ࡱ> {z  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxy}~Root Entry F2m_/q>+"<qVBA @_ g2ɀ\p Ninetrees Ba= ThisWorkbook= 6&8(@"1Arial1Arial1Arial1Arial1Arial1 Arial1Arial1Arial1Arial1Arial1h8Cambria1,8Calibri18Calibri18Calibri1Calibri1Calibri1<Calibri1>Calibri1?Calibri14Calibri14Calibri1 Calibri1 Calibri1Calibri1Calibri1 Calibri1Calibri1Arial11>1<Arial1Arial"$"#,##0_);\("$"#,##0\)!"$"#,##0_);[Red]\("$"#,##0\)""$"#,##0.00_);\("$"#,##0.00\)'""$"#,##0.00_);[Red]\("$"#,##0.00\)7*2_("$"* #,##0_);_("$"* \(#,##0\);_("$"* "-"_);_(@_).))_(* #,##0_);_(* \(#,##0\);_(* "-"_);_(@_)?,:_("$"* #,##0.00_);_("$"* \(#,##0.00\);_("$"* "-"??_);_(@_)6+1_(* #,##0.00_);_(* \(#,##0.00\);_(* "-"??_);_(@_)0.0 0.000 0.0000 0.00000 0.000000 0.0000000 0.00000000 0.0E+00 0E+00 0.000E+00 0.0000E+00;\g 0.0000E+00;\? 0.000E+00;\? 0.000E+00;\g 0.00E+00;\g 0.00E+00;\? 0.0000E+00;\0.000000000000000.00000000000000.000000000000 0.00000000000 0.0000000000 0.000000000 0.0E+00;\                                                                      ff + ) , *      P  P         `            a>  #   " " & "   # #           " " "              p  p "x@ &x@     x@  @      H 0      L3 0 D3  D* ||e$d}A} 00\);_(*ef;_(@_) }A} 00\);_(*ef;_(@_) }A} 00\);_(*ef;_(@_) }A} 00\);_(*ef;_(@_) }A} 00\);_(*ef;_(@_) }A} 00\);_(*ef ;_(@_) }A} 00\);_(*L;_(@_) }A} 00\);_(*L;_(@_) }A} 00\);_(*L;_(@_) }A} 00\);_(*L;_(@_) }A} 00\);_(*L;_(@_) }A} 00\);_(*L ;_(@_) }A} 00\);_(*23;_(@_) }A} 00\);_(*23;_(@_) }A} 00\);_(*23;_(@_) }A} 00\);_(*23;_(@_) }A}  00\);_(*23;_(@_) }A}! 00\);_(*23 ;_(@_) }A}" 00\);_(*;_(@_) }A}# 00\);_(*;_(@_) }A}$ 00\);_(*;_(@_) }A}% 00\);_(*;_(@_) }A}& 00\);_(*;_(@_) }A}' 00\);_(* ;_(@_) }A}( 00\);_(*;_(@_) }}) }00\);_(*;_(@_)    }}* 00\);_(*;_(@_) ??? ??? ??? ???}-}/ 00\);_(*}(}0  00\);_(*}A}1 a00\);_(*;_(@_) }A}2 00\);_(*;_(@_) }A}3 00\);_(*?;_(@_) }A}4 00\);_(*23;_(@_) }-}5 00\);_(*}}7 ??v00\);_(*̙;_(@_)    }A}8 }00\);_(*;_(@_) }A}9 e00\);_(*;_(@_) }x}:00\);_(*;_(  }}; ???00\);_(*;_(??? ???  ??? ???}-}= 00\);_(*}U}> 00\);_(*;_( }-}? 00\);_(*}(}]00\);_(*}(}_00\);_(*}(}bL 00\);_(*}(}cL 00\);_(*}(}def00\);_(* 20% - Accent1M 20% - Accent1 ef % 20% - Accent2M" 20% - Accent2 ef % 20% - Accent3M& 20% - Accent3 ef % 20% - Accent4M* 20% - Accent4 ef % 20% - Accent5M. 20% - Accent5 ef % 20% - Accent6M2 20% - Accent6  ef % 40% - Accent1M 40% - Accent1 L % 40% - Accent2M# 40% - Accent2 L渷 % 40% - Accent3M' 40% - Accent3 L % 40% - Accent4M+ 40% - Accent4 L % 40% - Accent5M/ 40% - Accent5 L % 40% - Accent6M3 40% - Accent6  Lմ % 60% - Accent1M 60% - Accent1 23 % 60% - Accent2M$ 60% - Accent2 23ږ % 60% - Accent3M( 60% - Accent3 23כ % 60% - Accent4M, 60% - Accent4 23 % 60% - Accent5M0 60% - Accent5 23 %! 60% - Accent6M4 60% - Accent6  23 % "Accent1AAccent1 O % #Accent2A!Accent2 PM % $Accent3A%Accent3 Y % %Accent4A)Accent4 d % &Accent5A-Accent5 K % 'Accent6A1Accent6  F %(Bad9Bad  %) Calculation Calculation  }% * Check Cell Check Cell  %????????? ???