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\noindent {\LARGE M}{\large ath} {\LARGE 370} {\LARGE F}{\large all} {\LARGE 98}
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{\Large Quiz {\bf 7}}\hspace{7cm} & \hspace{1.65in} & {\bf\large Numerical~Analysis}\\
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{\bf\large Name}: \makebox[3in]{\hrulefill}  & \hspace{1.5in} & \\
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Date: \makebox[2in]{\hrulefill} & \hspace{1.5in} & {\bf Friday November 20} \\
Time Begun: \makebox[2in]{\hrulefill} & \hspace{1.5in} & Ron Buckmire \\ 
Time Ended: \makebox[2in]{\hrulefill} & \hspace{1.5in} & \\
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{\Large {\bf Topic :}} Approximation Theory

{\small The idea behind this quiz is for you to get more experience finding a function of best fit}

{\Large {\bf Instructions: }}
\begin{itemize}
\item[1.] Once you open the quiz, you have as much time as you need to complete it, but record your start time and end time at the top of this sheet.
\item[2.] You may use the book or any of your class notes.  You must work alone.
\item[3.] If you use your own paper, please staple it to the quiz before coming to class.  If you don't have a stapler, buy one.
\item[4.] After completing the quiz, sign the pledge below stating on your honor that you have adhered to these rules.  
\item[5.] Your solutions must have enough details such that an impartial observer can read your work and determine HOW you came up with your solution.
\item[6.] Relax and enjoy...
\item[7.] {\bf This quiz is due on Monday November 23}, in class.  NO LATE QUIZZES WILL BE ACCEPTED.
\end{itemize}

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{\bf Pledge:} I, \makebox[2in]{\hrulefill}, pledge my honor as a human being and Occidental student, that I have followed all the rules above to the letter and in spirit.
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Math 370 Fall 1998 \hfill{Quiz {\bf 7}}
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\vspace{-7.5ex}   {\large\bf EXPLAIN YOUR ANSWERS}\\
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$x$ & 1.0000  & 2.0000 &  4.0000  & 5.5000 & 7.0000 \\
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$y$ &  2.2361 & 10.9329 & 24.6765  & 42.8382 & 65.0486
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Consider the experimental data above to postulate a relationship of $y=P(x) = c_1 x^{c_2}$ between the input and output experimental data.
{\bf a.}  [{\it 2 points}] Derive transformations involving $Y=Y(x,y)$ and $X=X(x,y)$ which change the nonlinear relationship $y=c_1 x^{c_2}$ into a linear one between $Y$ and $X$
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{\bf b.}  [{\it 6 points}] Use \matlab's {\tt linefit} function or some other calculations to find $c_1$ and $c_2$. (Show all your calculations, such as \matlab commands and what output it produces.)
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{\bf c.}  [{\it 2 points}] What is the least square error between the experimental data and the curve of best fit? That is evaluate $E = \sum_{k=0}^n (y_k - P(x_k))^2$
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