An experiment running turbines for various lengths of time (Nelson, 1982) recorded the propor- tion of turbine wheels (y; = Fissures/Turbines) out of a total of m; turbines developing fissures (narrow cracks) as shown in Table 1). A suitable model for the data may be a binomial glm. Table 1: The number of turbine wheels developing fissures and the number of hours they are run Hours Turbines Fissures 100 39 1000 53 1400 33 OT IA ON NO 1800 73 2200 30 6 2600 39 9 3000 42 9 1 00 -1 3400 13 6 3800 34 22 10 4200 40 21 11 4600 36 21 Note that: . use the hours run-time as the explanatory variable . use the proportion of turbine wheels developing fissures (i.e., Fissures/Turbines) as the de- pendent variable. 1. Fit a binary regression model with the logit link function. Interpret the results. 2. Fit a binary logistic regression model with the probit link function. 3. Fit a binary logistic regression model with the complementary log-log link function. 4. Plot the proportion of turbine wheels developing fissures against the number of hours of use and indicate which link seems more appropriate. 5. Compare the results of the three models, and indicate which model you prefer