Every Fourth of July, Nathan€™s Famous in New York City holds a hot dog eating contest, which we discuss in Exercise 2.98. Table 2.21 on page 86 shows the winning number of hot dogs and buns eaten every year from 2002 to 2011, and the data are also available in HotDogs. Figure 2.70 shows the scatterplot with the regression line.

Exercise 2.98 Table 2.21

Year .................Hot Dogs
2011.......................62
2010.......................54
2009.......................68
2008.......................59
2007.......................66
2006.......................54
2005.......................49
2004.......................54
2003.......................45
2002.......................50

Figure 2.70

(a) Is the trend in the data mostly positive or negative?
(b) Using Figure 2.70, is the residual larger in 2007 or 2008? Is the residual positive or negative in 2010?
(c) Use technology to find the correlation.
(d) Use technology to find the regression line to predict the winning number of hot dogs from the year.
(e) Interpret the slope of the regression line.
(f) Predict the winning number of hot dogs in 2012. (Bonus: Find the actual winning number in 2012 and compute the residual.)

(g) Why would it not be appropriate to use this regression line to predict the winning number of hot dogs in 2020?

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70 - 65 60 55 50 45 40 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 Year Hot Dogs