We are using the number of passenger cars produced in the united states from 1999 through 2016 to fit different auto-regressive models. the data is provided below:
year

units produced (000)

1999

5,577.5

2000

5,471.0

2001

4,808.1

2002

4,957.3

2003

4,453.6

2004

4,165.8

2005

4,265.9

2006

4,311.5

2007

3,867.2

2008

3,731.3

2009

2,195.6

2010

2,731.1

2011

2,977.0

2012

4,109.0

2013

4,368.8

2014

4,253.1

2015

4,162.8

2016

3,916.6

a. fit a third-order autoregressive model to the number of passenger cars produced in the united states and test for the significance of the third-order autoregressive parameter (slope). (use a = 0.05.)

b. if necessary, fit a second-order autoregressive model to the number of passenger cars produced in the united states and test for the significance of the second-order autoregressive parameter (slope). (use a = 0.05.)

c. if necessary, fit a first-order autoregressive model to the number of passenger cars produced in the united states and test for the significance of the first-order autoregressive parameter (slope). (use a = 0.05.)