;% are

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CASE I: #ETERMINE $NCERTAINTY IN E=ERIMENTALLY MEAS$RE#

9$ANTITY

E%imae uncerain. 'rom in%rumen or +ial rea+ing (. calculaing he mean an+

%an+ar+ +e,iaion o' a %e3uence o' he %ame mea%uremen- "or our )ur)o%e%/ he

%an+ar+ +e,iaion can (e u%e+ a% a mea%ure o' he uncerain. i' a 3uani. i% mea%ure+

%e,eral ime%- I' no/ e%imae uncerain. (. oher mean% (a%e+ on in%rumen gauge

characeri%ic%-

CASE II: ROA!ATIN! ERROR TO CALC$LATE $NCERTAINTY IN A "INALRES$LT

"or a ,aria(le ha one an% o calculae/ 3/ hich i% a 'uncion 7'8 o' %e,eral

,aria(le% 6/ ./ < >/ he uncerain. in 3 7re)re%ene+ (. 38 +ue o uncerainie% in 6/ ./

an+ < i% gi,en (.:

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