Question $2(25$ points$)$

This assignment will use Transit Monthly Data.xlsx$,$ the number of transit rides on a transportation system from June $2013$ up until May $2017.$ Our goal is to build a regression model to predict the ride volume for the following $12$ months.

Model A:

a$)(2$ pts$)$ Does a linear trend appear to fit these data well? Explain why or why not. Reference any tables$/$figures that you need to make your point.

b$)(2$ pts$)$ Is there evidence of some seasonal pattern in the sales data? If so$,$ characterize the seasonal pattern $($monthly$,$ quarterly, or yearly$).$

c$)(5+2+2=9$ pts$)$ Build a regression model with$/$without trend $($no trend, linear or nonlinear trend, depending on your answer in part a$)$ and with$/$without seasonality $($depending on your answer in part b$).$ To validate your model, use the last $12$ months as a validation data set.

I. Copy and paste your $R$ code and display the regression output.

II$.$ What are the RMSE and MAPE of your model based on the validation data? Discuss the overall performance of you model.

III. Fill in the table with your predictions for the following $12$ months.

Note: If it is not clear if the data has trend and seasonality, build models with trend and$/$or seasonality and compare them.

$\backslash$table$[[$Month$-$Year,$\backslash$table$[[$Trips$/$month$],[($Prediction$)]]],[$Jun$-17,],[$Jul$-17,],[$Aug$-17,],[$Sep$-17,],[$Oct$-17,],[$Nov$-17,],[$Dec$-17,],[$Jan$-18,],[$Feb$-18,],[$Mar$-18,],[$May$-18,]]$

$\backslash$table$[[$Month Trips$/$month$,$Highest Temperature

$92$