Question

Is Your Car “Made in the U.S.A.”? The phrase “made in the U.S.A.” has become a familiar battle cry as U.S. workers try to protect their jobs from overseas competition. For the past few decades, a ma- jor trade imbalance in the United States has been caused by a flood of imported goods that enter the country and are sold at lower cost than comparable American-made goods. One prime concern is the automotive industry, in which the number of imported cars steadily increased during the 1970s and 1980s. 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 in the table represent the numbers 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.

Year	x, (Year - 1969)	y, Number of Imported Cars
1969	0	1.1
1970	1	1.3
1971	2	1.6
1972	3	1.6
1973	4	1.8
1974	5	1.4
1975	6	1.6
1976	7	1.5
1977	8	2.1
1978	9	2.0
1979	10	2.3
1980	11	2.4
1981	12	2.3
1982	13	2.2
1983	14	2.4
1984	15	2.4
1985	16	2.8
1986	17	3.2
1987	18	3.1
1988	19	3.1
1989	20	2.8
1990	21	2.5
1991	22	2.1
1992	23	2.0
1993	24	1.8
1994	25	1.8
1995	26	1.6
1996	27	1.4
1997	28	1.4
1998	29	1.4
1999	30	1.8
2000	31	2.1
2001	32	2.2
2002	33	2.3
2003	34	2.2
2004	35	2.2
2005	36	2.3
2006	37	2.3
2007	38	2.4
2008	39	2.3
2009	40	1.8

1. Using a scatterplot, plot the data for the years 1969–1988. Does there appear to be a linear relationship between the number of imported cars and the year?

2. Use a computer software package to find the least-squares line for predicting the number of imported cars as a function of year for the years 1969–1988.

3. Is there a significant linear relationship between the number of imported cars and the year?

4. Use the computer program to predict the number of cars that will be imported us- ing 95% prediction intervals for each of the years 2007, 2008, and 2009.

5. Now look at the actual data points for the years 2007–2009. Do the predictions obtained in step 4 provide accurate estimates of the actual values observed in these years? Explain.

6. Add the data for 1989–2009 to your database, and recalculate the regression line. What effect have the new data points had on the slope? What is the effect on SSE?

7. Given the form of the scatterplot for the years 1969–2009, does it appear that a straight line provides an accurate model for the data? What other type of model might be more appropriate? (Use residual plots to help answer this question.)

Answer 1