129
7/23/2019 OPSI-2015-I-01 http://slidepdf.com/reader/full/opsi-2015-i-01 1/129 A study was made on the amount of converted sugar in a certain process at various temperatures. The data were coded and recorded as follows: Estimate the linear regression line. T, (x) Converted ugar, y !esidual " #." $.$"%$&$'' #.$#&%* "." '.# $.$"+%*#$+ '.'#*&+"& ". #.% $.$"#$*%*% #.&#"+&+% ".* .# $.$"%*+& .'#$&+'*+ ".& .% $.$"$* .&'#'$$' ".% #. $.$%' #.#''&''# ".+ #.+ $.$&$&%" #.%'%'%& ".' "$. $.$%%"# "$."'&&'# ".# .* $.$'$"$ .'#$" ". . $.$#%"+*# ."'"&#*+ "$.% $.$*$$"*+' "$.&+#+* !esumen stadísticas de la regresión Coeciente d $.'$'$+&& Coeciente d $.&##+* !- austad $.&&&*"#" Error t/pico $.+*+$' & 01servacion "" A23455 6E 7A!5A28A Grados de libert !egresi9n " !esiduos Total "$ Coefcientes 5ntercepci9n +.&"*+*+*+ 7aria1le " ".#$ $$ " An;lisis de los residuales Observación onóstico para " #.'' ' #.&$*+*+*+ * #.%#&%&%&%

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A study was made on the amount of convertedsugar in a certain process at various temperatures. Thedata were coded and recorded as follows:Estimate the linear regression line.

T, (x) Converted ugar, y !esidual" #." $.$"%$&$'' #.$#& % *

"." '.# $.$"+%*#$+ '.'#*&+" &". #.% $.$"#$*%*% #.&#" +&+%".* .# $.$" %* +& .'#$&+'*+".& .% $.$ "$ * .&'# '$$'".% #. $.$ % ' #.#''&' '#".+ #.+ $.$ &$ &%" #.%'% '%&".' "$. $.$ %% "# "$."'&&'#".# .* $.$ '$" $ . ' #$ "". . $.$ #%"+*# ."'"&#*+

"$.% $.$*$$"*+' "$.&+ #+*

!esumen

stadísticas de la regresiónCoe ciente d $.'$'$ +&&Coe ciente d $.& ##+*!- a ustad $.&&&*"# "Error t/pico $.+* +$' &01servacion ""

A2345 5 6E 7A!5A28AGrados de libert

!egresi9n "!esiduos

Total "$

Coefcientes5ntercepci9n +.&"*+*+*+7aria1le " ".#$ $ $ "

An;lisis de los residuales

Observación onóstico para" #. ' ' '

#.&$*+*+*+* #.%#&%&%&%

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& #.'+%&%&%%% #. &+*+*+&+ ." ' ' '*' .*$#"#"## .&# $ $ "

.+'

"$ .#%$ $ $"" "$.$*"#"#

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<ip9tesis<$ y no es funci9n de x 1=$<" y es funci9n de x 1>?$

igni canciaα $.$% %@

Criterioe recha a <$, si Bcalc?Bcrit B crit $.$$&"*& %e recha a <$, si pcalc>pcrit

C;lculos

a de cuadra io de los cua F lor crítico de F *.+$$$ $ " *.+$$$ $ " #. % ""$% $.$"& '*.+$"' ' ' $.&$$" "'. $"#"#"#

Error típico Estadístico t Probabilidad In erior !"# Superior !"#n erior !"$%#$. &+*#$ +. *+*'%*+ +.'#+%E $$% &.* " % #% #.%$%*" ## &.* " % #%$.+$*"+'*& . *"#&* $.$"& ' $.&&&+*"+ *."'*%%$ $.&&&+*"+

!esultados de datos de pro1a1ilidad

&esiduos Percentil Y $." ' ' ' &.%&%&%&%% '.#$.+$*+*+*+ "*.+*+*+*+ #."$.$#&%&%&% .' ' ' ' #.%

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uperior !"$% Superior !"#n erior !"$%#uperior !"$%##.%$%*" ## #.%$%*" ## &.* " % #% #.%$%*" ##*."'*%%$ *."'*%%$ $.&&&+*"+ *."'*%%$

$.# " ". ".& ".+ ".# .$

&

+

#

"$

"

Converted ug

y calc

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.

!esidual

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r, y

$.# "

$.#

$.+

$.&

$.$

$.

$.&

$.+

$.#

"

".Variable X 1

Residuos

$.# " ". ".& ".+ ".#$

&

+

#

"$

"Variable X 1 Curva de re

Variable X 1

Y

$ $ &$ +$$

&

+

#

"$

"

Gráfco de probab

Muestra p

Y

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". ".& ".+ ".# .

ráfco de los residuales

Variable X 1 .

resión ajustada

Dron9stico para D

#$ "$$ " $

ilidad normal

rcentil

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e han o1tenido los siguientes datos de presi9n de saturaci9n del etanol para diferena. uponiendo Fue no se conoce la funcionalidad entre T (x) y s (y), a ustar un mod1. A uste los par;metros de lecuaci9n e Antoinec. A uste los par;metros de la ecuaci9n de Antoine modi cadad. A uste los par;metros de la ecuaci9n 65 !

