Question 1 [3+4+8+2+3=20] The data in the file beetles.cau shows the number of insects killed after exposure to various (standardized) doses of an insecticide. 1.1 Fit a logistic regression model logit ( P(killed | dose)) = Po + 81 x dose + 82 x (dose)'. Write the values of the three coefficient estimates here: Bo = : B1 = : B2= 1.2 Estimate the probability $ that a beetle exposed to a dose of 0.5 units of the insecticide will not survive. 1.3 Find an approximate 90% confidence interval for o in Question 1.2. 1.4 Use the Wald statistic to test at the 1% level of significance whether the estimated coefficient of (dose)? is statistically significant. 1.5 Assess the quality of the fit. Show one of your diagnostic plots (a rough freehand version will be acceptable) and indicate the relevant features on it that point to a satisfactory or unsatisfactory fit. dose exposed killed -1.523 59 6 -1.026 60 13 -0.567 62 18 -0.137 56 28 0.265 63 52 0.644 59 53 1.002 62 61 1.341 60 60