(*
CALCULUS 265 Honors
Fall Semester 2000
8:00 to 8:50 MTTF
Carver 0002

Instructor: Hentzel
Office: 432 Carver
Office Hours: 9:00-10:00 MTTF

E-mail  hentzel@iastate.edu
phone  294-8141
Website

http://www.public.iastate.edu/~mathclasses/honors.265

Tuesday, September  5:  Section 12.9
p899:15,17,19 
p900:31


page 900 problem 31.


Find the Least Squares Regression Line for the points

(0,6) (4,3) (5,0), (8,-4), (10,-5)
*)

a = {{0,1},{4,1},{5,1},{8, 1},{10, 1}};

c = {6, 3, 0, -4, -5};

Solve[ (Transpose[a].a).{m,b} == Transpose[a].c]

(*
               945         175
Out[1]= {{b -> ---, m -> -(---)}}
               148         148

The line of regression is y = -175/148 x + 195/148;
*)
a1 = ListPlot[{{0,6},{4,3},{5,0}, {8,-4}, {10,-5}}];
a2 = Plot[-175/148 x + 945/148,{x,0,10}];
a3 = Show[a1,a2,PlotLabel->"Line of Regression"];


Page 899 problem 15.


Cost[{x_,y_}] := 3*Sqrt[x^2 + 2^2] + 2*Sqrt[(y-x)^2+1] + (10-y);


               3 Sqrt[2] + 2 Sqrt[3]          1
Out[7]= {{y -> ---------------------, x -> -------}}
                         6                 Sqrt[2]

Out[8]= {{y -> 1.28446, x -> 0.707107}}

In[9]:= Cost[{x/.Out[7],y/.Out[7]}]

Out[10]= {10 + 4 Sqrt[2] + Sqrt[3]}

In[11]:= N[%]

Out[11]= {17.3889}