4. Fit a cubic model if you have not yet done so. Is the fit significantly better than your model in part 2? Are there any patterns in the residuals plotted against x? Does it appear that there are missing terms in the model? Summarize your findings.

In Chapter 12 we examined the effect of foreign competition in the automotive industry as the number of imported cars steadily increased during the 1970s and 1980s.10 The American auto industry rebounded, and the number of imported cars decreased over the period 1987–1997. Since the number of imported cars began to increase again in 1998, let us examine the pattern of the number of imported cars beginning with 1998. This time the years have been coded using x=Year-1997.

If you look at a scatterplot of these data, you will find that the number of imported cars does not appear to follow a linear relationship over time, but rather a curvilinear relationship. The problem is to decide whether a polynomial model is appropriate, and if so, to decide on the order of the polynomial

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Year x y Year y 1998 1 1.4 2007 10 2.4 1999 2 1.7 2008 11 2.3 2000 3 2.0 2009 12 1.8 2001 4 2.1 2010 13 1.8 2002 5 2.2 2011 14 1.9 2003 6 2.1 2012 15 2.1 2004 7 2.1 2013 16 2.2 2005 2006 66 8 2.2 2014 17 2.1 9 2.3 2015 18 1.9