The following data contains the monthly number of airlines tickets sold by a travel agency for four years.

Month	Year	Tickets
January	1	605
February	1	647
March	1	636
April	1	612
May	1	714
June	1	765
July	1	698
August	1	615
September	1	588
October	1	685
November	1	711
December	1	664
January	2	630
February	2	696
March	2	670
April	2	671
May	2	724
June	2	787
July	2	724
August	2	651
September	2	589
October	2	697
November	2	750
December	2	705
January	3	664
February	3	704
March	3	691
April	3	672
May	3	753
June	3	787
July	3	751
August	3	695
September	3	643
October	3	724
November	3	803
December	3	705
January	4	720
February	4	757
March	4	707
April	4	692
May	4	828
June	4	827
July	4	763
August	4	710
September	4	673
October	4	793
November	4	852
December	4	710

Our goal is to build a regression model to predict the demand for the following 12 months.

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) (5+2+2 = 9 pts) Build a linear trend model or nonlinear trend regression model (depending on your answer in part a). Do not add a seasonality factor to this model. To validate your model, use the last 12 months as a validation data set.

1. Copy and paste your R code and display the regression output.
2. What are the RMSE and MAPE of the trend model based on the validation data? Discuss the overall performance of you model.
3. Fill in the table with your predictions for the following 12 months.

Month	Year	Tickets (Prediction)
January	5
February	5
March	5
April	5
May	5
June	5
July	5
August	5
September	5
October	5
November	5
December	5

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

d) (5+2+2= 9 pts) Build a regression model with trend and seasonality. To validate your model, use the last 12 months as a validation data set.

1. Copy and paste your R code and display the regression output.
2. What are the RMSE and MAPE of the trend model based on the validation data? Discuss the overall performance of you model.
3. Fill in the table with your predictions for the following 12 months.

Month	Year	Tickets (Prediction)
January	5
February	5
March	5
April	5
May	5
June	5
July	5
August	5
September	5
October	5
November	5
December	5

e) (3 pts) Between the two models (part b and part d), which model will you use? Explain your answer.