#$3$ Develop two forecast models for the AmTrk ridership data $($as shown on next slide$)$: first the linear model A$,$ then the non$-$linear model B with addition of the seasonality terms.

Model $A$: $a0+a{1}^{***}t$

Model $B$: $b0+b{1}^{***}t+b{2}^{**}sin(2^{**}\frac{t}{12})+b{3}^{**}cos(2^{***}{}^{**}\frac{t}{12})$

Plot AmTrk ridership data vs$.$ time for the first $48$ month with appropriate $x-y$ coordinate labeling. Graphically assess the long$-$term trend from the raw data. Build the multiple regression model $Ax=b$ for Model A and Model $B$ respectively based on the first $48$ month data. Compute $\{a0,a1\}$ and $\{b0,b1,b2,b3\}$ using Matlab function Alb.

With the preceding forecast models predict the ridership for the next $6$ month beyond $48$th month since Jan $1991.$ Compare with the actual, calculate the monthly forecast errors, and estimate the RMS $($Root Mean Square$)$ errors for a$)$ three$-$month forecast, and b$)$ six$-$month forecast. What is your evaluation of the comparative forecast performance of Model A versus Model B based on the RMS errors?

$($Follow the examples on previous lecture notes for multiple regression.$)$