Reference no: EM132266897
Assignment -
You are required to conduct all your computer analyses with Minitab.
Problem 1 - The U.S. National Collegiate Athletic Association (NCAA) conducted a study of graduation rates for student athletes who were freshmen during the 1984»1985 academic year. The following table shows the data.
|
Group
|
Sample Size
|
Graduates
|
|
White females
|
796
|
498
|
|
White males
|
1625
|
878
|
|
Black females
|
143
|
54
|
|
Black males
|
660
|
197
|
a) Fit a logistic regression model for the probability of graduation with race and gender of the student athlete as predictors as well as the interaction between race and gender.
b) Test if the interaction term is significant at α = 0.05.
c) Interpret your fitted model.
Problems 2-3 are based on the Female Horseshoe Crabs and their Satellites data.
The crab data came from a study of nesting horseshoe crabs (J. Brockmann, Ethology, 102: 1-21, 1996). Each female horseshoe crab in the study had a male crab attached to her in her nest. The study investigated factors that affect whether the female crab had any other males, called satellites, residing nearby her. The response outcome for each female crab is her number of satellites.
Note: color = Color (1 = light medium, 2 = medium, 3 = dark medium, 4 = dark), spine = spine condition (1 = both good, 2 = one worn or broken, 3 = both worn or broken), width = carapace width (cm), weight = weight (kg), satell = number of satellites.
Source: Data provided by Dr. Jane Brockmann, Zoology Department, University of Florida; study described in Ethology, 102: 1-21, 1996.
Problem 2 -
a) Fit a Poisson model for number of satellites with weight and width as predictors.
b) Are both predictors significant at α = 0.05? Why?
c) Perform model reduction if possible.
d) Estimate E(Y) for female crabs of average weight, 2.44 kg in the reduced model.
e) Interpret your modelling results.
Problem 3 -
Let Y = 1 if a crab has at least one satellite, and Y = 0 otherwise.
a) Fit the logistic regression model for probability of having at least one satellite with weight and width as predictors.
b) Are both predictors significant at α = 0.10? Why?
c) Construct a 90% confidence interval to describe the effect of width on the odds of a satellite.
d) Perform model reduction if possible.
e) Find out the fitted probability at a width of 25 cm.
f) Find the width at which the predicted probability equals 0.5.
g) Interpret your modelling results and compare the results with that of Problem 2.
Problem 4 -
To determine the treatment and management of diabetes it is necessary to determine whether the patient has chemical diabetes or overt diabetes. The data presented in diabetes_assg04.mtb is from a study conducted to determine the nature of chemical diabetes. The measurements were taken on 145 nonobese volunteers who were subjected to the same regimen. Many variables were measured, but we consider only three of them. These are, insulin response (IR), the steady-state plasma glucose (SSPG), which measures insulin resistance, and relative weight (RW). The diabetic status of each subject was recorded. The clinical classification (CC) categories were ordinal with overt diabetes (1), chemical diabetes (2), and normal (3).
a) Fit continuation-ratio model for diabetes data.
b) Fit cumulative logit (proportional odds) model for diabetes data.
c) Interpret and compare your modelling results in a) and b).
Attachment:- Assignment Files.rar