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Refer to the following artificial data:
Denote by M0 the logistic model with only an intercept term and by M1 the model that also has x as a linear predictor. Denote the maximized log likelihood values by L0 for M0, L1 for M1, and Ls for the saturated model. Recall that G2(Mi) = -2(Li - Ls), i = 0, 1. Create a data file in two ways, entering the data as (i) ungrouped data: 12 individual binary observations, (ii) grouped data: three summary binomial observations each with sample size = 4. The saturated model has 12 parameters for data file (i) but three parameters for data file (ii).a. Fit M0 and M1 for each data file. Report L0 and L1 (or -2L0 and -2L1) in each case. Note that they do not depend on the form of data entry.b. Show that the deviances G2(M0) and G2(M1) depend on the form of data entry. Why is this? (Hint: They depend on Ls. Would Ls depend on the form of data entry? Why? Thus, you should group the data to use the deviance to check the fit of a model.)c. Show that the difference between the deviances, G2(M0 | M1), does not depend on the form of data entry (because Ls cancels in the difference). Thus, for testing the effect of a predictor, it does not matter how you enter the data.
A rental agent claims that the mean monthly rent, mu, for apartments on the east side of town is less than $725. A random sample of 13 monthly rents for apartments on the east side has a mean of $724, with a standard deviation of $15.
suppose that xy have joint density function fxy7yx2 on the region defined by 0ltyltx2lt1determine
Use the rules to find an F -statistic for testing whether the term is present, assuming an unrestricted model. Do any of your answers change if you assume a restricted model instead?
You're in charge of an experiment to evaluate a treatment which is advertised as being 90% effective at killing a particular insect. You plan an experiment in which the treatment is tested on 200 insects.
A IRS auditor randomly selects 3 tax returns from 48 returns of which 9 contain errors. What is the probability that she selects none of those containing errors? Round to four decimal places.
Past experience has shown that for every 100,000 items produced in a plant by the morning shift, 200 are defective, and for every 100,000 items produced by the evening shift, 500 are defective.
Suppose an appliance manufacturer is doing a regression analysis,using quarterly time-series data, of the factors affecting its sales of appliances.
approximately what proportion of the area under a normal curve with mean ? and standard deviation ? falls to the right
Perform a categorical data analysis on the majors of students enrolled in the MBA program. Report on your findings, along with a table showing the frequency distribution and at least one chart (pie chart or bar chart) that illustrates the points r..
1. A topological space (S, T ) is called perfectly normal iff for every closed set F there is a continuous real function f on S with F = f -1({0}).
a gambler has a fair coin with one head and one tail and a two-headed coin. he selects one of the coins at random and
Test that the mean SAT score for math in 1999 is greater than that in 1989 at α = 0.05. Assume the variances are equal. Test for the equality of the variances at α = 0.05.
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