+ Comma,( Comma [0]-&Currency.. Currency [0]/Explanatory TextG5Explanatory Text %0 F Followed Hyperlink   1Good;Good  a%2 Heading 1G Heading 1 I}%O3 Heading 2G Heading 2 I}%?4 Heading 3G Heading 3 I}%235 Heading 49 Heading 4 I}%6( Hyperlink 7InputuInput ̙ ??v% 8 Linked CellK Linked Cell }% 9NeutralANeutral  e%"Normal :Noteb Note   ;OutputwOutput  ???%????????? ???<$Percent =Title1Title I}% >TotalMTotal %OO? Warning Text? Warning Text %XTableStyleMedium2PivotStyleLight16`[IPoly Fitc Sample data! PolynomialCurveFit8L+', 3  @@  =title->1<--- the number of data pairs below (auto filled)proof of 3rd-order accuracyabcd by formulaby valueX[i]f(X[I]) f(x) PredErrorby fitx calculatedpoly3rd2nd Corr Coef Coef of Det X variance Y variancePolynomial curve fitx=f(x)->Sample data for which theCC=CoD=TonsCostf(x)=1.266+0.752x%Statistics for Business and EconomicsMansfield. P 3847http://www.mne.psu.edu/me82/Learning/Stat_2/stat_2.htmlAladdin failed potCC stated as 0.48 for linear fitSUMMARY OUTPUTRegression Statistics Multiple RR SquareAdjusted R SquareStandard Error ObservationsANOVA RegressionResidualTotal InterceptdfSSMSFSignificance F Coefficientst StatP-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% X Variable 1Aladdin theoretical X Variable 2 X Variable 35http://www.cohort.com/costatpolynomialregression.html coefficientsx^2%coefficient of multiple determination,http://www.nuhertz.com/statmat/dataplot.html1http://www.itl.nist.gov/div898/strd/lls/lls.shtmlWampler15th-order polynomialFilip10th-order polynomial<--- the order of fit (1 ..10)B0B1B2B3B4B5B6B7B8B9B10b0b1b2b3b4b5b6b7b8b9b10Wampler2Wampler3Wampler4 R-SquaredWampler5e=smaller sample sizeNISTPolyFit53rd-order polynomial test data, f(x) = a+bx+cx^2+dx^33Coefficients for f(x) = b0 + b1x^1 + b2x^2 .. bnx^nUsing NIST CoefsOriginal NIST data orderx^1x^0XYX^2X^3 calculated by polyfit; cf. aboveAladdin data to comparewith the testbedAladdin field dataBattVBAT VBAT bridgeRD2 RD2 to Gnd Reff to Gnd 1e12=openohmshowswhen notsampledOffset3 3314-4c5_566~x7t78;878K9G9 : ccPK![Content_Types].xmlN0EH-J@%ǎǢ|ș$زULTB l,3;rØJB+$G]7O٭VRv`dDJ| W%9ߘo41a%$g9 7,k2=p9Ѭ3ІMM!}rBq>8>o?MI\]12ol 鎑)Rhs Wth8j  XjulABd7yFۥom ^ejc{m8w6ۃpס7D~w~m(,9ݠs%\G]w9 Pf1*bB14!'%ZtNd3Ɉ@)|CA1eyY YRX{o_}/߼ӛ>{򏖗3IՉ_g|?E=}V~?_ۗOk$Uɧ,1=ND یc\LیiD3D]z"ut:x>\ptDrX'Q B:Ut,e:C8-Sfu<$QdAN;H\:>a Gu/KYˇT8;Y9eR,wpJEx]辅}H1EUl.Qw}2}g_s(KE$ Ͻ_T=!paAxN{|r9/ꡘㄧVhQɖRyju7ƽ)oɔjABÒxR*@4bXq0؁l/>#pFmLok0e:a O2G*L]ì]%V=|1pW! 0`.Wlj9HV3rq44K`fzV mV ,Sw\j-bmX)C7-`8HL^xu*N/43 z6H;8Cdm2iVֵy뤽V,ַr/9[kvxm:;k;v%y117e,1{@`VAz,96ؘpRXwa nְ lIhTSepRf3EX &$"JPp!'!{EQX?ݭh>m9銲ԗ찭L<>JBs0\8z ibiORoB}($.(]33333@~ U< QRM  lKI$I$@~ KPy@K<33333@~ U= QRMK@K@z@K@~ U= EN  E  E  E  EE KK PKL KKPKLLLL   Ss!9! D   Ss!)