Gmm<gH% %%.*$ '$*% '&$ ""'.%&% "%&."%$ " $.'%% &".

a. uponiendo Fue no se conoce la funcionalidad entre T (x) y s (y), a ustar un mod

Gmm<gH% %%.

*$ '$*% '&$ ""'.%&% "%&."%$ " $.'%% &".

e tienen tres posi1ilidades, exponencial, potencia y polin9mica

a". otencia a $." '+ #"%1 ".#+' " &#

x y lnx lny ycalc residuos% %%. *. "##'%# &.$ *%+&*#$ % ."&$+$*+ *.'% * +*%

*$ '$ *.&$"" '*# &. &#& % & '*. % $"# *. % $"'*% ' *.%%%*&#$+ &.%'&'"$ '#% '.'%*$'+ $.'%*$'+ *&$ ""'.% *.+###' &% &.'++&*#***+ " %.&&% '# '. &% ''##&% "%&." *.#$+++ & %.$*'+$"'& * "%+.*"%'%% . "%'%%"%$ " $.' *. " $ *$" %. %$'$"%" + " $.*"%*"+ $.*#&+#* "%% &". &.$$'***" %.&##% &&"'+ '.&$$+ % "&.& *'%"

!esumen

stadísticas de la regresiónCoe ciente d $. %&&*Coe ciente d $. $ $+'+

T GICH

T GICH

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!- a ustad $. # $##""Error t/pico $.$%%*''+#01servacione '

A2345 5 6E 7A!5A28AGrados de libert a de cuadra edio de los cuadr F lor crítico de

!egresi9n " ".+'$ " *# ".+'$ " *'%* %&&.#% "*' 2 !"!#$%%!!esiduos % $.$"%***&* $.$$*$+++#+

Total + ".+#+ &%#"

Coefcientes Error típico Estadístico t Probabilidad In erior !"#5ntercepci9n .$%#+*&*& $. * &" '.$" $%$ &#% $.$$$ $%*% .#" %++&'7aria1le " ".#+' " &# $.$#$$ *.*& "' $'* .+#% E $$+ ".++ $'$"

a . olinomica

x x y ycalc error% + % %%. %+.& $&'+" $% $.% $&'+"

*$ $$ '$ '". +& #%'"&* ". +& #%'"*% " % ' .*+& #%'"&* &.+*%'"&&$ "+$$ ""'.% "" .' $&'+" $% . $&'+"&% $ % "%&." "%*.%& #%'"& $.%%'"& #+%$ %$$ " $.' " *.+ "& #%'"& . "& #%'%% *$ % &". &$.$ +" $&'+ ".#'*#$ %

!esumen

stadísticas de la regresiónCoe ciente d $. &Coe ciente d $. #&#&%'!- a ustad $. '' +#+Error t/pico *. $*"$&#01servacione '

A2345 5 6E 7A!5A28A

Grados de libert a de cuadra edio de los cuadr F lor crítico de!egresi9n '$&$."%'+ "*% $.$'##$ % "*"'.'+"'+ 2 2&'#$%%!!esiduos & &".$* % *# "$. % ##$ % &

Total + '$#"." '"

Coefcientes Error típico Estadístico t Probabilidad In erior !"#5ntercepci9n ''.%"& #%' ".%%%"#% *.% +$#% &$" $.$ #*'+ "'.++'& %&7aria1le " &.$$&$&'+ "." &# *&' *.%% & $%$"" $.$ *% +#" '." ' % %7aria1le $." +% *#" $.$"* ' % .$%$+'$& &' $.$$$# %# $.$#''"$%"

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a*. Exponencial

x y lny ycalc error% %%. &.$ *%+&*# %+.% # # '# $.+ #

*$ '$ &. &#& % & ' . %% """ . %% ""*% ' &.%'&'"$ # . # ""%''% &.'"$'##&&$ ""'.% &.'++&*#** ""'. " #%#+ +# $.&" #%#+*&% "%&." %.$*'+$"'& "%$.++#+'*" &+ *.&*"* +#"%$ " $.' %. %$'$"%" " .%" %" & $' ".#" %" &%% &". %.&##% && &%. '' '#* " &.$'' '#*

!esumen

stadísticas de la regresión

Coe ciente d $. #+'" #Coe ciente d $. '*&%'!- a ustad $. +#"&#'Error t/pico $.$ " ""01servacione '

A2345 5 6E 7A!5A28AGrados de libert a de cuadra edio de los cuadr F lor crítico de

!egresi9n " ".+#"''$$& ".+#"''$$&&' "#'#.'%"% 1 2()#$%%'!esiduos % $.$$&&'%'' $.$$$# %"%*

Total + ".+#+ &%#"Coefcientes Error típico Estadístico t Probabilidad In erior !"#

