{VERSION 3 0 "SUN SPARC SOLARIS" "3.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 
0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }
{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 
0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Text Output" -1 2 1 
{CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 }1 0 0 -1 
-1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 2 6 1 {CSTYLE "" -1 -1 "" 0 1 0 0 
0 0 0 0 0 0 0 0 2 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple
 Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 
3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }
{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 
0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 203 "read \"/home/mat331
/Worksheets1/lsq_data.txt\";\npts:=line_pts():\nplot(pts,style=point);
\nepsilon:= (m,b, pt) ->  (m*pt[1] + b - pt[2]);\n\nE :=(m,b, pts) -> \+
sum( ( epsilon(m, b, pts[i]))^2 , i=1..nops(pts));\n" }}{PARA 6 "" 1 "
" {TEXT -1 82 "defined line_pts(), bad_line_pts(), quadratic_pts(), cu
bic_pts(), and circle_pts()" }}{PARA 13 "" 1 "" {INLPLOT "6&-%'CURVESG
6$777$$\"1*******)*Gne)!#:$!1+++EJyutF*7$$!1*****Rr.=e)F*$!1+++8*QeL#!
#97$$!1*****R(>&*3$*F*$!1+++c%3#zBF27$$\"1+++SJd3aF*$!1+++kE_\\6F27$$!
1++++-!e*y!#;$!1+++bU^o:F27$$!1+++m;7s))F*$!1+++t=r5CF27$$!1+++s>.2_F*
$!1+++J*p5*>F27$$\"1+++q/Y9pF*$!1+++*yRA`)F*7$$!1+++AzkXwF*$!1+++3Gh9B
F27$$\"1+++5]'yw'F*$!1+++\\ivQ!*F*7$$!1+++W)Q1'))F*$!1+++#R'3cBF27$$!1
+++'ypR=*F*$!1+++<-*)[BF27$$\"1+++Sr%>y(F*$!1*****pp(37#)F*7$$\"1,++gN
]W!*F*$!1+++$3Fc,'F*7$$\"1+++?'pf#RF*$!1+++B*[pE\"F27$$!1+++Q$e'\\vF*$
!1+++Q(3@I#F27$$\"1+++gP8.$)F*$!1+++$[!ypyF*7$$!1,++>q&)Q$)F*$!1+++hq6
QBF27$$!1+++3:\"yU(F*$!1+++9^9*>#F27$$\"1++++cZ%Q#F@$!1+++xl<p:F27$$!1
+++Ozxn\")F*$!1+++E#y&\\AF2-%'COLOURG6&%$RGBG$\"#5!\"\"\"\"!Fdr-%&STYL
EG6#%&POINTG-%+AXESLABELSG6$%!GF\\s-%%VIEWG6$%(DEFAULTGF`s" 2 547 204 
204 5 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 10020 10061 10056 
10074 0 0 0 20530 0 12020 0 0 0 0 0 0 0 1 1 0 0 0 577 205 0 0 0 0 0 0 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(epsilonGR6%%\"mG%\"bG%#ptG6\"6$%)
operatorG%&arrowGF*,(*&9$\"\"\"&9&6#F1F1F19%F1&F36#\"\"#!\"\"F*F*F*" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"EGR6%%\"mG%\"bG%$ptsG6\"6$%)opera
torG%&arrowGF*-%$sumG6$*$)-%(epsilonG6%9$9%&9&6#%\"iG\"\"#\"\"\"/F;;\"
\"\"-%%nopsG6#F9F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "s
olve( \{ diff(E(m,b,pts), m) = 0,\n        diff(E(m,b,pts), b) = 0\}, \+
\{m,b\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%\"bG$!+B?*Qa\"!\")/%
\"mG$\"+,?!)*G*!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(
stats):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "fit[leastsquare[
[x,y]]]([[10,15,17,19],[3,4,5,6]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#/%\"yG,&#!#z\"$z\"\"\"\"%\"xG#\"#eF(" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 49 "xvalues:=    [ seq( pts[i][1], i=1..nops(pts)) ];" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(xvaluesG77$\"***Gne)!\")$!+9P!=e)!
\"*$!+u>&*3$*F+$\"*9t&3aF($!*?+e*yF+$!+m;7s))F+$!+s>.2_F+$\"*ZgW\"pF($
!+AzkXwF+$\"*,lyw'F($!+W)Q1'))F+$!+'ypR=*F+$\"*9Z>y(F($\"*c.X/*F($\"*i
pf#RF($!+Q$e'\\vF+$\"*wLJI)F($!+>q&)Q$)F+$!+3:\"yU(F+$\")cZ%Q#F($!+Ozx
n\")F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "yvalues:=    [ se
q( pts[i][2], i=1..nops(pts)) ];" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%
(yvaluesG77$!+EJyut!\"*$!+8*QeL#!\")$!+c%3#zBF+$!+kE_\\6F+$!+bU^o:F+$!