@ D   Ss! D  Ss! @ L KKPKLLLL  Ss!9 Ss!)@ Ss! Ss! @ L KKPKLLLL  Ss!9 S;s!)@ Ss! S s! @  L KKPKLLLLSSSSSL KK PKL     KK PKL  E  E  E  EEN KKP~  E Js!9G Js!9 1D @D @D D @D D @D  Js!)@N KKPTTKL ~  E? J|Pkj/ J}Pkj/  ; 1L@L@LL@LL@L J~Жs"@N KKP L E@J  J   Js!)@N KKP _|~ cj@ ^  b~  E@ J kD@ J kD@   JH5@ KKP _}~ `@ ^  a~  E@ J}Pkj_@ J|Pkj_@   J~ЖsB@E KKP _~~ `j@ ^  a{~  E@ Jq@ Jq@   J]tYLM@O KKP _/`j@%DDDD ^  a~  E@ J|Pkj@ J{Pkj@   JHU@O KK _P @ @ K  a~  E@ Jψ @ Jψ @   Jn[^@ODl5(6NXEV@@@ffX8:js !"#$%&'()*+,-./0 1 2 3 4 5 6 7 8 9 : ; < = > ?  KK! Kܶm۶m? D D  ]z~ K@/ KI$I$@ D DDD ]{ L~ E @ J= @ J= @   J kd@ O R!K!K?"!!( LL~ !Ks@!K@$!#!(LDDD! L!O"K"K++?#!~ "Kt@"Km۶m@ !" L "IIO#K#K?$!~ #Ku@#Kn۶m۶@(!# L #IIO$K$dPuPu?%!~ $Kv@$K%I$I@#!$ L $IIO%K%KH$I$?&!~ %K@%Kܶm۶m@!% L%E&K&KBA?'!~ &K`x@&K$I$I@"!& LSSSSE'K'K::?(!~ 'KPy@'KI$I$@&!' LSSSS (K(K433333? !~ (K@z@(K@'!( LSSSS )K )KL *K *KL +K +KL +E,K ,KL ,E-K -KL .K .KL /K /KL 0K 0KL 1K 1KL 2K3K4K5K6K7K8K9K:K;K<K=K>K?KDlpppjljj"" @ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_@KAKBKCKDKEKFKGKHKIKJKKKLKMKNKOKPKQKRKSKTKUKVKWKXKYKZK[K\K]K^K_KDl `abcdefghijkl`KaKbKcKdKeKfKgKhKiKjKkKlK    ?   (  r  0 ?@Z],TWR9 $<Run Polynomial Curve Fit<Sh    pf{(kLY @?Text Box 2"9 3 PK![Content_Types].xmlJ0*miG]`Hm6 Xwt?. g#Wi3E).+7 >ON ޑ1ˋz "+R RhB.} /<^ITխ%rHK4uK~I0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!6drs/shapexml.xmlYn7}/HPG%JU6@.n}a.%)so~J\r\hc#QA239$OUNʚ:6W_<0򁛜kk-gO_,wCn:㇨Yb&+[ute;w|ngNk'ygRgM 'aa'Rä*zm4E1dX]!KCYiKC`ϕ\Vw>8Gk} gGQgA+src9=ʰ7GT ;Yz!=APŇ~eʼn_?Ɗ+v2㦔.E\hnz7}]4G6|lpuMEAj6vFNM#`e$#W=|M]k^,FIT+6*.V&]9hG\؋Vr+o ;׏jTi)Ub4v֒QJaA{[DrM ՄC-K.XmKKvMg\Y^kB\va*V*HGZU#6hf%FsrJ7eYmV!/22wI|>` oSh |V5_IFd{|d> ‚A uٹF,0N3Dcb*LƇ'7וX1q-O(&݆,\ I5b6?h֠чc4MSw>bǀx$pnq*KNk(( ƈie$:uC_UIfa<2!IA#Ĭ(un.n )k`yČ^^m!Hyfs)@vA97r #0 4-߷.@u^?~p.Ţ,Kw4w,as *Jk}uX/#X%ʄ)S}-4;Tk,"נ/[5O|_Gu=}x: V \Sjk2PK!Ŏ-9$drs/downrev.xml|_O0M5M!ÁBHPDoecӵ%m{ɷ;QJG Ĥ xYMb`KhPl 9~(D{st-CM^f˕,4m'9&%`Wku:ϟ1B\^T[`+ϗi8_gR[ @ Sheet1ggD g2ɀ Sω1  dMbP?_*+%&?'?(?)?MJHP OfficeJet T Series Printer@l od,,Y8HP OfficeJet T Series Printer,, ` B K dY8"d,,??&U} 11$ F Column AUSWWWW WWWWWW  W W  W W WW W T TTTT T TTT TTTTTTT  " Er Et Eu Es ? B (F .o 1Fn 3G :G @G FG LG RG TǫGLJ?T~졟-?MJ~@KWFK.^}@ DK:>1 D~ L & ?@!(?5)~ -.Ipp/ -?1F?1 11 L@L@LL@LL @LL @LL @LL @LL @LL@LL@L L@L 33B!4aTR'?:?;@S?AF@GLЇ@MRAS T87R?TEɨ2 ?~ M$@Jh|?u%@ $K ]DK*S@ LKI1 L~ LTe@ @ @! #C(@@)~ -?.<K/d]K?1Fv%7?13st!4? 5J:?@; <H~ @?AS#G? BcF?G HdL?M NeR?S Tg @ @M4@Jv@ %Kd^BK$W@K*"T41~ LTu@ Z'Z @ @!#URm۶m? $q(@")~ -@.; h;o/ڊe?1Fč?13> @{U!4ׁsF?:@O@;~ @@ASr)?F@~@GL@ AMR@S?@ M>@J?KKmv@K!WO@K0Uyn1~ L@ W(WB@? @1@!~ # $p(@)~ -@.ko/?W[?1F7a?13 S!4w-!l? 5K:@v@; <I~ @@AS,)? BIF@PG HIL@M NIR@S TI@@MD@Jv@K@IB=K2D@K c-Tw1~ LT@ W)W!6? @<@!#qy? $D(@)~ -@.ioN/io?1FX?13H{"!~ 40S@ 7Ej 8Ek:@T@; =M~ >?~ @@ASt{Ic? CM~ DS?F@`@G IM~ JS?L@AM OM~ PS?R@S UM~ VS?