5ntercepci9n .#$ *#"& $.$&++ %%+ +$. %&"$ &' .*# #E $$# .+# % +%'7aria1le " $.$& $"%+ $.$$""*$#& &*.*&&%+'""%' ". **+E $$' $.$&+"$#+

e selecciona el modelo polin9mico

1. Ecuaci9n de Clausius Clapeyron

Gmm<gH T GJH ln( s) ("KT) s calc% %%. #."% &.$ *%+&*#$ $.$$**%&$ %%.&""+*&&

*$ '$ *$*."% &. &#& % & $.$$* #' ' . %+&''*% ' *$#."% &.%'&'"$ '#% $.$$* &%"' *.&"* &*%&$ ""'.% *"*."% &.'++&*#***+ $.$$*" **+ "" .'#$"+&% "%&." *"#."% %.$*'+$"'& * $.$$*"&*"' "% .* '++%$ " $.' * *."% %. %$'$"%" + $.$$*$ &%& " .&&%*%% &". * #."% %.&##% &&"'+ $.$$*$&'* &".*$ #"#

T GICH

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!esumen

stadísticas de la regresiónCoe ciente d $. $#&'%Coe ciente d $. #"'$**

!- a ustad $. '#$&&Error t/pico $.$ &#&$%'01servacione '

A2345 5 6E 7A!5A28AGrados de libert a de cuadra edio de los cuadr F lor crítico de

!egresi9n " ".+#*"+$%& ".+#*"+$%* * ' '.'*%#% ) "!*#$%%"!esiduos % $.$$*$#% ' $.$$$+"'$%&"

Total + ".+#+ &%#"

Coefcientes Error típico Estadístico t Probabilidad In erior !"#5ntercepci9n $."$' %%% $. *# &% +#.&*% %#+%$# ". +"+E $$# " .*% +%%+7aria1le " &' #."''& ".#'$*$ + % . ''*$+ $ &.#+%"E $$# %$*&.**'%%

c. Ecuaci9n de Antoine

A L C"#. "" *#$&."%$*## #% &".+#

Gmm<gH T GJH s calc error% %%. #."% % .$ +*'$+*"& *." +*'$+*

*$ '$ *$*."% '#.&''* #&% " #.&''* #&%*% ' *$#."% "$*.""""*# ' & +.""""*# '&$ ""'.% *"*."% "*&." "'&+'% * "+.+ "'&+#&% "%&." *"#."% "' .#$'& +$*+ "#.'$'& +%$ " $.' * *."% $.+%%'''"*$ . %%'''"%% &". * #."% ' .*%# $# &' *'.&%# $#

'#.*% '+$ *%".% '% . * *&$ ' $.$$$+$++

&*.$% &'##$ %"+. %* $ .&% %+%"#C ln( siK s") ("KT"MC) T T

&".+# $.$$*# $$. & *$#+ $.$$* #' $.$$$+$$* &% % %%%1(*

$.%%""&++ $.$$* &%"' $.$$$+%* "#' $.$$$*+$&"$.'& #'* % $.$$*" **+ $.$$$'$%'**' $.$$$% & '".$"&$*'*+ $.$$*"&*"' $.$$$'%% $" $.$$$'++%*". '"*'"* $.$$*$ &%& $.$$$#$&%%*& $.$$$ #'*

T GICH

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".&+& +$$& $.$$*$&'* $.$$$#%"'$&+ $.$$" &''".+$ '%&$% $.$$ #&& % $.$$"$%&"&"* $.$$ '%"$%

% %%!!('(

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es temperaturas.lo emp/rico a los datos

lo emp/rico a los datos

$ % *$ *%$

%$

"$$

"%$

$$

%$

*$$

f(x) = $." '+ #"&!N = $. $ $+'+

$

%

"$

"%

$

bX AY

xlnbaln ylnax y b

+=+=

=

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$ &% %$ %% +$

' x-".#+' " &#

+ ,mm-g.

Gmm<gHower ( Gmm<gH)

Column B

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%$ %% +$

error

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%$ %% +$

error

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'

+"$+E $$%

Column B4inear (Column B)

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tKIC $ "$ $ *$ &$$ $ $.$$ $.$$* $.$$ $

"$$ $.$** $.$&* $.$%* $.$+% $.$'#$$ $."'# $." $. $. &* $. +'

*$$ $.&*" $.&+ $.& & $.% ' $.%+"&$$ $.'#' $.# # $.#' $. "* $. %'

%$$ ". & ". * ".*&& ".* ' ".&%"+$$ ".' ".#% ". "* ". '% .$*''$$ .&*" .& .%+ .+* .'"#$$ *."%& *. * *.*$# *.*#+ *.&++

$$ *. %' &.$&" &." ' &. "* &."$$$ &.#*& &. + %.$"# %.""" %. $%""$$ %.'# %.#'# %. '+ +.$'% +."'%" $$ +.'#+ +.# +. % '." '. $%"*$$ '.#&# '. %' #.$++ #."'+ #. #+"&$$ #. %+ .$+ ."# . + .&"

