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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 $$% &.* " % #% #.%$%*" ## &.* " % #%$.+$*"+'*& . *"#&* $.$"& ' $.&&&+*"+ *."'*%%$ $.&&&+*"+
!esultados de datos de pro1a1ilidad
&esiduos Percentil Y $." ' ' ' &.%&%&%&%% '.#$.+$*+*+*+ "*.+*+*+*+ #."$.$#&%&%&% .' ' ' ' #.%
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uperior !"$% Superior !"#n erior !"$%#uperior !"$%##.%$%*" ## #.%$%*" ## &.* " % #% #.%$%*" ##*."'*%%$ *."'*%%$ $.&&&+*"+ *."'*%%$
$.# " ". ".& ".+ ".# .$
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Converted ug
y calc
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.
!esidual
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r, y
$.# "
$.#
$.+
$.&
$.$
$.
$.&
$.+
$.#
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".Variable X 1
Residuos
$.# " ". ".& ".+ ".#$
&
+
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"Variable X 1 Curva de re
Variable X 1
Y
$ $ &$ +$$
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+
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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 *. $*"$servacione '
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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".&+& +$$& $.$$*$&'* $.$$$#%"'$&+ $.$$" &''".+$ '%&$% $.$$ #&& % $.$$"$%&"&"* $.$$ '%"$%
% %%!!('(
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es temperaturas.lo emp/rico a los datos
lo emp/rico a los datos
$ % *$ *%$
%$
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$$
%$
*$$
f(x) = $." '+ #"&!N = $. $ $+'+
$
%
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$
bX AY
xlnbaln ylnax y b
+=+=
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$ &% %$ %% +$
' x-".#+' " &#
+ ,mm-g.
Gmm<gHower ( Gmm<gH)
Column B
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%$ %% +$
error
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%$ %% +$
error
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'
+"$+E $$%
Column B4inear (Column B)
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tKIC $ "$ $ *$ &$$ $ $.$$ $.$$* $.$$ $
"$$ $.$** $.$&* $.$%* $.$+% $.$'#$$ $."'# $." $. $. &* $. +'
*$$ $.&*" $.&+ $.& & $.% ' $.%+"&$$ $.'#' $.# # $.#' $. "* $. %'
%$$ ". & ". * ".*&& ".* ' ".&%"+$$ ".' ".#% ". "* ". '% .$*''$$ .&*" .& .%+ .+* .'"#$$ *."%& *. * *.*$# *.*#+ *.&++
$$ *. %' &.$&" &." ' &. "* &."$$$ &.#*& &. + %.$"# %.""" %. $%""$$ %.'# %.#'# %. '+ +.$'% +."'%" $$ +.'#+ +.# +. % '." '. $%"*$$ '.#&# '. %' #.$++ #."'+ #. #+"&$$ #. %+ .$+ ."# . + .&"
"%$$ "$.$ "$. "% "$.**" "$.&&' "$.%+*"+$$ "". +* "".*# "".& ' "".+"& "".'*""'$$ " .&** " .%& " .+++ " .'# " .# #"#$$ "*.% " "*.'$+ "*.#
y ycalc x x x* x&$ %'. "*$%#" $ $ $ $
"$$ ''. &% #++ $.$** $.$$"$# *.% *'E $$% "."#% E $$+
$$ "+".&" #*% $."'# $.$*"+#& $.$$%+* '% $.$$"$$*##*$$ #". $* "+ $.&*" $."#%'+" $.$#$$+ $.$*&%$'"%&$$ &$+.+ #+"# $.'#' $.+" *+ $.&#'&&*& $.*#*+"' +%$$ %"'.#+%*& ". & ".%& %+& ". "%#+&& .*' %$*++$$ +"". %& #& ".' *. "" +& %.'%&%#%$ "$.*" "+%'$$ + +.'#*$+# .&*" %. $ '+" "&.*+++ *&. % '%"#$$ '##.$+'# *."%& . &''"+ *".*'%$ +* #. %'$%*+
