$3$ 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.

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

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. $)$