Question 1 (20 pts) Consider the dataset wavesolder. This dataset presents the number of defects in electronic circuit boards arising from an experiment design with three replicates and seven predictors. We can assume the replicates are independent. suppressMessages (library (faraway) ) data (wavesolder) str (wavesolder) ## 'data. frame' : 16 obs. of 10 variables: ## $ y1 : int 13 4 20 42 14 10 36 5 29 10 . . ## $ y2 : int 30 16 15 43 15 17 29 9 0 26 ## $ y3 : int 26 11 20 46 17 16 53 16 14 9 . . . ## $ prebake : Factor w/ 2 levels "1", "2": 1 1 1 1 1 1 1 1 2 2 ## $ flux Factor w/ 2 levels "1", "2": 1 1 1 1 2 2 2 2 1 1 ## $ speed : Factor w/ 2 levels "1", "2": 1 1 2 2 1 1 2 2 1 1 # # $ preheat : Factor w/ 2 levels "1", "2": 1 2 1 2 1 2 1 2 1 2 . ## $ cooling : Factor w/ 2 levels "1", "2": 1 2 1 2 2 1 2 1 2 1 ## $ agitator: Factor w/ 2 levels "1", "2": 1 2 2 112 212 ## $ temp : Factor w/ 2 levels "1", "2": 1 2 2 1 2 1 1 2 1 2 a) (5 pts) Compute the mean and variance of the number of defects within each group of three replicates. Plot the variance against the mean, both in log scale. Comment on the relationship you see and the viability of fitting a Poisson model to the response. b) (5 pts) Fit a Poisson model for the number of defects considering all seven predictors. Does this model fit the data? Explain. c) (10 pts) Fit a quasi-Poisson model with the same model formula as in b). Use an F-test to assess the significance of individual predictors. What predictors are significant? Which level of the significant predictors will lead to higher rates of defects