@@~ M?J@Kx /9K^~J@KX+^1~ L@ W*Wm? @C@!(@ @)~ -@.WB/~:p?1F?13C!4I +? 6M7n]8+zu^K@:@@; =N~ >?@@S?A CN~ DS$@F@@G IN~ JS?L@M ON~ PS?R@ =S UN~ VS? @@MN@JЋ@ &K̸%46Ke~@K2c1~ L@ W+W~>1@ @K@! #E(@@)~ -@.Q;zk/.n?1FF}?13%,r 46;Nё? 6N7TQy[8t{3Q@:@9@; =O~ >?~ @@AS4 @ CO~ DS?F@9@G IO~ JS?L@# AM OO~ PS?R@ΑS UO~ VS?@@MQ@J@KM2Kvpv@KqtԹ1~ L@ X,~ X9@  @Q@!#קJ?( @$@)~ -@. ͼx/|a2U0?1F? 13< 4-? 6O7h8@@:@&@; =P~ >?~ @@AS#@ CPDSMbP?F@&@G IP~ JS?L@@M OP~ PS?R@b2S UP~ VS? @@ MT@Jz@ Z' Z K)`. Km@  Ki/\ 1~ LT@ ("@(@)~ - @ .eۜ\u~ /S@ 1FcĦ? 1 3u~  4ea? 6P 7?P埑 8|M@ : @ I@; =Q~ >?~ @ @ ASK; @ CQ DS-C6? F @.@G IQ~ JS? L @ AM OQ~ PS? R @dS UQ~ VS?  @ @ MV@J#@ W( W;P]P? K(n1' K9a@  KM;b4 1~ L@ - ($@0@)~ -"@ .?B /_vO? 1F,? 1 3ϭT  4J{/L? 6Q 7;bئ'v 8q? :"@7@; =R~ >?~ @"@ ASN @ CR DSh㈵> F"@o@G IR~ JS? L"@M OR~ PS? R"@ "S UR~ VS? "@ @ M?J @ W) WL}? K?~ @&@ AS"*@ Cf F&@ `AG If J(ů? L&@M Of Pө? R&@(S Uf V[gb?   M^@Jn@ W+ Wis @ K@ Ki| @  KhگDy 1~ L@ W/~ W5@ W?x@ W"Nsy2@ WW~ -(@ .gi]j /;On? 1F?1 3@oR 4h"lxz? 6T 7Fv$ 8#AR+ :(@tA;~ @(@ ASgy#@~ C? F(@,AG L(@TAM R(@drS !M@`@J"@ X,~ X4@K@*C?K{l@K@1~ L@T@ X0~ X8@X. A XXX~ -*@.8&p/EJY?1FF?13$糧K4oT? 6U7[-*(8wR 9?:*@A;~ @*@AS9])@F*@lAGL*@AMR*@6SMa@J@Kpw*@KX%9@KYbO_@1~ L@~ -,@.IIQ_}1/z6?1FKNѺ?132{C[4s? 6V7[FY_7d8o!?:,@Y#;~ @,@AS"-R0@F,@y#GL,@/MR,@YSM?J@ -K8ש-!@KODP$!R@KAZXL@1~ L@Y Y7 Y+ Y8 Y9 Y: Y; Y< Y=~ -.@.A/ݓ?1F_q?13$(Z4ͪ? 6W7[сx 8?>>:.@`(A;@.@S4@AF.@`(AGL.@`"AMR.@¨OSMd@J@Y Y2  Y3  Y4  Y5  \6Km<'(@K÷;b@K!^.IR@1~ LT@ W1W8c!@W{%?W{@Wls\&4WK骠@WW{Y@WK骠@WW{Y@~ -0@.k/z6?1FR%Y?131m~ 4pS@:0@FDD;~ @0@AS닄K:@F0@1AGL0@vSMR0@/HSM@e@J!@ W.~ W? WV3wQ@ WV3wQ@ W@ WJ|?KP l/@KGIƍn@K N@1~ L@@ W>WcVH@W>T?W#QTW@WJQQs6WcA3H@W zI@WcA3H@W zI@~ -1@.ǜ%h/0' ?1FA -?13FТGi4m{? 6f7f0?8TK[$?:1@\;~ @1@AS^cކ@@F1@[GL1@ړOMR1@zSMf@J@ W/~ W2@ W%eM,m@ WZv})@  WW K?p3@K:w@Kq@1~ L@ W@WE\xzWެV?Wl;)AWjD;W詿W& W詿W& ~ -2@.xR/Y?1Fz?136"4H.!?:2@>z;~ @2@AS5$D@F2@>=zGL2@>MR2@>\S w~ Mg@Jffffff$@ X0~ X3@ X8r@  XXX KXOAE7@K]@1@K6@1~ LS@ XAX?$bX#M ?X|CXaY;XZ+cX:K/aXZ+cX:K/a~ -3@.W];/J +?1FW|?13>(<)4,eX? 6h7^W @:3@r;~ @3@ASx]I@F3@rfGL3@rMR3@rS xK\/Z;;@K0 ,@KH@1~ L@~ -4@.)﫾/ /z6>?1F@AJ?13eۜ\u~ 4S@:4@;@4@SO@AF4@rGL4@9MR4@VٜSKYD~ K`e@\ \7  \+  \8  \9  \:  \; \< \=KFKX?@K^`@KOu@1~ L@@ v~ -5@." /o?1Fyc?13}I448E?KKT@ W1W~nT@ W.? WYG @ W`? W$#MM? Wp^@W$#MM?Wp^@KA@KNNmۓ@KKq@1~ LS@8c!@fVH@\xzݑ?$b~ -6@.[D3/ܵ|?1Fϔ?13 -4( y?K@K@ X>XA'Ff @ X9`W? XO*@ XJ|? X07H? X΃1@X07H?X΃1@K` D@KDI>:@K~Į@1~ L@~ -7@.\c/[ Ac?1F@?13ioN4io?KD@~ K@KPV*F@K'G@K&k"B@1~ L@~ -8@.%y~ /@V@1F?1134ׁ?~ -9@.jI! /Pn?1FE?113Ipp4 -?~ -:@.3̫/}гY?1F ?1139W4z):? # y~ -;@.qfQ/x?1Fe?113?B4_vO?,@,h@~ -<@.+m/镲 ?1Fy=?113EH4MJ?@@~ -=@.H{"!~ /0S@1F`̠?113Rw4 qh?H@@H@T@~ ->.< /-?1F bE? 113lEr4q -?D&<lzgAc}KMuK{uu 9!9"9#9$9%9&9'9(9)9*9+9,9-9.9/90-91-92-93-94-95-96-97-98-99-9:-9;-9<-9=-9>-9?-9 "@@ "@@~ -?@ .$1"7  /lV}? 1F+׷?!11 3WB 4~:p?~ !-@@!.$糧K!/oT?!1F@?"1!1!