An experiment was conducted to test whether the clutch size that a type of bird produces is optimal in terms of maximizing the survival of the offspring. A log-linear model was fit for modeling the number of surviving offspring as a function of the original clutch size C and the amount of manipulation M, which was measured by the number of eggs added or removed. The analysis of deviance table as well as the predicted parameters are given below:

Model Residual deviance df Bj se ( B; ) Null model 732.74 617 + C 662.25 616 0.238 0.028 + M 649.01 615 0.017 0.035 + M2 637.22 614 -0.028 0.009 (a) Using likelihood ratio tests, determine which predictor variables are sig- nificant. (b) Compute the 95% confidence interval for the parameter of the original clutch size C. (c) Comment on under- or overdispersion for this model. (d) Write down the fitted model, where Bo = -2.928. Using the fitted model, determine the value of M maximizing expected offspring survival M. (e) Determine if any manipulation of the clutch size decreases the survival chances of the young