"%$$ "$.$ "$. "% "$.**" "$.&&' "$.%+*"+$$ "". +* "".*# "".& ' "".+"& "".'*""'$$ " .&** " .%& " .+++ " .'# " .# #"#$$ "*.% " "*.'$+ "*.#

y ycalc x x x* x&$ %'. "*$%#" $ $ $ $

"$$ ''. &% #++ $.$** $.$$"$# *.% *'E $$% "."#% E $$+

$$ "+".&" #*% $."'# $.$*"+#& $.$$%+* '% $.$$"$$*##*$$ #". $* "+ $.&*" $."#%'+" $.$#$$+ $.$*&%$'"%&$$ &$+.+ #+"# $.'#' $.+" *+ $.&#'&&*& $.*#*+"' +%$$ %"'.#+%*& ". & ".%& %+& ". "%#+&& .*' %$*++$$ +"". %& #& ".' *. "" +& %.'%&%#%$ "$.*" "+%'$$ + +.'#*$+# .&*" %. $ '+" "&.*+++ *&. % '%"#$$ '##.$+'# *."%& . &''"+ *".*'%$ +* #. %'$%*+

$$ # ".'"#%*' *. %' "%.+%'#& +". %#"$#% &%."+# *%"$$$ "$$ .'* ' &.#*& *.*+'%%+ "" . %#'++ %&+.$& +'*""$$ ""$ .''+&% %.'# **.&$#& " *."$$%% """+." """ $$ " $%.* +'# +.'#+ &+.$& ' + *" .& * "+ " $.%#*'""*$$ " &.'"*&+ '.#&# +".% ""$& &#*.*++ #& *' *.&+&$"&$$ "* ".% #"" #. %+ #$. $ *+ '"#.*+$"#' +&**.+**#*"%$$ "%$".# %* "$.$ "$". # #$" "$ . % "$&$". " %"+$$ "+$ .%"%'" "". +* " +.#%%"+ "& #.'+ '' "+$ . **"'$$ "+ .'"'+ " .&** "%&.%' &# " ".##+' *# &.#"#&"#$$ "#$".+"'& "*.% " "#&.'"% #" %"$.&+%*# *&"" .'*%

"

"

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"

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7aria1le + $.$#$* +%7aria1le ' $.$$"%' #'

!esultados de datos de pr

Percentil Y .+*"%'# % $

'.# &'*+#& "$$"*."%'# &' $$"#.& "$% + *$$

*.+#& "$% &$$#. &'*+#& %$$

*&. "$% +* +$$* .&'*+#& '$$

&&.'*+#& " #$$%$ $$%%. +*"%' "$$$+$.% +*"%# ""$$+%.'# &'*' " $$'".$% +*"+ "*$$'+.*"%'# % "&$$#".%'# &'& "%$$#+.#& "$%* "+$$

."$% +* "'$$

'.*+#& "" "#$$

"+$$ "#$$ $$$

ycalc

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a de cuadra io de los cua F lor crítico de F %+ **$%.% #"** .*+ "**+.&"' + *. " &E $"%++ &.&#* * +$#.%# *#%

%'$$$$$

Error típico Estadístico t Probabilidad In erior !"# Superior !"#n erior !"$%#"+. $$*+ * *.%*"% " + $.$$&'$"+' ".%%+*$" .#+ #"% ".%%+*$"+'.*+% "%& .&'# + + ". %#+E $$+ & $. #'+*' '#+.#*$* ' & $. #'+*''$. %$" + &.&&++"$#" $.$$$ #&" &'". &+ $+ "% .& # *' &'". &+ $+*$. & '#&% *. '+$#&# $.$$'"$#$ **."' +" "++.**" ' **."' +"

+.*" ++' .'*++"%'# $.$" *&#"% *". $* *' *.*#%$$'"* *". $* *'$.+#+ '"%+ .* *"#%'+ $.$*%+% # $."* $*+*% *."%+$+&'% $."* $*+*%

$ $$ &$$

+$

&$

$

$

$

&$

+$

#$

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$.$*' '"* ."%+ %*"% $.$%* # #% $."+ & +&* $.$$"+&""* $."+ & +&*$.$$$' +'& ". # %"& $.$' $*# $.$$$"'*'& $.$$****&# $.$$$"'*'&

1a1ilidad

$ "$ $ *$ &$ %$ +$ '$$

$$

&$$

+$$

#$$"$$$

" $$

"&$$

Gráfco de probabilidad normal

Muestra percentil

Y

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$.$$"+&""*$.$$****&#

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'$ #$

al

#$ $

al

#$ $

al

$ "$$

al

$ "$$

al

"$$ " $

al

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n="

TimeKh G(C<*)*CLrHK Ccalc$ $."$%" $."$%" . % #&* $ %. "#'E $"% $.$#$* $.$#$*%"+ .% " #%++ %

"$ $.$+"& $.$+"&*$#+ .' $*&%&& "$"% $.$&' $.$&+ +%&% *.$%'+$'+# "%$ $.$*% $.$*% $+ # *.* '$"' # $% $.$ '& $.$ '&%" ' *.% ' " ' %

*$ $.$ " $.$ $ #'" *.#+* * #& *$*% $.$"+ $.$"+$&% & &."*%"++%+ *%&$ $.$" * $.$" ++ &.* #"%+$ &$

P $.$%*'

$ % "$

%&.%

&

*.%

*

.%

".%

"$.%

$

f(x) = $.$%!N = $.