@11 L@L@LL@LL @LL @LL @LL @LL @LL@LL@L L@L !3tP!4,Ԛ?~ "-@@".1m~ "/pS@"1F8  ?#1!1"3칎i "4On?~ #-A@#.>(<)#/,eX?#1F?$1!1#3'Wy#4sh|??~ $-A@$.$/ׁ?$1F`Un5?%1!1$3`2Z$4oŏ1?~ %-B@%.tP%/,Ԛ?%1Fy%y?&1!1%3@yO%4I&†?~ &-B@&.ǺK&/' ?&1F?'1!1&3~%!σ&4 $(~?~ '-C@'.:1'/<,?'1F?(1!1'3Q;zk'4.n?~ (-C@(.3B!(/aTR'?(1FtJ?)1!1(3ǺK(4' ?~ )-D@). S!)/w-!l?)1FT]?*1!1)3[D3)4ܵ|? )7i~ *-D@*.%,r */6;Nё?*1F3?+1!1*3uz*4X?~ *6*73B!*8aTR'?~ +-E@+.u~ +/ea?+1F0{?,1!1+3-+4"uq ?~ +6@+7C!+8I +?~ ,-E@,.{ 7~ ,/@S@,1FP;2?-1!1,3X,4 -?~ ,6$@,7$1"7 ,8lV}?~ --F@-.2{C[-/s?-1F@'?.1!1-3 ͼx-4|a2U0?~ -6.@-7$(Z-8ͪ?~ .-F@..FТGi./m{?.1F0N+?/1!1.38&p.4EJY?~ .64@.7eۜ\u~ .8S@~ /-G@/.}I//48E?/1FPL"s??01!1/3y\D/4|a2U0?~ /69@/7Ipp/8 -?~ 0-G@0.EH0/MJ?01FϽ@?11!103ڊoC040*D?~ 06>@07lEr08q -?~ 1-H@1.`2Z1/oŏ1?11F@ ]?21!113:114<,?~ 16A@17`2Z18oŏ1?~ 2-H@2.X2/ -?21F5j?31!123\c24[ Ac?~ 26D@27[D328ܵ|?~ 3-I@3.9W3/z):?31F@v?41!133 "34ͪV?~ 36F@378&p38EJY?~ 4-I@4.칎i 4/On?41FB0?51!143gi]j44;On?~ 46I@47 "48ͪV?~ 5-J@5.uz5/X?51F?61!153IIQ_}154z6?~ 56K@57;Ad58Ciq?~ 6-J@6. "6/ͪV?61Fh ?71!163ҋS64b=y?~ 66N@67jI! 68Pn?~ 7-K@7.;Ad7/Ciq?71F0?81!173%y~ 74@V@~ 76@P@77c%I78 ?~ 8-K@8.>F)8/ǘ?81Fк?91!183;Ad84Ciq?~ 86Q@87<K88d]K?~ 9-L@9.ݪ9/S㥛?91FSrY?:1!193A94ݓ?~ 96R@97`98z6?~ :-L@:.c%I:/ ?:1F kdߐ?;1!1:3>F):4ǘ?~ :6T@:76R~ :8+ݓ?~ ;-M@;.1);/OjM?;1FM?<1!1;3k;4z6?~ <-M@<.`</z6?<1F=?=1!1<3.H<4M O?~ =-N@=.Pq0\D =/d]Fx?=1F*׎?>1!1=3jI! =4Pn?~ >-N@>.SLRW >/9m4?>1F}#??1!1>3ݪ>4S㥛?~ ?-O@?.st!?/??1Fks?@1!1?3ǜ%h?40' ?DKl$quuuuuuuuuu@-5A-5B-5C-5D-5E-5F-5G-5H-5I-5J-5K-5L-5M-5N-5O-5P-5Q-5R-5~ @-O@@.> @{U!@/ׁsF?@1F`(?A1!1@3D>>@4lV}?~ A-P@A.C!A/I +?A1Fչ?B1A1AR11L@L@LL@LL @LL @LL @LL @LL @LL@LL@L L@L A33̫A4}гY?~ B-@P@B.ϭT B/J{/L?B1F?C1A1B3c%IB4 ?~ C-P@C.@oRC/h"lxz?C1Fr?D1A1C3xRC4Y?~ D-P@D.$(ZD/ͪ?D1F1?E1A1D3; h;oD4ڊe?~ E-Q@E.6"E/H.!?E1FR ?F1A1E3koE4?W[?~ F-@Q@F. -F/( y?F1FB?G1A1F3qfQF4x?~ G-Q@G.RwG/ qh?G1F3}?H1A1G3<KG4d]K?~ H-Q@H.@yOH/I&†?H1Fŏh?I1A1H31)H4OjM?~ I-R@I.y\DI/|a2U0?I1FM?J1A1I3W];I4J +?~ J-@R@J.lErJ/q -?J1F@ֳ?K1A1J3>dJ4(~k ?~ K-R@K.~%!σK/ $(~?K1FQq?L1A1K3+mK4镲 ?~ L-R@L.ڊoCL/0*D?L1F1a?M1A1L3`L4z6?~ M-S@M.ҋSM/b=y?M1F@ c-?N1A1M3)﫾/ M4z6>?~ N-@S@N..HN/M O?N1FD`4?O1A1N3?K N4H.?~ O-S@O.D>>O/lV}?O1F/S^?P1A1O3" O4o?~ P-S@P.>dP/(~k ?P1Fpa}?Q1A1P3Pq0\D P4d]Fx?~ Q-T@Q.?K Q/H.?Q1F C?R1A1Q36R~ Q4+ݓ?~ R-@T@R.6R~ R/+ݓ?R1FCas? A1R3SLRW R49m4?* hu$uuuuuuuuuuuuuuuu 9!R 1   (   n   c 4NChart 15:'x] @  g2ɀPPPZaajk&?'?(?)?"??3&PHPL0(  L 3d23   M4 RR3QQ ;R44Q ;R33Q3_  MM   dR R R R R R K"#S S4ES S 4 RR3QQ ;R11Q ;R33Q3_  MM  !!dR R R R K"#S S4ES S 4D$% 00 3O& Q4$% 0 3O& Q4FA  l 3Os3*"" & ! 43*?ffffff????& ! ! 43d" 44Ds E(B?L? G??[& ? K[S S 4Reee*Kven-USKuY >@ Sheet2ggD ThisWorkbook Sheet1 Module1=__SRP_2  !"