4.24 Refer to the following articial data: x number of trials number of successes 0 4 l 1 4 2 2 4 4 Denote by M0 the logistic null model and by M1 the model that also has a: as a predictor. Denote the maximized log-likelihood values by Lu for M0, L1 for M1, and L3 for the saturated model. Create a data le in two ways, entering the data as (i) ungrouped data: 12 individual binary observations, (ii) grouped data: 3 summary binomial observations each with sample size = 4. a. Fit Mo and M1 for each data file. Report Lo and L1 (or -2Lo and -2L1) in each case. Do they depend on the form of data entry? b. Show that the deviances for Mo and M1 depend on the form of data entry. Why is this? (Hint: The saturated model has 12 parameters for data file (i) but 3 parameters for data file (ii).) c. Show that the difference between the deviances does not depend on the form of data file. Thus, for testing the effect of x, it does not matter how you enter the data