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$ % "$ "% $ % *$ *% &$ &%$

$.$

$.$&

$.$+

$.$#

$."

$."

"% $ % *$ *% &$ &%

*+#' &'"x . %**"#"$++%&+*

Column 64inear (Column 6)

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CcalcColumn L

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'.& &% $ % & $$.% &% $ % & $

* &% $ % & $#+.* &% $ % & $

!esumen

stadísticas de la regresión ++.%+'++ &Coe ciente d $. & &*' 'Coe ciente d $. $"&* &+!- a ustad $.''# *$&Error t/pico +.%&+&$&#'01servacione "$

A2345 5 6E 7A!5A28AGrados de libert a de cuadra io de los cua F lor crítico de

!egresi9n % "%+'.'$'** *"*.%&"&+' '.*"+ + & $.$*#* &*!esiduos & "'".& "++' & .#%%&"+' Total "'* ."

Coefcientes Error típico Estadístico t Probabilidad In erior !"#5ntercepci9n ++.%+'++ & *&. % '%++ ". $&%$* * $." %+&"& "+*.+" $'7aria1le " .++%"#'* $.'+# *& * *.&++$'+%& $.$ %+'%"# $.%*$ #"'7aria1le # .++$#& & %.+*%+ *. &&% +% $.$* "&&* "".&#& %7aria1le * $.$"#***** $.$$+ # . "$*#%$% $.$&*++"* $.$*%# &7aria1le & "'. $"$$ " %.++ +#%%& *.$**#%% & $.$*#+*&"+ * . & %' #

7aria1le % $. * #'"&& $. %" '#+* $. &"'"*# $.&$''$"#& $. * &'+ #

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?? a$= ".#Q a"="+.&#******Qa =*.*''% #"% Qa""= "+.%Qa = "'. $"$$ "?? xp= ":.":"Qyp= ":.":"Q?? Gx yH=meshgrid(xp,yp)Q?? =a$Ma"RxMa RyMa""Rx.- Ma Ry.- Ma" Rx.RyQSSS nde ned function or varia1le Ua" U. ?? a$= ".#Q a"="+.&#******Qa =*.*''% #"% Qa""= "+.%Qa = "'. $"$$ "?? xp= ":.":"Qyp= ":.":"Q?? =a$Ma"RxMa RyMa""Rx.- Ma Ry.- Ma" Rx.RyQ?? mesh(x,y, )

?? contour(x,y, )?? meshc(x,y, )?? surf(x,y, )?? surfc(x,y, )?? ++.%+'+ .++%"#'* # .++$#& & $.$"#***** "'. $"$$ " $. * #'"&&SSS ++.%+'+ .++%"#'* # .++$#& & $.$"#***** "'. $"$$ " $. * #'"&& VError: nexpected WAT4AL expression. ?? a$= ++.% .++%"#'* # .++$#& & $.$"#***** "'. $"$$ " $. * #'"&&SSS a$= ++.% .++%"#'* # .++$#& & $.$"#***** "'. $"$$ " $. * #'"&& VError: nexpected WAT4AL expression. ?? a$= ++.%+'++ *'Qa"= .++%"#'* &Qa =# .++$#& &&Qa""= $.$"#******Qa

a" =

$. *

?? xp="$:":#$Qyp=":.$%: Q?? Gx yH=meshgrid(xp,yp)Q?? =a$Ma"RxMa RyMa""Rx.- Ma Ry.- Ma" Rx.RyQ?? surfc(x,y, )??

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** + .'%"'** + .'%"'** + .'%"'** + .'%"'

.++%"#'* # .++$#& & $.$"#***** "'. $"$$ " $. * #'"&&

F

Superior !"#n erior !"$%#uperior !"$%#*$.&'+'&'+ "+*.+" $' *$.&'+'&'+&.#$$$ % $.%*$ #"' &.#$$$ %"%*.#*+'&' "".&#& % "%*.#*+'&'$.$$$#&*'* $.$*%# & $.$$$#&*'*".&% &*#&+ * . & %' # ".&% &*#&+

$.&++'**& $. * &'+ # $.&++'**&

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Qa"= +. #+"&*"#'Q

Qa" = +. #+"&*"#'Q

= "'. $"$$ "*Qa" = $. * #'"&&

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a a""'. $"$$ " +. #+"&*"

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5ntercepci9n + & "%.&$ "& * &$.& %&&$" ".'*"+E $$' %#&.*# %*a" .*'% .&*+"*&$" $. *% " % (!!%'(2 "&.##"*%&'a + "". '#**'* $.%*" **" % !1'*1%' . "## "a* &*. % "". '#**'* *.#*&'#%"" $.$" "##"' ' . &"## "a"" . % "%. $"*+ " +.$+#%* *% $.$$"'%&%% "*".* +*+*a *+.'% "%. $"*+ " .&"'%&%&" % %!%2&&" .* +*+* &

a** "#.% "%. $"*+ " ". "+ %+%% 2''&%&) %'.%'+*+*a" " .% "*.*&&'$#' ".&+" %*** % 2%('"" %*.#$*++%#a"* "$ . % "*.*&&'$#' #."#+'+%&% $.$$$&& '&. &+**&a * +* "#."#%'' % *.&+& &+%' $.$"' +$$# "$ .'&#$"+

