5.47 A study, described in the paper “Prediction of Defibrillation Success from a Single Defibrillation Threshold Measurement” (Circulation [1988]:

1144 –1149) investigated the relationship between defibrillation success and the energy of the defibrillation shock (expressed as a multiple of the defibrillation threshold). The accompanying data are from this study.

Energy of Shock Success (%)

0.5 33.3 1.0 58.3 1.5 81.8 2.0 96.7 2.5 100.0

a. Construct a scatterplot of y 5 success and x 5 energy of shock. Does the relationship appear to be linear or nonlinear?

b. Fit a least-squares line to the given data, and construct a residual plot. Does the residual plot support your conclusion in Part (a)? Explain.

c. Consider transforming the data by leaving y unchanged and using either x9 5 Ïx or x" 5 ln(x). Which of these transformations would you recommend? Justify your choice by appealing to appropriate graphical displays.

d. Using the transformation you recommended in Part (c), find the equation of the least-squares line that describes the relationship between y and the transformed x.

e. What would you predict success to be when the energy of shock is 1.75 times the threshold level? When it is 0.8 times the threshold level?