31. Failures in aircraft gas turbine engines due to high cycle fatigue is a pervasive problem. The article "Effect of Crystal Orientation on Fatigue Failure of Single Crystal Nickel Base Turbine Blade Superalloys" (J. of Engr. for Gas Turbines and Power, 2002: 161-176) gave the accompany ing data and fit a nonlinear regression function in order to predict strain amplitude from cycles to failure. Obs Cycfail Strampl Obs Cycfail Strampl 1 1326 .01495 11 7356 .00576 2 1593 .01470 12 7904 .00580 3 4414 .01100 13 79 .01212 4 5673 .01190 14 4175 .00782 5 29,516 .00873 15 34,676 .00596 6 26 .01819 16 114,789 .00600 7 843 .00810 17 2672 .00880 8 1016 .00801 18 7532 .00883 9 3410 .00600 19 30,220 .00676 10 7101 .00575

a. Construct scatterplots of y versus x, y versus ln(x), ln(y) versus ln(x), and 1@y versus 1@x.

b. Which transformation from part (a) does the best job of producing an approximate linear relationship?

c. Use the selected transformation to predict am plitude when cycles to failure 5 5000.

2. Give an operational definition for measuring the fuel efficiency of a car. In your definition, take into account factors such as the driving speed, octane rating, distance driven, tire pressure, and driving terrain.