!esultados de datos de pro1a1ilidad + &

Percentil Y

*.******** *%$"$ &%#"+.++++++' %*

*.******* %*%*$ %+*

*+.++++++' %#$&*.******* % %

%$ % +%+.++++++' %+*.******* +$$

'$ + $'+.++++++' +&%#*.******* +&#

$ +%*+.++++++' +%+

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ycalc%**.+ %% ".*'%%#&.+ %%+&.*'%

+%+.*'%&%+.+ %*%".*'%%##.+ %

+"+.%+"+.%

%&+%++ &+ &+ &

babilidad normal

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" .% "$ . % +*

+$ #$ "$$ " $

stra percentil

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!esultados de datos de pro1a1ilidad

Percentil Y

+. % +%"#.'% '*". % #&*.'% %%+. % ""$+#.'% "#". % " %

*.'% "*$

Wodelo y=a$Ma"x"Ma x Ma" x"x

E " x"x D Dcalc" "$ " .% " % +% +&.$*#* *#

" "% "#$ ' '*.+"##""%** "% "# '$ # #".& %+# *%& "+ " **+ % %.$" $' %% " + & & ""$ ""$.$ %'% %+ " *$ +*$ " " ".+* #*&+' % *% #'% " % " %."$"%$$%# # &$ "" $ "*$ "*$.$+$ &&+

!esumen

Estadísticas de la regresiónCoe ciente de $. %&# #%Coe ciente de $. $ #"'*!- a ustado $. #& "#$*Error t/pico ".$$*%*'"&*01servacione #

A2345 5 6E 7A!5A28AGrados de libert a de cuadra dio de los cua F alor crítico de!egresi9n * &&+ .#&++%* "&#'.+"%%%" "&''."&'*$+ 1 *2)*#$%%!!esiduos & &.$ #*&'" ".$$'$#+' #

Total ' &&++.#'%

Coefcientes Error típico Estadístico t Probabilidad In erior !"#5ntercepci9n ".*$' "%#%# *.#"+&&%%+ $.*& % "#"& $.'& $$$'# "". $**+'&#7aria1le " ".& '''#"++ $.''"'+&*& ". &$'" %# $." & '&%'& *.+&$%* &

$ "

".%

"

$.%

$

$.%

"

".%

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5ntercepci9n ++.%'& '$' "*.' "%*#%% &.# '"# * $.$$#&'#+ #. # # "$#7aria1le " &."*%#% &&% &.%**%'# & $. " ' %"" $.&"* *&$#% "+.' *$ %7aria1le .* "#$*&* .%''$$ % $. $$ +# "' $.&"#%&'''* .&'+' #"%%7aria1le * +. '%++$#%& +.#&*% && $. "'$" +' $.&""$ '"' " .' %" '**

!esultados de datos de pro1a1ilidad

Percentil Y +. % +%

"#.'% '*". % #&*.'% %%+. % ""$+#.'% "

#". % " %*.'% "*$

Wodelo & cuadratica completa

E " x"x" x x x"x" "$ " .% "$$ "%+. % " %

" "% "&& % "#$* "% "# % * & '$& "+ " %+ &&" **+

% " + *+" +'+ & &+ " *$ &&" $$ +*$' % *% + % " % #'%# # &$ '#& "+$$ "" $

!esumen

Estadísticas de la regresiónCoe ciente de $. #++ ##Coe ciente de $. '* % *!- a ustado $. $+&$''Error t/pico $.'' #"$%&'01servacione #

A2345 5 6E 7A!5A28AGrados de libert a de cuadra dio de los cua F alor crítico de

!egresi9n % &&+%.+#$% # # *."*+"$%% "& %.&&##%+ $.$$$++#*#*!esiduos "." &&' #% $.% ' *+"&

Total ' &&++.#'%$.

$.

$.

$.

$.

$.

$.

$.

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Coefcientes Error típico Estadístico t Probabilidad In erior !"#a% *$. "#$*'%& "+.$%'*+"" ". %&'&*## $." &$*&"'% *#."'" ""$*a1 &.$&&$ '+ "$.#+ "# * . " "**+ # $."%'&+$* '$.#"$&&+&+a2 ".%#%'$ &% +.' $"%+'%& *. " $#& "' $.$#&'' "%' '.* #' "*%%

a11 *. "+'"%*+" ".&#$ '*%#' ."' $ '%$* $."+" '# * *."%%* +#%

a22 "."&*%#+ *% $.% +&&&+% ."' #** ' $."+" & +"" "." "% "%'&a12 *. +'$ '#+" ".'+'#&+#$% . &* ##&'' $."%* *+&# "".%'*&%#'&

!esultados de datos de pro1a1ilidad

Percentil Y +. % +%

"#.'% '

*". % #&*.'% %%+. % ""$+#.'% "#". % " %

*.'% "*$

E emplo ".& 7amos a desarrollar una ecuaci9n para los datos so1re la capacidad de calor de v

