Used car dealerships generally have sales quotas that they strive to hit each month, quarter, and calendar year. Consequently, buying a used car toward the end of those periods presents a$.$ great opportunity to get a good deal on the car. The accompanying file includes monthly sales data for used cars $($Cars$)$ from $2014-2019.$

Click here for the Excel Data File

a$.$ Estimate the linear regression models using seasonal dummy variables with and without the trend term. Which is the preferred model?

With trend. based on the value of

adjusted $R^2$

b$.$ Use the preferred model to forecast used car sales in the first two months of $2020.$

Note: Round coefficient estimates to at least $4$ decimal places and final answers to $2$ decimal places.

$\backslash$table$[[$Month$,$Forecast$],[$Month $1,],[$Month $2,]]$

$\backslash$table$[[,$A$,$B$,$C$,$D$],[1,$Date,Cars,,$],[2,$January$/14,188,,],[3,$February$/14,229,,],[4,$March$/14,201,,],[5,$April$/14,226,,],[6,$May$/14,226,,],[7,$June$/14,262,,],[8,$July$/14,249,,],[9,$August $114,283,,],[10,$September$/14,283,,],[11,$October$/14,252,,],[12,$November$/14,226,,],[13,$December$/14,230,,],[14,$Januar$/15,226,,],[15,$February$/15,198,,8],[16,$March$/15,221.,,],[17,$April $\frac{?}{15},216,,],[18,$Mar$/15,247,,],[19,$June$/15,249,,],[20,$July$/15,264,,],[21,$August$/15,280,,],[22,$Septermber$/15,274,,],[23,$October$/15,227,,],[24,$November$/15,233,,],[25,$December $\frac{?}{15},223.,,],[26,$Lanuary$/16,228,,],[27,$Februay$/16,183,,],[28,$March$/16,200,,],[29,$April$/16,218,,],[30,$May$/16,239.,,],[31,$June$/16,260,,],[32,$July$/16,279,,],[33,$August$/16,284,,],[34,$September$/16,292.,,],[35,$October$/16,218,,],[36,$November$/16,236,,],[37,$December $\frac{?}{16},241,,],[38,$January$/17,204,,],[39,$Februan$/17,192,,],[40,$March$/17.,215,,],[41,$April$/17,223,,],[42,$May$/17,244,,],[43,$June$/17,253,,],[44,$suly$/17,280,,],[45,$August$/17.,256,,],[46,$September $\frac{?}{17},271,,],[47,$October$/17,217,,],[48,$November $17,224,,],[49,$December$/17,233,,],[50,$January$/18,225,,],[51,$February$/18,202,,],[52,$March $\frac{?}{18},211,,],[53,$April $\frac{?}{18},220,,],[54,Ma\frac{y}{18},230,,y$