Exercise 1: Moth data The larvae of the tobacco budworm, Heliothis virescens, are responsible for much damage to cotton crops in the United States, and Central and Southern America. As a result of intensive cropping practices and the misuse of pesticides, particularly synthetic pyrethroids, the insect has become an important crop pest. Holloway (1989) conducted an experiment to examine levels of resistance in the adult moth to the pyrethroid trans-cypermethrin. In the experiment, batches of pyrethroid-resistant moths of each sex were exposed to a range of doses of cypermethrin two days after emergence from pupation. The number of moths which were knocked down (movement of the moth is uncoordinated) or dead (the moth is unable to move and does not respond to a poke from a blunt instrument) was recorded 72 hours after treatment. The file moth.cau for each moth records the dose of cypermethrin (Dose), sex (Sex with 1 = Male and 2 = Female) and whether the moth was knocked down or dead (Affected with 1=Yes and 0=No). Read this file into R calling it moth. 1. Produce a cross tabulation of Affected by Sex. Comment. Any R output produced to answer this question along with the R commands should be placed in Appendix 1 which should be the first appendix at the end of all of your solutions. Include the commands for reading the file moth.csu into R and calling it moth. 2. Produce a boxplot of Dose by Sex. Comment. Any R output produced to answer this question along with the R commands should be placed in Appendix 2 which should be the second appendix at the end of all of your solutions. 3. Produce a scatter plot of Affected versus Dose with different symbols or colours for Sex. Add a spline for males and a spline for females. Comment. Any R output produced to answer this question along with the R commands should be placed in Appendix 3 which should be the third appendix at the end of all of your solutions. 4. Treating Dose as being continuous and Sex as a factor find the logistic regression that fits the data best using AIC. Make sure your first two models are those given in the table below, you may need to consider models with a higher order of Dose or models that have interaction between Sex and Dose. Write down the equation of the optimal model obtained using AIC. If possible, interpret this model. Any R output produced to answer this question along with the R commands should be placed in Appendix 4 which should be the fourth appendix at the end of all of your solutions. Model Number Predictors in the model AIC Dose + Dose"+Dose* 2 Sex + Dose+Dose-+Dose 5. Assess how well the model you have selected using AIC fits the data. Include a classification table with the cutoff being the prior probability of being affected estimated from the data. Comment on sensitivity, specificity and overall percentage correct. Any R output produced to answer this question along with the R commands should be placed in Appendix 5 which should be the fifth appendix at the end of all of your solutions. 6. Evaluate the predictive power of the model you found in 4. Comment. Any R output produced to answer this question along with the R commands should be placed in Appendix 6 which should be the sixth appendix at the end of all of your solutions