T GJH Cp GcalKmol JH

*$$ " .+%&$$ +.'& Cp=1$M1"TM1%$$ * .# Cp=1$M1"TM1+$$ *'.'& Cp=1$M1"T'$$ &".'% Cp=1"T#$$ &%.$+

$$ &'.#*"$$$ %$."+

Cp=1"T T GJH Cp GcalKmol JH Cpcalc residual*$$ " .+% "+. $*#"%'# .'&+"#& "$%&$$ +.'& .%*#& "$%* &. $"%'# &'&%$$ * .# #."'*$ +*"+ &.+ + '*+#&+$$ *'.'& **.#$'+*"%' *. * *+#& ""'$$ &".'% * .&& *+#& .*$''+*"%'#$$ &%.$+ &%.$'+#& "$% $.$"+#& "$%*

$$ &'.#* %$.'""&&'*+# .##"&&'*+#&"$$$ %$."+ %+.*&+$% +* +."#+$% +*"+

!esumen

$

&

$

&

+

110 xaa y ++=

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Estadísticas de la regresiónCoe ciente de $. %*"$"*Coe ciente de $. $+& %#!- a ustado $.#&''#%""%Error t/pico &.$*& $%%'"

01servacione #

A2345 5 6E 7A!5A28AGrados de libert a de cuadra dio de los cua F

!egresi9n " " $+&.%*%$+ " $+&.%*%$+ '&".$&*'***!esiduos ' ""*. +* &$# "+. #$&+ '

Total # " "'#.& #*

Coefcientes Error típico Estadístico t Probabilidad5ntercepci9n $ Err:%" Err:%" Err:%"

7aria1le " $.$%+*&+$%* $.$$ $+ #+* '. ""#&+ .*"%*%E $$#

Cp=1$M1"TM1 T

T GJH T- Cp GcalKmol JH Cpcalc residual*$$ $$$$ " .+% " .# %#*** $. & %#****&$$ "+$$$$ +.'& +.+$&"$'"& $."*%# #%'%$$ %$$$$ * .# * .%$"+$'"& $. #* #%'+$$ *+$$$$ *'.'& *'.% $#*** $."&' "+++'

'$$ & $$$$ &".'% &".#'%%*%'" $." %%*%'"&#$$ +&$$$$ &%.$+ &%.*%" +& $. " +& #+$$ #"$$$$ &'.#* &#.$ "*+ $% $." "*+ $&#

"$$$ "$$$$$$ %$."+ & .##*'% $. '+ %

!esumen

Estadísticas de la regresiónCoe ciente de $. '&% &Coe ciente de $. & " &

!- a ustado $. ##' #Error t/pico $. #&# $ %%01servacione #

A2345 5 6E 7A!5A28AGrados de libert a de cuadra dio de los cua F

!egresi9n ' '. +#%' + * #. #& #+* & "#. +&#!esiduos % $.&$%+"&##" $.$#"" '+

Total ' ' #.*'&"#'%

#

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Coefcientes Error típico Estadístico t Probabilidad1$ %.$%+"*$ % $.#+'+&"%'+ %.# '&&" $.$$ "$ #*'1" $.$ % "$'" $.$$ # $ #* * . + &+ " &.# &'*E $$'1 &.$*%"E $$% ." '&&E $$+ "#.*+ #$+& #.#$#+$E $$+

257E4 Temperatura 7elocidad de a resi9n x" x<igh $$ "$ % " "

Widdle "'% '.% $ $ $4ow "%$ % "% " "

Experiencia x" x x* x"x" x x" " " $ " "

" " $ " "* " " $ " "& " " $ " "% " $ " " $+ " $ " " $' " $ " " $# " $ " " $

$ " " $ ""$ $ " " $ """ $ " " $ "" $ " " $ ""* $ $ $ $ $"& $ $ $ $ $"% $ $ $ $ $

!esumen

Estadísticas de la regresión a% a1Coe ciente de $. ' "$++ * !2) & ('*Coe ciente de $. && " #+!- a ustado $.#&% '%+$Error t/pico * .*$'"" +

11.11. Se ha realizado un experimento en base al diseño de Box–Behnken, obteniéndose los siguientes dat#a $ %&uste un modelo de Segundo orden.#b $ 'ue tipo de super(i ie se obtendr)*#c $ +uales son las ondi iones de x 1, x , - x para al anzar un punto esta ionario*#d $ 'ue ondi iones de opera i/n usted re omienda para al anzar una vis osidad er ana a 0 *

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y = partes de 0 por "$$ millones de partes de aire.

or los residuales, se puede decir Fue es cuadratica

Superior !"# In erior !"$%# uperior !"$%##&.* &#+*$' +.$ # #$$+ #&.* &#+*$'"$.' '& #" "+.$'#'%+'' "$.' '& #"" .' +*#$"# &.*" $%'% " .' +*#$"#

ncentraciones de 0 y 20 en la atm9sfera. 4os datos

"$ "% $ % *$

X1

D

$ " * & % + ' #

"$#+&

$

&+#

X1

Ex

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residual$. +"+$+""&".+"##""% '