$&'()*+,-./012346789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqstuvwxyz{|}~nh#xME (SLSS<N0{00020819-0000-0000-C000-000000000046}8(%HxAttribute VB_Name = "ThisWorkbook" Bas0{00020P819-0C$0046} |GlobalSpacFalse dCreatablPredeclaIdTru BExposeTemplateDerivBustomizD2nj#xME (SLSS<N0{00020820-0000-0000-C000-000000000046}8(%HxAttribute VB_Name = "She@et1" Bast0{00020820- C$0046} |Global!SpacFalse dCreatablPre declaIdTru BExposeTemplateDeriv$Bustom izD2 The input data should be in the following order.+ Title or remark for documentationU Number of X, Y pairs of data to follow (must be greater than or equal to 3): X, Y data pairs (maximum of MaxDataPoints pairs)C An augmented matrix is produced from the independent and dependantH matrices. This matrix is then reduced to the minimum degree required to solve the matrix.; X0 X1 ... Xn | XOY a 0 0 0 0 | b; X1 | c 1 0 0 0 | d; . | ----> e f 1 0 0 | g; . | h i j 1 0 | k; Xn .......X2n | XnY l m n o 1 | p" Coefficients are then calculated, A0 = b / a, A1 = d - c*A0, etc.,6 to satisfy the polynomial A3*x^3 + A2*x^2 + A1*x + A0x constants]@ *Xdp integers]] floating point]0]H`x]] ]8Ph]] strings] arrays dim (row, col)] * *] *P] ,] *] .] .0] .h] .] .] . .HZero all arrays 0 * 0+f 0+j 2 * 0 2+d 2 0 0 , 0+h 0 0 . 0+l 0+n 0+p 0+r 0+v 0+x 0+t 0> Clear the coefficient and correlation fields in the worksheetE7:O7$zB@H |B@~8 Clear the predicted Y and error fields in the worksheetC9:D109$zB@H |B@~B6:B6$zB@HPoly Fit$B@"! Activate the workSHEET of choice$': (row, column)$'b (row, column)$'6 0 6 0 $ 0+vEfirst 3 rows are Title, order-of-fit, and # of data pairs, X=column 1 0 $ 0+x Y=column 2 0 SumPowersOfX of X^J for each X" SumPowersOfXY for all powers of X'P 6+h% double <- integer, implicit typecast 0 6 P 0$x 0$x 'P$j 0$x +j/ X^0 * Y, effectively summing Y 2 : 2$h 0$v 2 2+h 2 : $h 0$v 2 :  2 : +h 2$j 0$v 2 0$x **/nxME(6 << < (` !@*L@,L@.Lx@0 @2 `4@6 @8 `:@< `>@@ @B @ `D@F @H `J@L @N `P@R @T @V @X `Z`\@^ ``Pb dH( fh h j l( n`H p r tv@( xx`&%@EA$*\Rffff*055fa65f01!  @ ` &  $  J N@ 8  2 \ @h  J N P h Bp B B BH B  (   <@  "  &   0Ph    ( 8HXhx   8 HXp  ( @  X Dh   >   0 @ @X & &   j .   & (  :( h  F  ( <( 6h       6$@ h <   @ :P" "0X 2p     2(8Ph0    . ( HX x  &(@H  0 FH$  *<  `  p 42   0v@2 8 Hh""  j8   J X 4h: (0@H(h     PolynomialCurveFit Macro Copyright 2004, 1985l Richard L.Messederndo Down East Engineering A New England Heritage Company +1 207 462 8462 www.DownEastEngineering.com/C This program uses a Gaussian transformation on statistics obtainedG from X, Y input data to produce a curve fit to a 3rd order polynomial.12+j 2 0$j'Z Z 6'\ 6 '8 6 6 '@ 6$h$h$h  @'^ 6 P Z Z  @'` ^5 Fill augmented matrix prior to solving linear system 0 : 2 : 0 2 $h 0 2+d 2 0$j 0 *+dF 03 Use Gaussian transforms to produce solution matrix 0 : 0 0$d'L 2 * 0 2$d L 0 2+d 2 2 0  2 0$d 0 0$d'N 4 * 2 4$d 0 4$d N 2 4+d 4 2 0+ Calculate coefficients from reduced matrix *$d$d+f 0 : 0 *$d 0+f 2 0 0$f 0 2$d 2$f 0+f 2 0' Calculate coefficient of determination'> 0 : > 0$f 0$j '> 0 > Z Z 6 '> P Z Z 6 'B B?'