The case study in Chapter 12 examined the effect of foreign competition in the automotive industry as

Question:

The case study in Chapter 12 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 U.S. automobile industry has been besieged with complaints about product quality, worker layoffs, and high prices and has spent billions in advertising and research to produce an American-made car that will satisfy consumer demands. Have they been successful in stopping the flood of imported cars purchased by American consumers? The data shown in the table give the number of imported cars (y) sold in the United States (in millions) for the years 1969-2009. To simplify the analysis, we have coded the year using the coded variable x = Year - 1969.

By examining 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 exhibits a curvilinear response. The question, then, is to decide whether a second-, third-, or higher-order model adequately describes the data.
1. Plot the data and sketch what you consider to be the best-fitting linear, quadratic, and cubic models.
2. Find the residuals using the fitted linear regression model. Does there appear to be any pattern in the residuals when plotted against x? What model do the residuals indicate would produce a better fit?
3. What is the increase in R2 when you fit a quadratic rather than a linear model? Is the coefficient of the quadratic term significant? Is the fitted quadratic model significantly better than the fitted linear model? Plot the residuals from the fitted quadratic model. Does there seem to be any apparent pattern in the residuals when plotted against x?
4. What is the increase in R2 when you compare the fitted cubic with the fitted quadratic model? Is the fitted cubic model significantly better than the fitted quadratic? Are there any patterns in a plot of the residuals versus x? What proportion of the variation in the response y is not accounted for by fitting a cubic model? Should any higher-order polynomial model be considered? Why or why not?