$.%'&*"'+&$.$" $' %$.$ %'% %$'$.*+$"+%*+

$."$"%$$%*#$.$+$ &&+$"

Parece e'ponencial

Superior !"# In erior !"$%# uperior !"$%#. ## *%'+ "". $**+'&# . ## *%'+

$.+&& #*"%# *.+&$%* & $.+&& #*"%#

$

$

$

&$

+$

#$

"$$

" $

"&$

Y * & % + ' # Column O

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.$#""+'&+* +.$ +*'#$* .$#""+'&+*$.$ &#&$#& $."*''* &&% $.$ &#&$#&

D Dcalc esidual+% '&.++&"&'$ .++&"&'$ &' '#. *+ +' +. *+ ++'# '#."'$$"& *.# #%$ +

% .%$$ #'"+ .& $" #&*""$ "$&."++*%&* %.#**+&%'$" "$+.'$*%$+% "%. +& *&

" % " #.+%+"+*" *.+%+"+*$#+"*$ "*'. "%"*&* '. "%"*& #+

Superior !"# In erior !"$%# uperior !"$%#

$ " * & % + ' #

Column 5

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"$&.#+%' $% #. # # "$# "$&.#+%' $%#.&%"*'*+" "+.' *$ % #.&%"*'*+"&.#**" " % .&'+' #"%% &.#**" " %

%. '+%" $& " .' %" '** %. '+%" $&

D Dcalc residual+% +&.''+ $ $. *$' #$' ' .+ *%* +% $.+ *%* +%# #". #& " " $.$"%$#'

% &.* " & %" $.+$#$%$&#

""$ "$ .# %#*# $."$&"+"'" " ."*%*# # $."*%*# #*" % " %.%$'$ + $.%$'$ +$#"*$ " .+#&*%' $.*"%+& ""'

$ " * & % + ' # Column 5

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Superior !"# In erior !"$%# uperior !"$%#"$$.$$' #+" *#."'" ""$* "$$.$$' #+"

.' &+ & '$.#"$&&+&+ .' &+ &%$.%$$ "$ % '.* #' "*%% %$.%$$ "$ %

.%###*$&$' *."%%* +#% .%###*$&$'

*.&$#+ %&&% "." "% "%'& *.&$#+ %&&%*.+* &$*$ "".%'*&%#'& *.+* &$*$

por de 1enceno como funci9n de la temperatura. 4os valores experimentales se muestran en l

T"KT

*$$ &$$ %$$ +$$ '$$ #$$ $$ "$$$ ""$$ Column E

2112

2

222

2

11122 x xa xa xa x +++

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es cuadratica

alor crítico de F ".+ * 'E $$'

In erior !"# Superior !"# In erior !"$%# uperior !"$%#Err:%" Err:%" Err:%" Err:%"

$.$%"&%"+$% $.$+" &$%$" $.$%"&%"+$% $.$+" &$%$"

alor crítico de F %.#"' *E $$

$$ *$$ &$$ %$$ +$$ '$$ #$$ $$ "$$$ ""$

$.&

$.*

$.

$."

$

$."

$.

$.*

$.&

C p

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In erior !"# Superior !"# In erior !"$%# uperior !"$%#'. #+&'&+ ' .# %'#' '# '. #+&'&+ ' .# %'#' '#

$.$#'#+"*+* $."$ ' $'# $.$#'#+"*+* $."$ ' $'#&.+$$$E $$% *.&'$ E $$% &.+$$$E $$% *.&'$ E $$%

x*"

$"

x*x* x"x x"x* x x* 7iscosidad 7isCA4C$ " $ $ %*% %"$ " $ $ %#$ %+ .'%$ " $ $ % + +$+. %$ " $ $ %+* %#+" $ " $ +&% +* ." %" $ " $ &%# &* .*'%" $ " $ *%$ *+#.+ %" $ " $ +$$ +$%.#'%" $ $ " % % + *.#'%" $ $ " +&# +&*.+ %" $ $ " %* %*+.*'%" $ $ " +%+ + '." %$ $ $ $ +%* + &$ $ $ $ % + &$ $ $ $ + $ + &

a2 a( a11 a22 a(( a122' !2* $2! $'* 1& * $(* '* $1& *

A .*'% <

s en la tabla P11.5, donde la variable respuesta es la vis osidad de un pol!mero"

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"$ "% $ % *$ *% &$ &%

$

$

&$

+$

#$

"$$

" $"&$

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Example . 5n a two stage compressor, the worPing gas leaving the rst stagecompression is cooled (1y passing it through a heat exchanger) 1efore it enterssecond stage of compression to increase the e[ciency G ."*H. The total worP ina compressor (X) for an ideal gas, for isentropic compression, is given 1y

where cp is the speci c heat of the gas at constant pressure, P is the ratio of speheat at constant pressure to that at constant volume of the gas, and T" is the teat which the gas enters the compressor. Bind the pressure, p , at which intercoolshould 1e done to minimi e the worP input to the compressor. Also determine thminimum worP done on the compressor.

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f heut to

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