Vacation destinations often run on a seasonal basis, depending on the primary activities in that location. Amanda Wang is the owner of a travel agency in Cincinnati, Ohio. She has built a database of the number of vacation packages (Vacation) that she has sold over the last 12 years. The accompanying file includes quarterly data on the number of vacation packages sold. Year Quarter Vacation 2008 1 500 2008 2 147 2008 3 1314 2008 4 673 2009 1 984 2009 2 584 2009 3 1449 2009 4 1125 2010 1 209 2010 2 458 2010 3 1357 2010 4 544 2011 1 483 2011 2 280 2011 3 1392 2011 4 780 2012 1 340 2012 2 1003 2012 3 1692 2012 4 783 2013 1 781 2013 2 409 2013 3 1657 2013 4 792 2014 1 671 2014 2 769 2014 3 1068 2014 4 520 2015 1 616 2015 2 775 2015 3 1215 2015 4 514 2016 1 232 2016 2 492 2016 3 1581 2016 4 1028 2017 1 551 2017 2 869 2017 3 1114 2017 4 476 2018 1 405 2018 2 412 2018 3 1121 2018 4 554 2019 1 666 2019 2 729 2019 3 1283 2019 4 923 1. Estimate the linear regression models using seasonal dummy variables with and without the trend term. Which is the preferred model?   2. Use the preferred model to forecast the quarterly number of vacation packages sold in the first two quarters of 2020.

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Vacation destinations often run on a seasonal basis, depending on the primary activities in that location. Amanda Wang is the owner of a travel agency in Cincinnati, Ohio. She has built a database of the number of vacation packages (Vacation) that she has sold over the last 12 years. The accompanying file includes quarterly data on the number of vacation packages sold.

Year Quarter Vacation
2008 1 500
2008 2 147
2008 3 1314
2008 4 673
2009 1 984
2009 2 584
2009 3 1449
2009 4 1125
2010 1 209
2010 2 458
2010 3 1357
2010 4 544
2011 1 483
2011 2 280
2011 3 1392
2011 4 780
2012 1 340
2012 2 1003
2012 3 1692
2012 4 783
2013 1 781
2013 2 409
2013 3 1657
2013 4 792
2014 1 671
2014 2 769
2014 3 1068
2014 4 520
2015 1 616
2015 2 775
2015 3 1215
2015 4 514
2016 1 232
2016 2 492
2016 3 1581
2016 4 1028
2017 1 551
2017 2 869
2017 3 1114
2017 4 476
2018 1 405
2018 2 412
2018 3 1121
2018 4 554
2019 1 666
2019 2 729
2019 3 1283
2019 4 923

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

 

2. Use the preferred model to forecast the quarterly number of vacation packages sold in the first two quarters of 2020.

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

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