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 Engineering for Gas Turbines and Power, 2002: 161–176)

gave the accompanying data and fit a nonlinear regression model in order to predict strain amplitude from cycles to failure. Fit an appropriate model, investigate the quality of the fit, and predict amplitude when cycles to failure 5

.5000 Ha: b , 4 3 H0: b 5 4 3

x 5 10 15 20 25 30 45 60 y 16.3 9.7 8.1 4.2 3.4 2.9 1.9 1.3

a. Construct a scatter plot of y versus x and comment.

b. Construct a scatter plot of the (ln(x), ln(y)) pairs and comment.

c. What probabilistic relationship between x and y is suggested by the linear pattern in the plot of part (b)?

d. Predict the value of moisture content when frying time is 20, in a way that conveys information about reliability and precision.

e. Analyze the residuals from fitting the simple linear regression model to the transformed data and comment.