Chapter 5.4, Problem 61E

Refer to the heart transplant data given in the previous exercise.

1. a. Find a transformation of x and/or y that straightens the plot. Construct a scatterplot for your transformed variables.
2. b. Using the transformed variables from Part (a), fit a least-squares line and use it to predict the number waiting for a heart transplant in 2016 (Year 11).
3. c. The prediction made in Part (b) involves prediction for an x value that is outside the range of the x values in the sample. What assumption must you be willing to make for this to be reasonable? Do you think this assumption is reasonable in this case? Would your answer be the same if the prediction had been for the year 2026 rather than 2016? Explain.

   The following table gives the number of heart transplants performed in the Unites States each year from 2006 to 2015 (U.S. Department of Health and Human Services, optn.transplant.hrsa.gov/data/view-data-reports/national-data/, retrieved April 22, 2017):

a. Construct a scatterplot of these data. Describe how the number of heart transplants has changed over time from 2006 to 2015.

b. Find the equation of the least-squares line that describes the relationship between y = Number of heart transplants performed and x = Year.

c. Calculate the 10 residuals and construct a residual plot.

d. Are there any features of the residual plot that indicate that the relationship between year and number of heart transplants performed would be better described by curve rather than a line? Explain.