\begin{slide}
%\large
{\bf HW6 handed out Lect 7, due Lect 9}\\

\begin{small}
Below is "plot.ps' which is  plot of some data which was simulated according 
to the model 
\[
y_i = f(t_i) + \epsilon_i, ~~~i = 1, \cdots, 100
\]
where the $\epsilon_i$ are independent 
Gaussian (pseudo) random variables 
with common variance.

A table "hw6.dat"  containing  $t_i, y_i$ appears on the next page. 
You will find hw6.dat and plot6.ps in the coursepage 
in the  hw6 directory. 

Use the R tutorial (or any other spline smoothing program if you 
prefer), to fit a cubic smoothing spline to this data. 
The R tutorial is found in the R directory in the course 
page, goto the cubic.spline subdirectory and read R.html\\

Method 1: Eyeball method. Try several different smoothing parameters $(\lambda)$, 
and examine the plots until you find a $\lambda$ that makes the 
curve seem appropriate to the data. \\ 
%(Use {\tt smooth.Pspline(x, y, spar=(yournumberhere), method=1}

Method 2:  Use the GCV method, which is given as an option in the tutorial.\\ 
\end{small}
\setlength{\unitlength}{\textwidth}
\centerline{\epsfxsize=0.9\unitlength\epsffile{plot6.ps}}
\end{slide}
\begin{slide}
%\twocolumn
Some of the data: 
\begin{small}
\begin{verbatim}
0.01 -0.095115585
0.02 -0.055414668
0.03  0.097941183
0.04 -0.074766765
0.05  0.038402129
0.06 -0.434194115
0.07 -0.212602635
0.08 -0.341563521
0.09 -0.466058171
0.10 -0.305601445
0.11 -0.585033899
0.12 -0.395114048
0.13 -0.259369872
0.14 -0.541031506
0.15 -0.497907669
0.16 -0.384445006
0.17 -0.343292281
0.18 -0.357539778
0.19 -0.677392782
0.20 -0.646095368
0.21 -0.421976991
0.22 -0.712665060
0.23 -0.401646085
\end{verbatim}
\end{small}
\end{slide}