$$ # ".'"#%*' *. %' "%.+%'#& +". %#"$#% &%."+# *%"$$$ "$$ .'* ' &.#*& *.*+'%%+ "" . %#'++ %&+.$& +'*""$$ ""$ .''+&% %.'# **.&$#& " *."$$%% """+." """ $$ " $%.* +'# +.'#+ &+.$& ' + *" .& * "+ " $.%#*'""*$$ " &.'"*&+ '.#&# +".% ""$& &#*.*++ #& *' *.&+&$"&$$ "* ".% #"" #. %+ #$. $ *+ '"#.*+$"#' +&**.+**#*"%$$ "%$".# %* "$.$ "$". # #$" "$ . % "$&$". " %"+$$ "+$ .%"%'" "". +* " +.#%%"+ "& #.'+ '' "+$ . **"'$$ "+ .'"'+ " .&** "%&.%' &# " ".##+' *# &.#"#&"#$$ "#$".+"'& "*.% " "#&.'"% #" %"$.&+%*# *&"" .'*%
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7aria1le + $.$#$* +%7aria1le ' $.$$"%' #'
!esultados de datos de pr
Percentil Y .+*"%'# % $
'.# &'*+#& "$$"*."%'# &' $$"#.& "$% + *$$
*.+#& "$% &$$#. &'*+#& %$$
*&. "$% +* +$$* .&'*+#& '$$
&&.'*+#& " #$$%$ $$%%. +*"%' "$$$+$.% +*"%# ""$$+%.'# &'*' " $$'".$% +*"+ "*$$'+.*"%'# % "&$$#".%'# &'& "%$$#+.#& "$%* "+$$
."$% +* "'$$
'.*+#& "" "#$$
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ycalc
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a de cuadra io de los cua F lor crítico de F %+ **$%.% #"** .*+ "**+.&"' + *. " &E $"%++ &.&#* * +$#.%# *#%
%'$$$$$
Error típico Estadístico t Probabilidad In erior !"# Superior !"#n erior !"$%#"+. $$*+ * *.%*"% " + $.$$&'$"+' ".%%+*$" .#+ #"% ".%%+*$"+'.*+% "%& .&'# + + ". %#+E $$+ & $. #'+*' '#+.#*$* ' & $. #'+*''$. %$" + &.&&++"$#" $.$$$ #&" &'". &+ $+ "% .& # *' &'". &+ $+*$. & '#&% *. '+$#&# $.$$'"$#$ **."' +" "++.**" ' **."' +"
+.*" ++' .'*++"%'# $.$" *&#"% *". $* *' *.*#%$$'"* *". $* *'$.+#+ '"%+ .* *"#%'+ $.$*%+% # $."* $*+*% *."%+$+&'% $."* $*+*%
$ $$ &$$
+$
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$
$
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$.$*' '"* ."%+ %*"% $.$%* # #% $."+ & +&* $.$$"+&""* $."+ & +&*$.$$$' +'& ". # %"& $.$' $*# $.$$$"'*'& $.$$****&# $.$$$"'*'&
1a1ilidad
$ "$ $ *$ &$ %$ +$ '$$
$$
&$$
+$$
#$$"$$$
" $$
"&$$
Gráfco de probabilidad normal
Muestra percentil
Y
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$.$$"+&""*$.$$****&#
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'$ #$
al
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al
$ "$$
al
$ "$$
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n="
TimeKh G(C<*)*CLrHK Ccalc$ $."$%" $."$%" . % #&* $ %. "#'E $"% $.$#$* $.$#$*%"+ .% " #%++ %
"$ $.$+"& $.$+"&*$#+ .' $*&%&& "$"% $.$&' $.$&+ +%&% *.$%'+$'+# "%$ $.$*% $.$*% $+ # *.* '$"' # $% $.$ '& $.$ '&%" ' *.% ' " ' %
*$ $.$ " $.$ $ #'" *.#+* * #& *$*% $.$"+ $.$"+$&% & &."*%"++%+ *%&$ $.$" * $.$" ++ &.* #"%+$ &$
P $.$%*'
$ % "$
%&.%
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.%
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"$.%
$
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 & &.$ #*&'" ".$$'$#+' #
Total ' &&++.#'%
Coefcientes Error típico Estadístico t Probabilidad In erior !"#5ntercepci9n ".*$' "%#%# *.#"+&&%%+ $.*& % "#"& $.'& $$$'# "". $**+'aria1le " ".& '''#"++ $.''"'+&*& ". &$'" %# $." & '&%'& *.+&$%* &
$ "
".%
"
$.%
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5ntercepci9n ++.%'& '$' "*.' "%*#%% &.# '"# * $.$$#&'#+ #. # # "$#7aria1le " &."*%#% &&% &.%**%'# & $. " ' %"" $.&"* *&$#% "+.' *$ %7aria1le .* "#$*&* .%''$$ % $. $$ +# "' $.&"#%&'''* .&'+' #"%%7aria1le * +. '%++$#%& +.#&*% && $. "'$" +' $.&""$ '"' " .' %" '**
!esultados de datos de pro1a1ilidad
Percentil Y +. % +%
"#.'% '*". % #&*.'% %%+. % ""$+#.'% "
#". % " %*.'% "*$