+t=r5CF+$!+J*p5*>F+$!+*yRA`)F($!+3Gh9BF+$!+\\ivQ!*F($!+#R'3cBF+$!+<-*)
[BF+$!+(p(37#)F($!+$3Fc,'F($!+B*[pE\"F+$!+Q(3@I#F+$!+$[!ypyF($!+hq6QBF
+$!+9^9*>#F+$!+xl<p:F+$!+E#y&\\AF+" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 43 "fit[leastsquare[[x,y]]]([xvalues,yvalues]);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#/%\"yG,&$!+B?*Qa\"!\")\"\"\"%\"xG$\"+5?!)*G*
!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "\nQ :=(m,b, pts) -> \+
sum( ( epsilon(m, b, pts[i]))^4 , i=1..nops(pts));" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%\"QGR6%%\"mG%\"bG%$ptsG6\"6$%)operatorG%&arrowGF*-%
$sumG6$*$)-%(epsilonG6%9$9%&9&6#%\"iG\"\"%\"\"\"/F;;\"\"\"-%%nopsG6#F9
F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "simplify(diff(Q(m
,b,pts), m)) = 0;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#/,6%\"bG$!+&3\\G@
&!\"%*&)%\"mG\"\"#\"\"\"F%\"\"\"$!+9&)zhM!\"&F+$\"+,Wg)4&!\"$*$F*F-$!+
!pa3T\"F4*$)F+\"\"$F-$\"+f_cEJF(*$)F%F:F-$!+e))[=8!\"(*&F+F.F%F-$\"+W*
*))=\\F(*$)F%F,F-$!+KQm.>F1*&F+F-FFF-$\"+*)*H=R\"F1$!+\"34OD%F4F.\"\"!
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "solve( \{ diff(Q(m,b,pt
s), m) = 0,\n        diff(Q(m,b,pts), b) = 0\}, \{m,b\});" }}{PARA 12 
"" 1 "" {XPPMATH 20 "6+<$/%\"mG,&$\"+:y6%>*!#5\"\"\"%\"IG$!+Psjq\\!#6/
%\"bG,&$!+*Qr=a\"!\")F*F+$\"+[<7!4$F)<$/F%,&F'F*F+$\"+Psjq\\F./F0,&F2F
*F+$!+[<7!4$F)<$/F%$\"+Om)>K*F)/F0$!+TpW\\:F4<$/F0,&$!+0\"38a\"F4F*F+$
!+-M&*)4*F)/F%,&$\"+%[nZL*F)F*F+$!+IQ#*R?F.<$/F0,&FJF*F+$\"+-M&*)4*F)/
F%,&FPF*F+$\"+IQ#*R?F.<$/F0,&$!+%)R$z_\"F4F*F+$!+3(3cZ$F)/F%,&$\"+*R^8
O*F)F*F+$!+[_u=&*F.<$/F%,&F`oF*F+$\"+[_u=&*F./F0,&FjnF*F+$\"+3(3cZ$F)<
$/F0,&$!+fhLJ:F4F*F+$!+?i\\BRF)/F%,&$\"+l2e&Q*F)F*F+$!+F;e!*))F.<$/F0,
&F`pF*F+$\"+?i\\BRF)/F%,&FfpF*F+$\"+F;e!*))F." }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 44 "assign(\{m = .9321986636, b = -15.49446941\});" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "plot( [pts,m*x+b],x=-10..
10,color=[red,blue], style=[point,line]);" }}{PARA 13 "" 1 "" 
{INLPLOT "6&-%'CURVESG6%777$$\"1*******)*Gne)!#:$!1+++EJyutF*7$$!1****
*Rr.=e)F*$!1+++8*QeL#!#97$$!1*****R(>&*3$*F*$!1+++c%3#zBF27$$\"1+++SJd
3aF*$!1+++kE_\\6F27$$!1++++-!e*y!#;$!1+++bU^o:F27$$!1+++m;7s))F*$!1+++
t=r5CF27$$!1+++s>.2_F*$!1+++J*p5*>F27$$\"1+++q/Y9pF*$!1+++*yRA`)F*7$$!
