Programming Assignment Three

$\def\R{{\bf R}} \hangindent\parindent \item{5a.} The data in the file{\tt\ file05a.dat }was normally distributed with unit variance around a specific instance of the linear model $$ F_a(x)=\sum_{i=0}^3 a_i x^i.$$ Use the least squares method to find the values of the parameters $a_i$ that maximize the likelihood of the data. Estimate the errors in the parameters. \medskip \item{5b.} The data in the file{\tt\ file05b.dat }was normally distributed with unit variance around a specific instance of the linear model $$ G_b(x)=\sum_{i=0}^3 b_i\cos\big(x\sqrt i\big).$$ Use the least squares method to find the values of the parameters $b_i$ that maximize the likelihood of the data. Estimate the errors in the parameters. \medskip \item{5c.} Use $G_b(x)$ to model the data in{\tt\ file05a.dat }and $F_a(x)$ to model the data in{\tt\ file05b.dat}. Plot the data and the model for each of the above cases. What can be said about the goodness of fit?$

Last Updated: Mon Mar 19 23:06:32 PST 2001