Wodelo & cuadratica completa
E " x"x" x x x"x" "$ " .% "$$ "%+. % " %
" "% "&& % "#$* "% "# % * & '$& "+ " %+ &&" **+
% " + *+" +'+ & &+ " *$ &&" $$ +*$' % *% + % " % #'%# # &$ '#& "+$$ "" $
!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
$ " * & % + ' #
"$#+&
$
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residual$. +"+$+""&".+"##""% '
$.%'&*"'+&$.$" $' %$.$ %'% %$'$.*+$"+%*+
$."$"%$$%*#$.$+$ &&+$"
Parece e'ponencial
Superior !"# In erior !"$%# uperior !"$%#. ## *%'+ "". $**+'&# . ## *%'+
$.+&& #*"%# *.+&$%* & $.+&& #*"%#
$
$
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.$#""+'&+* +.$ +*'#$* .$#""+'&+*$.$ &#&$#& $."*''* &&% $.$ &#&$#&
D Dcalc esidual+% '&.++&"&'$ .++&"&'$ &' '#. *+ +' +. *+ ++'# '#."'$$"& *.# #%$ +
% .%$$ #'"+ .& $" #&*""$ "$&."++*%&* %.#**+&%'$" "$+.'$*%$+% "%. +& *&
" % " #.+%+"+*" *.+%+"+*$#+"*$ "*'. "%"*&* '. "%"*& #+
Superior !"# In erior !"$%# uperior !"$%#
$ " * & % + ' #
Column 5
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"$&.#+%' $% #. # # "$# "$&.#+%' $%#.&%"*'*+" "+.' *$ % #.&%"*'*+"&.#**" " % .&'+' #"%% &.#**" " %
%. '+%" $& " .' %" '** %. '+%" $&
D Dcalc residual+% +&.''+ $ $. *$' #$' ' .+ *%* +% $.+ *%* +%# #". #& " " $.$"%$#'
% &.* " & %" $.+$#$%$&#
""$ "$ .# %#*# $."$&"+"'" " ."*%*# # $."*%*# #*" % " %.%$'$ + $.%$'$ +$#"*$ " .+#&*%' $.*"%+& ""'
$ " * & % + ' # Column 5
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Superior !"# In erior !"$%# uperior !"$%#"$$.$$' #+" *#."'" ""$* "$$.$$' #+"
.' &+ & '$.#"$&&+&+ .' &+ &%$.%$$ "$ % '.* #' "*%% %$.%$$ "$ %
.%###*$&$' *."%%* +#% .%###*$&$'
*.&$#+ %&&% "." "% "%'& *.&$#+ %&&%*.+* &$*$ "".%'*&%#'& *.+* &$*$
por de 1enceno como funci9n de la temperatura. 4os valores experimentales se muestran en l
T"KT
*$$ &$$ %$$ +$$ '$$ #$$ $$ "$$$ ""$$ Column E
2112
2
222
2
11122 x xa xa xa x +++
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es cuadratica
alor crítico de F ".+ * 'E $$'
In erior !"# Superior !"# In erior !"$%# uperior !"$%#Err:%" Err:%" Err:%" Err:%"
$.$%"&%"+$% $.$+" &$%$" $.$%"&%"+$% $.$+" &$%$"
alor crítico de F %.#"' *E $$
$$ *$$ &$$ %$$ +$$ '$$ #$$ $$ "$$$ ""$
$.&
$.*
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In erior !"# Superior !"# In erior !"$%# uperior !"$%#'. #+&'&+ ' .# %'#' '# '. #+&'&+ ' .# %'#' '#
$.$#'#+"*+* $."$ ' $'# $.$#'#+"*+* $."$ ' $'#&.+$$$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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"$ $ *$ &$ %$ +$ '$ #$ $ "$$
Gráfco de probabilidad normal
Muestra percentil
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ta1la
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$Column B
2
210 T bT bb ++
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residual*
"$. %"$. %
*%.#'%
"#.+ %"#.+ %
%.#'%#.#'%
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%&
aleatorio
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"%$ " .% "$ . %
$ & + # "$ " "&
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" .% * "'.'%"$ . % "'.'% '".%
."#& % +$$.#'"*'$#%
.'%#+$"&%"
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h $.$$$$$"
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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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