1+++AzkXwF*$!1+++3Gh9BF27$$\"1+++5]'yw'F*$!1+++\\ivQ!*F*7$$!1+++W)Q1')
)F*$!1+++#R'3cBF27$$!1+++'ypR=*F*$!1+++<-*)[BF27$$\"1+++Sr%>y(F*$!1***
**pp(37#)F*7$$\"1,++gN]W!*F*$!1+++$3Fc,'F*7$$\"1+++?'pf#RF*$!1+++B*[pE
\"F27$$!1+++Q$e'\\vF*$!1+++Q(3@I#F27$$\"1+++gP8.$)F*$!1+++$[!ypyF*7$$!
1,++>q&)Q$)F*$!1+++hq6QBF27$$!1+++3:\"yU(F*$!1+++9^9*>#F27$$\"1++++cZ%
Q#F@$!1+++xl<p:F27$$!1+++Ozxn\")F*$!1+++E#y&\\AF2-%'COLOURG6&%$RGBG$\"
*++++\"!\")\"\"!Fdr-%&STYLEG6#%&POINTG-F$6%7S7$$!#5Fdr$!1++g/ck\"[#F27
$$!1nmm;p0k&*F*$!1,6j[q+TCF27$$!1LL$3<XZ=*F*$!1RdPewk0CF27$$!1mmmT%p\"
e()F*$!1./\"fK#)eO#F27$$!1nmm\"4m(G$)F*$!1m)3IS`eK#F27$$!1LL$3i.9!zF*$
!1.0fIZ,'G#F27$$!1nm;/R=0vF*$!1SOb\"=z!\\AF27$$!1,+]P8#\\4(F*$!1jk\"*f
X$3@#F27$$!1mm;/siqmF*$!1(z4v\">Gr@F27$$!1****\\(y$pZiF*$!1_*G47c=8#F2
7$$!1LLL$yaE\"eF*$!1[\"*4V=I\"4#F27$$!1mmm\">s%HaF*$!1.D68;eb?F27$$!1*
*****\\$*4)*\\F*$!1.5Y%4p`,#F27$$!1+++]_&\\c%F*$!1!QW$f9*\\(>F27$$!1++
+]1aZTF*$!1oc6E,3O>F27$$!1mm;/#)[oPF*$!1`;x2\\u+>F27$$!1LLL$=exJ$F*$!1
I^Y:zse=F27$$!1LLLL2$f$HF*$!1]Ng6S8B=F27$$!1++]PYx\"\\#F*$!1))pqR)H<y
\"F27$$!1MLLL7i)4#F*$!1#f6>8!3X<F27$$!1****\\P'psm\"F*$!1NQz$fp[q\"F27
$$!1****\\74_c7F*$!1&zTDlzlm\"F27$$!1:LL$3x%z#)F@$!1,Rs:\"Gmi\"F27$$!1
ILL3s$QM%F@$!1V]SL,%**e\"F27$$!1^omm;zr)*!#=$!1,**4)=n.b\"F27$$\"1WLLe
zw5VF@$!1?:q>?E4:F27$$\"1.++v$Q#\\\")F@$!1sYx\\)zMZ\"F27$$\"1NLLe\"*[H
7F*$!1)4pf7M[V\"F27$$\"1++++dxd;F*$!1X6z6$4\\R\"F27$$\"1,++D0xw?F*$!18
\"*>q1&eN\"F27$$\"1,+]i&p@[#F*$!1!*35E%f!=8F27$$\"1+++vgHKHF*$!1[0w#p)
4w7F27$$\"1lmmmZvOLF*$!1S_d2^RQ7F27$$\"1,++]2goPF*$!1/3s#[Q\")>\"F27$$
\"1KL$eR<*fTF*$!1y<H(**f;;\"F27$$\"1-++])Hxe%F*$!1<s[x$z<7\"F27$$\"1mm
;H!o-*\\F*$!1.0AA[D%3\"F27$$\"1,+]7k.6aF*$!1cwv\\3.X5F27$$\"1mmm;WTAeF
*$!1'z&=ZAo15F27$$\"1****\\i!*3`iF*$!1CdcU\"[`m*F*7$$\"1NLLL*zym'F*$!1
395Z1oy#*F*7$$\"1OLL3N1#4(F*$!1P`O&GdK)))F*7$$\"1pm;HYt7vF*$!1!R4(G#36
\\)F*7$$\"1-+++xG**yF*$!1\"3oE(RwI\")F*7$$\"1qmmT6KU$)F*$!1/jT!zoxr(F*
7$$\"1OLLLbdQ()F*$!13!fg(4Q[tF*7$$\"1++]i`1h\"*F*$!1^_#>_OX&pF*7$$\"1-
+]P?Wl&*F*$!1P#**e7xvd'F*7$$\"#5Fdr$!1,++uF[shF*-F^r6&F`rFdrFdrFar-Ffr
