An ERCP is a medical procedure used most often to treat tumors or gallstones. The numbers of ERCP procedures in the United States are shown in Table 65 for various years.

Let y be the number (in thousands) of ERCP procedures in the year that is x years since 2010.
a. Construct a scatterplot of the data.
b. Find the linear regression equation.
c. Construct a residual plot.
d. Find the year and the residual represented by the highest point in the residual plot. What does this tell you about the corresponding data point in the scatterplot and the regression line?
e. An ERCP involves a duodenoscope, which is a medical scope that is difficult to clean. In fact, the scope has been tied to deadly superbug outbreaks in hospitals in more than five cities. Research shows that 10% to 30% of duo- denoscopes remain contaminated after attempted cleaning. Assuming the exact percentage of contaminated duodenoscopes is 20%, predict the number of ERCP procedures that will involve contaminated duodenoscopes in 2015. Do you have much faith in your prediction? Explain.

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Table 65 Numbers of ERCP Procedures in the United States Number of ERCP Procedures (thousands) Year 2010 2011 2012 2013 2014 584 600 622 642 669