
\section*{Homework 3}\label{p2hw1}

\begin{itemize}
\item Using the commands in the
Mathematica workbook \texttt{M3\_P2\_AffineModel.nb}, answer the
questions below.
\item The answers should by written in a word-document, named  \texttt{"your last name"\_M3\_HW3.doc}
\item You may work together with your
fellow group members if you wish, but should submit individual copies
of your work.
\end{itemize}
\begin{enumerate}
\item Using the total distance function $H_4(m,b)$, find the optimal model for the test data, i.e.
\begin{center}
\begin{tabular}{|c|c|}
\hline
\textbf{Age (Months)} & \textbf{Score}\\\hline
20 & 95\\
27 & 90\\
30 & 98\\
35 & 103\\
41 & 112\\
44 & 109\\
46 & 115\\
\hline
\end{tabular}
\end{center} 
Provide a graphic evidence that the model is valid.
\item  Using the $P2$ distance function, fit the best model of the form $y=mx+b$ to the data about the growth of plant roots from Problem 1, i.e.
\begin{center}
\begin{tabular}{|c|c|}
\hline
\textbf{Day} & \textbf{Growth (mm)}\\\hline
0 &0\\
1 & 1.2\\
2 & 3.8\\
3 & 4.2\\
4 & 6.3\\
5 & 7.2\\
6 & 7.3\\
\hline
\end{tabular}
\end{center}
 Comment on whether a model of the form $y=mx$ or a model of the form $y=mx+b$ is most suitable for this data.
\end{enumerate}
