Answer Happy

3. In an experiment samples of beatles were exposed for five hours to different concentrations of gaseous carbon disulphide at various con- centrations. The total number of beatles who received each dose was recorded and the number of beatles killed at each dose was counted. The following R output was obtained. > d1=read.table(file.choose()) > attach(d1) > d1 Dose Total Killed 1.6907 59 6 1.7242 60 13 1.7552 62 18 1.7842 56 28 1.8113 63 52 1.8369 59 53 1.8610 62 61 1.8839 60 60 > Not-Total-Killed > cl=cbind (Killed, Not) > out1=glm(c1"Dose, family=binomial) > summary (out1) Call: glm(formula = c1 Dose, family = binomial) Deviance Residuals: Min 1Q Median -1.5941 -0.3944 0.8329 3Q 1.2592 Max 1.5940 Coefficients: Estimate Std. Error z value Pr(>121) (Intercept) -60.717 5.181 A с Dose 34.270 2.912 B D Signif. codes: O *** 0.001 ** 0.01 * 0.05 0.1 1 (Dispersion parameter for binomial family taken to be 1) Null deviance: 284.202 on 7 degrees of freedom

11.232 on 6 degrees of freedom Residual deviance: AIC: 41.43 Number of Fisher Scoring iterations: 4 > anova (out1) Analysis of Deviance Table Model: binomial, link: E Response: c1 Terms added sequentially (first to last) Df Deviance Resid. Df Resid. Dev NULL 7 284.202 Dose 1 F 6 11.232 > vcov (out1) (Intercept) Dose (Intercept) 26.83966 -15.082090 Dose -15.08209 8.480525 (a) Determine the missing information indicated by the letters A,B,C,D, E and F. Note that for E you are required to specify the link function. [6 Marks) (b) Explain what is meant by the Null Deviance. (2 Marks) (c) Explain what is meant by the Residual Deviance. [2 Marks] (d) What conclusions do you draw from the above R output? What would be your next steps in the R analysis? [4 Marks) (e) Calculate the fitted value for the third observation in the dataset (see the third row in the data file which is printed out near the top of the block of R code). [3 Marks]

= (f) Calculate an estimate of the variance of the fitted linear predictor n3 = @ x; for the third observation in the dataset. [ 4 Marks] (g) Using the delta method, find an approximate 95% confidence in- terval for the probability that a beatle is killed by exposure for five hours to a dose of 1.7552 units of gaseous carbon disulphide. [4 Marks]