Answer this questions in detail and it is Catagorical data analysis

1) An experiment analyzes imperfection rates for two processes used to fabricate silicon wafers for computer chips. For treatment A applied to 10 wafers, the number of imperfections is 8, 7, 6, 6, 3, 4, 7, 2, 3, 4. Treatment B applied to 10 other wafers has 9, 9, 8, 14, 8, 13, 11, 5, 7, 6 imperfections. Treat the counts as independent Poisson variates having means JA and uB. i) Fit a model of the form log(u) = a + Bx, where x = 0 for treatment A and x = 1 for treatment B. ii) Show that B = log(uB/uA) and interpret your estimate of B obtained in part (i) above. iii) Test HO: MA = uB against two sided alternative HI: HA # uB using Wald test. iv) Construct a Wald type 95% confidence interval for uB/JA. 2) The table shows the results of test-firing 25 ground to air missiles at targets of various speeds (x knots). y is binary variable taking values 0 (for miss) and 1 (for hit). Source: Montgomery & Peck 410 0 210 1 490 0 410 1 500 0 270 0 200 1 470 0 480 0 300 1 240 1 490 0 420 0 330 1 280 1 210 1 300 1 450 1 230 0 430 0 460 0 220 1 250 1 200 1 400 0 (Note: 410, 210, 490 are values of x and corresponding y's for them are 0, 1, 0) i) Fit the probit regression model d-1 (n(x)) = a + Bx for this data. ii) Estimate the probability that a missile fired at speed x = 350 knots will hit the target. 3) For known k 2 2 show that the negative binomial distribution with probability mass function, f ( y , k , 1 ) = 3+ 6 -1 (1741 24) y = 0, 1, 2, . . . belongs to the exponential family of distributions. Find the natural parameter for this distribution. 4) The table below shows the data (source: Agresti, Collectt ) from a study about y = whether a patient having surgery experienced a sore throat on waking (1 = yes, 0 = no) as a function of d = duration of the surgery (in minutes) and t = type of device used to secure the airway (1 = tracheal tube, 0 = laryngeal mask airway). Patient HOOD 83 25 65 35 OOHOOH-OOOOHHHOOHHHOODOO OOHOOHOHOOHOHHHHOHOHOHH HHHH 15 30 30 32 15 33 135 34 20 i) Fit a logistic regression model logit(n) = a + Pd and interpret the estimate of B. ii) What is the estimated probability of experiencing a sore throat on waking if the duration of the surgery is half an hour. iii) Use the likelihood ratio test to test the goodness of fit of the model. iv) Fit a logistic regression model logit() = a + Bt and interpret the estimate of B