6#%%LINEG-%+AXESLABELSG6$Q\"x6\"%!G-%%VIEWG6$;F]sF^bl%(DEFAULTG" 2 
548 288 288 2 0 1 0 2 9 0 4 2 1.000000 45.000000 45.000000 10030 
10061 10056 10074 0 0 0 20530 0 12020 0 0 0 0 0 0 0 1 1 0 0 0 464 902 
0 0 0 0 0 0 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "cpts:=circle_
pts();\nplot(cpts,style=point,scaling=constrained);" }}{PARA 12 "" 1 "
" {XPPMATH 20 "6#>%%cptsG777$$\"*KW!eP!\"*$\"+7OY-eF)7$$!+[H9V<!\")$\"
+`<sA^F)7$$!+!*QE97F/$\"+*41'o8F/7$$!+\"[\\i-#F)$!*(y6`qF)7$$!+'p*e7MF
)$!+`(4s7#F)7$$!+Dj&Gk)F)$\"+Yrvn9F/7$$!*S@'4()F)$\"+<P![3\"F/7$$!+/D#
zq\"F/$\"+SKy^vF)7$$!+%3:v(=F)$\"+`#oC9\"F/7$$!+2BLB9F/$\"+(y1VD\"F/7$
$!+^(eSK\"F/$\"+S_%\\H\"F/7$$!+<'4;C&F)$\"+l\"*yv8F/7$$!+\"ex[(GF)$!+l
RTC;F)7$$\"*&[#fN&F)$\"+?y?jYF)7$$!+<%\\k]\"F/$!*P07#HF)7$$!+)*p#pY\"F
/$\"+e?*H>\"F/7$$!+de?$[\"F/$!*=T,\"**F)7$$!+qm&=>'F)$!+7agZJF)7$$!+Ef
kE<F/$\"+I-TOUF)7$$!+Yrh6IF)$!+CeU$)=F)7$$!+a70)e\"F/$\"+!yIoS\"F)" }}
{PARA 13 "" 1 "" {INLPLOT "6'-%'CURVESG6$777$$\"1+++?V/eP!#;$\"1+++7OY
-e!#:7$$!1+++[H9V<!#9$\"1+++`<sA^F-7$$!1+++!*QE97F1$\"1+++*41'o8F17$$!
1+++\"[\\i-#F-$!1+++qy6`qF*7$$!1+++'p*e7MF-$!1+++`(4s7#F-7$$!1+++Dj&Gk
)F-$\"1+++Yrvn9F17$$!1,+++9i4()F*$\"1+++<P![3\"F17$$!1+++/D#zq\"F1$\"1
+++SKy^vF-7$$!1+++%3:v(=F-$\"1+++`#oC9\"F17$$!1+++2BLB9F1$\"1+++(y1VD
\"F17$$!1+++^(eSK\"F1$\"1+++S_%\\H\"F17$$!1+++<'4;C&F-$\"1+++l\"*yv8F1
7$$!1+++\"ex[(GF-$!1+++lRTC;F-7$$\"1+++][#fN&F*$\"1+++?y?jYF-7$$!1+++<
%\\k]\"F1$!1+++q`?@HF*7$$!1+++)*p#pY\"F1$\"1+++e?*H>\"F17$$!1+++de?$[
\"F1$!1,++!=T,\"**F*7$$!1+++qm&=>'F-$!1+++7agZJF-7$$!1+++EfkE<F1$\"1++
+I-TOUF-7$$!1+++Yrh6IF-$!1+++CeU$)=F-7$$!1+++a70)e\"F1$\"1+++!yIoS\"F-
-%'COLOURG6&%$RGBG$\"#5!\"\"\"\"!Fdr-%&STYLEG6#%&POINTG-%(SCALINGG6#%,
CONSTRAINEDG-%+AXESLABELSG6$%!GF`s-%%VIEWG6$%(DEFAULTGFds" 2 547 206 
206 5 0 1 0 2 9 0 4 1 1.000000 45.000000 45.000000 0 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 1 1 0 0 0 8168 0 0 0 0 0 0 0 }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 46 }{VIEWOPTS 1 1 0 2 1 1805 }