>d8 > B'> : >$'<d 6$j$h Z '< 6 P Z Z 'B < 6$h$h $ B$'<kp kh k` 0 : 0$f 0 + 0 ^+ `+ < + > +? Produce report containing coefficients, CoD and predicted datac:\temp\Poly.out.txt bCoefficients for Order : 0 : B 0$ Coefficient= 0$f 0Correlation Coefficient: >$Coefficient of Determination: >'X'R'T'Vg_N_ ______X_______ ______Y______ ___Predicted Y___ ___Deviation____ __Deviation Sqr__ 0 6$f 0+t 2 : 0$t 2$f 0$v 2 0+t 2 0$t 0$x 0+l X 0$l 'X 0$l 0+n R 0$n 'R 0$t \  0+p T 0$p 'T 0$x \  0+r V 0$r 'V 0 0$v 0$x+ 0$t? 0$lW 0$n 0$t 0 + 0$l 0 + 0Sum of deviations = XSum of deviations^2 = R. calculate correlation coefficient and ???? *? V T V$'>k(%Correlation coefficient (by errors) = > 8 T'J R 8'Hc' HG J H'jF(1: 8) = khV|PoH@%Attribute VB_Name = "Module1" ' PolynomialCurveFit MacrolCopyright 2004, 19852Richard L.Messeder*Down East EngineeringA New@land Htage Company"+1b7 462 8www.RQP`.com/"This program uses a Gaussian transformatiHon ststics obt aQd"from X, Y input data to,ducee)c f a$ 3}orz p.Ge!sho uld b the follow   Title r emarkr documen]onNumber of^pairlf_6 (mud!great th@Gor equal:3)BA(maximumAMaxDGPoint^An aug*ed ]rixf gAQd YAAi ndepent CantAces. w=@nEaAmiRn&de6e@q(uir@t¯so8lve]C[X0 X1 ... Xn@_|XOY#@a 0D | b( Aqc 1Gš.H->FҁWh i jk&n.X2aXnl m `fpCoe`fficiQ mrb+n calcu2l Kd,A0Ab / aG1@d - c*A0, etc.b 9srfy"5pj A3*x^3 P+ A221*x0 OpzExpl@A`G Sub(1[conV   ArraFyZ!15,2 2 *,`^P= 10b'}t egers Dim i, j, k As InB#%f, DU, Oi!(flo "nglCor r0,efOfDet Double 1 2, @F, SRSYMeanS~dS_error">ra  RowDivisA`Mult umY{D  SF G S@_total_devi`onYXVar`ceE(s@,ng&3b$!G' "a!?s d6(row, colD A8A(DgC|1)bG4S umPowFOfZX2 Y D(( _sq |6!TA$YP'_\>X?6'Zero all1Fni=0 To=a@L(i)A#j@EO#@)Next ji 2 )  j7! R/zX >YR ' Clear2_cge5cNeeQfi0elds`Vwo@rkshee^ Range("E7:O7").Selec.2p'ict}`Y"PC9:D109qh B6:B6W s(" Activqt ' SHEETchoic^c= C`ells( _I' LumnMe1, Fo 83"U*14A $ S8yp/ft 3 U ,`-of-5,# צ, X=X 1#d%{*Q Yu3w1Q'#3X^Jeach X?YC>pY2a8fn= 0B90a>' 1y <-, imc typec0ҡb@xY:+6*bfeY( 9 "d' X^J0ЍY@ff 3ively sumдg YS No'sIj(+ (!^ jb$Q;"2W\(jVtYA=z"qPJ2#:Y @ Y^ ⓳YЭ0C l- )DA* (j1" fP*j (/- ( (07L1))) k/ D1 YVariance = (DataPoints * SumYSquared - (8T))  If (X<> 0#) Then8 ' Fill augmentmatrix prior to solving linear system;F!i0 To Order j Aj(i, j)%PowersOfX(i +HNext j ArrayMax1 !Y(i):i ' Use Gauss transformsspro duwutio|n trv1 Step - RowDivis= qi)!_J/ W HE^i1A*0M* Mult@^j, iJ.}/k {//kAe@-KF@*#;GA3kQ7B@s C' Calculate coe fficis `from sd%qCG (0K(0, F5 B@0pŁBVJIR̀G5iSkE  (`h*jj&N"&g'' of determinaaAOfDeF0#cߥ!b!'+-Fv G!O fcD2@VA4gb0#1 Else 2% B% > HaCorr%Aqr('9) a  h*-aF( E BbΦ;*f/@р6(2)@J^  !2)nd IzfEf%vPCells(7, 5"r)D āLy16c8, c&g9e =G19' P$report ntaina퉙,@3D apM4ic1zd.!Open "c:\ yp\Poly.out.txt""xOutput As #1Pr, TitlB+&S "Upmb+|";~A,X Bt@; "9@= xnJ  ]2e_zX:@S$Abs842% c!OM'OrG<g+_deviR:#QSS_err"regre=`totalvh _N_ _Xc_AYcw0P!3DOU  "__f __"ql;@ Ps!sY5Ǜ_k) ^8τj F- b9+ 9 _sq9Z8[#R( Meang + T1"%q`$`+7 &3 @G%@i; 1; Tab(23);4;#6!)c87fdSW, 3QU 41Y2a1338&s+@um:, "n^q4;Z' crrFYłY? *?