Question

The accompanying dataset shows the monthly number of new car sales in the last three years. Develop a multiple regression model with categorical variables that incorporate seasonality for forecasting sales.

Data

Month   Year   Units
Jan   1   39,830
Feb   1   40,101
Mar   1   47,460
Apr   1   47,317
May   1   49,231
Jun   1   51,499
Jul   1   46,486
Aug   1   45,220
Sep   1   44,820
Oct   1   47,009
Nov   1   42,181
Dec   1   44,206
Jan   2   42,247
Feb   2   45,442
Mar   2   54,095
Apr   2   50,946
May   2   53,592
Jun   2   54,940
Jul   2   54,469
Aug   2   56,099
Sep   2   52,197
Oct   2   50,107
Nov   2   48,533
Dec   2   49,298
Jan   3   48,154
Feb   3   54,907
Mar   3   61,086
Apr   3   53,370
May   3   59,487
Jun   3   59,390
Jul   3   55,108
Aug   3   59,369
Sep   3   54,492
Oct   3   53,184
Nov   3   48,813
Dec   3   46,976

Develop a multiple regression model with categorical variables that incorporate seasonality for forecasting​ sales, where December is the reference month.

Units=____+​(_____​)•Year+​(____​)•Jan +​(____​)•Feb +​(_____​)•Mar +​(_____​)•Apr +​(_____​)•May+​(_____​)•Jun+​(_____​)•Jul+​(____​)•Aug+​(____​)•Sep+​(____​)•Oct+​(____​)•Nov

​(Round to the nearest integer as​ needed.)

* Please show how to get the results

Thank you

Answer 1

Units=37,745.3333+​(4,540.6667​)•Year+​(-3,416.3333)•Jan +​(-10.0000)•Feb +​(7,387.0000)•Mar +​(3,717.6667)•Apr +​(7,276.6667)•May+​(8,449.6667​)•Jun+​(5,194.3333)•Jul+​(6,736.0000​)•Aug+​(3,676.3333)•Sep+​(3,273.3333)•Oct+​(-317.6667​)•Nov

The setup of this model is:

The regression analysis is:

Month	Units	Year	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov
Jan	39830	1	1	0	0	0	0	0	0	0	0	0	0
Feb	40101	1	0	1	0	0	0	0	0	0	0	0	0
Mar	47460	1	0	0	1	0	0	0	0	0	0	0	0
Apr	47317	1	0	0	0	1	0	0	0	0	0	0	0
May	49231	1	0	0	0	0	1	0	0	0	0	0	0
Jun	51499	1	0	0	0	0	0	1	0	0	0	0	0
Jul	46486	1	0	0	0	0	0	0	1	0	0	0	0
Aug	45220	1	0	0	0	0	0	0	0	1	0	0	0
Sep	44820	1	0	0	0	0	0	0	0	0	1	0	0
Oct	47009	1	0	0	0	0	0	0	0	0	0	1	0
Nov	42181	1	0	0	0	0	0	0	0	0	0	0	1
Dec	44206	1	0	0	0	0	0	0	0	0	0	0	0
Jan	42247	2	1	0	0	0	0	0	0	0	0	0	0
Feb	45442	2	0	1	0	0	0	0	0	0	0	0	0
Mar	54095	2	0	0	1	0	0	0	0	0	0	0	0
Apr	50946	2	0	0	0	1	0	0	0	0	0	0	0
May	53592	2	0	0	0	0	1	0	0	0	0	0	0
Jun	54940	2	0	0	0	0	0	1	0	0	0	0	0
Jul	54469	2	0	0	0	0	0	0	1	0	0	0	0
Aug	56099	2	0	0	0	0	0	0	0	1	0	0	0
Sep	52197	2	0	0	0	0	0	0	0	0	1	0	0
Oct	50107	2	0	0	0	0	0	0	0	0	0	1	0
Nov	48533	2	0	0	0	0	0	0	0	0	0	0	1
Dec	49298	2	0	0	0	0	0	0	0	0	0	0	0
Jan	48154	3	1	0	0	0	0	0	0	0	0	0	0
Feb	54907	3	0	1	0	0	0	0	0	0	0	0	0
Mar	61086	3	0	0	1	0	0	0	0	0	0	0	0
Apr	53370	3	0	0	0	1	0	0	0	0	0	0	0
May	59487	3	0	0	0	0	1	0	0	0	0	0	0
Jun	59390	3	0	0	0	0	0	1	0	0	0	0	0
Jul	55108	3	0	0	0	0	0	0	1	0	0	0	0
Aug	59369	3	0	0	0	0	0	0	0	1	0	0	0
Sep	54492	3	0	0	0	0	0	0	0	0	1	0	0
Oct	53184	3	0	0	0	0	0	0	0	0	0	1	0
Nov	48813	3	0	0	0	0	0	0	0	0	0	0	1
Dec	46976	3	0	0	0	0	0	0	0	0	0	0	0