}&؃E I( / JneO@t (by GsO`0 $ De0HeGMS_= L /F 99߳ `/vsF(1oW b FqIClo3mxitb QSu rU~| 0  krU $`nn#x__SRP_3 #gSheet2%_VBA_PROJECT55dirrKME (SLSS<N0{00020820-0000-0000-C000-000000000046}8(%HxAttribute VB_Name = "She@et2" Bast0{00020820- C$0046} |Global!SpacFalse dCreatablPre declaIdTru BExposeTemplateDeriv$Bustom izD2a  *\G{000204EF-0000-0000-C000-000000000046}#4.1#9#C:\PROGRA~2\COMMON~1\MICROS~1\VBA\VBA7\VBE7.DLL#Visual Basic For Applications*\G{00020813-0000-0000-C000-000000000046}#1.7#0#C:\Program Files (x86)\Microsoft Office\Office14\EXCEL.EXE#Microsoft Excel 14.0 Object Library*\G{00020430-0000-0000-C000-000000000046}#2.0#0#C:\Windows\SysWOW64\stdole2.tlb#OLE Automation*\G{0D452EE1-E08F-101A-852E-02608C4D0BB4}#2.0#0#C:\WINDOWS\SysWOW64\FM20.DLL#Microsoft Forms 2.0 Object Library*\G{D1A27223-941C-4E57-BB3A-2490E93C727F}#2.0#0#C:\Users\NINETR~1\AppData\Local\Temp\VBE\MSForms.exd#Microsoft Forms 2.0 Object Library.E .`M 2*\G{2DF8D04C-5BFA-101B-BDE5-00AA0044DE52}#2.5#0#C:\Program Files (x86)\Common Files\Microsoft Shared\OFFICE14\MSO.DLL#Microsoft Office 8.0 Object Library EAnThisWorkbook015fa65f01!ThisWorkbookh% Sheet1025fa65f01% Sheet1j%Module1055fa65f01&Module100/ Sheet2045fa65f01 Sheet2H%hH0|EFba4UTI2!b 萭Mꅁ NIb_FDP.QFExcel+VBAWin16~Win32Win64xMacVBA6#VBA7# VBAProjectstdole`MSFormsCOfficeu ThisWorkbook| _EvaluateSheet1Module1bPolynomialCurveFit" ArrayMax1 ArrayMax2 MaxDataPointslli`jakb DataPoints7DegreeOrderACorrCoef CoefOfDetD1\D2\SRSN YMeanSquaredZMS_errorcG MS_regressionx RowDivisor RowMultŽ SumYSquared>ESS_error; SS_regressionTSS_total* Sum_deviationSumY :YMean XVariancep7 YVarianceTitle~ AugmentedmK Coefficient SumPowersOfXM* SumPowersOfXY1 DeviationAZ Deviation_sq Regressiona Total_errorYPredlXoYlRange  SelectionZClear WorksheetsActivate|CellsSqr(Sheet2Workbookk Worksheetx ! % 'HG0* pHd VBAProject4@j = r EA J< rstdole>stdole h%^*\G{00020430-C 0046}#2.0#0#C:\Windows\SysW OW64\e2.tlb#OLE Automation`MSForms>SFFrms3ED452EE1-E08F-@101A-8-02608C4D0BB4 EINDOWSEFM20.DLL#Microsoft :" ^ Ob Library/;D1uA00}#0#Gk0 AD1A27223-941C-4E57-BB3A-2490E9@3C727F6Users\NINETR~1\AppData\Local\Temp \VBE\U.exd<@".E .``M OfficOfQ@ic 22DF8D04C-5BFAh@B-BDE5JAjA422gram Files (x86)\@Common\jShared\OFFICE14 @7O sC( 8.0Ls&BnBThisWorkbooPkG TiEWkboPk 2 QHB1B%B,h""+"sSheet1G Se,t1 v2 !j ooduleoo@uBA2s 0/!U2222*b__SRP_0__SRP_1 NPROJECTwmkPROJECTK*rU~~~~~~~~k b Eon=    a i) A  VBAProject ThisWorkbookSheet1Module1Sheet2F /C:\PROGRA~2\COMMON~1\MICROS~1\VBA\VBA7\VBE7.DLLVBA Y 0F:C:\Program Files (x86)\Microsoft Office\Office14\EXCEL.EXEExcel Qy@0FC:\Windows\SysWOW64\stdole2.tlbstdole iP.E .`M C:\WINDOWS\SysWOW64\FM20.DLLMSForms aa`#rWN:$