STAT4073/6073 Assignment 4: Regression Modeling with Minitab

This assignment solution for STAT4073/6073 focuses on applying various regression techniques using Minitab. The solution begins by analyzing NCAA graduation rates using logistic regression, examining the impact of race and gender, including interaction terms, and testing for significance. Following this, the solution explores the Female Horseshoe Crabs and their Satellites data, utilizing Poisson regression to model the number of satellites based on crab weight and width, including model reduction and interpretation of results. The assignment then proceeds to fit a logistic regression model to predict the probability of a crab having at least one satellite, again considering weight and width as predictors, and constructing confidence intervals. Finally, the solution tackles the diabetes data, employing continuation-ratio and cumulative logit models, interpreting and comparing the results. The solution provides detailed step-by-step instructions with screenshots for each analysis performed in Minitab, ensuring a comprehensive understanding of the statistical modeling process.

Procedure with Screenshots
The procedures include screenshot of the procedures in Minitab
Starting Minitab
1) Click on the shortcut icon for Minitab in your desktop (PC). A new project will be
open as shown in below
2) Save the project in desired file directory using the file > Save project. (give desired
name)

Question 1
For this question import the NCAA.mtw data worksheet as follows
File > Open Worksheet
A new dialogue box will open prompting you to choose the file depending on the direction
you have saved the dataset. Select the dataset and click open.
After the data is uploaded the project will look like the screenshot below

Now we are ready to perform the regression
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.
To fit the model, do the following:
Step 1: stat > Regression > Binary Logistic Regression > Fit Binary Logistic Model.

Step 2: A new window named Binary Logistic Regression will open in the first dialogue box
select Response in Event/Trial as shown below
Step 3: Change the Event name from Event to Graduation, click on the Number of events
empty box and double click Graduates in the left panel. Next, click on the Number of trials
empty box and double click Sample Size in the left panel. Next, click on the Categorical
predictors: empty box and double click both Race and Gender in the left panel. At the end
you should have a window as shown below

Step 4: Below the Categorical predictors click Model button. In the new window that opens
under Predictors using a mouse highlight both Race and Gender and Add under Interaction
through order:
Step 5: Click ok
The results are contained in the attached Minitab Session file
b) Test if the interaction term is significant at α = 0.05.

The p-value for the interaction term is 0.989 < α=0.05. Therefore, at 95% significance
level there is insufficient evidence to show that the interaction term is statistically
significant in determining probability of graduation. Since the interaction is not significant,
we drop the interaction and perform the regression using race and genders as the only
predictors.
Follow steps in (b) above but exclude the interaction.
c) Interpret your fitted model.
In the reduced model, being of the black race does not affect the average probability of
graduation (zero coefficient). While being of the White race improves the average
probability of graduation by 1.0155. The female gender does not affect the average
probability of graduation (zero coefficient). While for male students the average
probability of graduation is reduced by -0.3524.
Problem 2.
Use the same procedure as in question (1) above to load the Crab data in the Minitab
Project.
a) Fit a Poisson model for number of satellites with weight and width as predictors.
To fit the model, do the following:
Step 1: stat > Regression > Poisson Regression > Fit Poisson Model.

Step 2: A new window named Poisson Regression will open. Click on the Response empty
box and double click Satel in the left panel. Next, click on the Continuous predictors: empty
box and double click both weight and width in the left panel. At the end you should have a
window as shown below
Step 3: Click ok to obtain the results.
The results are contained in the attached Minitab Session file

b) Are both predictors significant at α=0.05? Why?
No. The p-values for weight = 0.005 < α=0.05 therefore, weight is a significant predictor
of number of satellites a crab would have at 95% significance level. However, the p-value
for width = 0.326 > α = 0.05, therefore, width is insignificant predictors of number of
satellites a crab would have at 95% significance level.
c) Perform model reduction if possible.
The width is eliminated from the model since it is insignificant predictor.
Follow the procedure in (a) above but without including width. The results are attached in
the session file attached.
d) Estimate E(Y) for female crabs of average weight, 2.44 kg in the reduced model.
Click stat > Regression > Poisson Regression > Prediction. Input 2.44 under weight and
click ok. The results attached
e) Interpret your modelling results.

A unit increase in a Crabs weight increase the average number of satellites it has by 0.5893
units.
Problem 3.
a) Fit the logistic regression model for probability of having at least one satellite with
weight and width as predictors.
To fit the model, do the following:
Step 1: stat > Regression > Binary Logistic Regression > Fit Binary Logistic Model.
Step 2: Click on the Response empty box and double click Y in the left panel. Next, click on
the Continuous predictors: empty box and double click both weight and width in the left
panel. At the end you should have a window as shown below

Step 3: Click ok
The results are contained in the attached Minitab Session file
b) Are both predictors significant at α = 0.10? Why?
No only width is significant because it has p-value = 0.092 < α = 0.10.
c) Construct a 90% confidence interval to describe the effect of width on the odds of a
satellite.
To construct the CI, do the following:
Step 1: stat > Regression > Binary Logistic Regression > Fit Binary Logistic Model.

Step 2: Click on the Response empty box and double click Y in the left panel. Next, click on
the Continuous predictors: empty box and double click both width in the left panel. At the
end you should have a window as shown below
Step 3: Below the Categorical predictors click Options button. Change the confidence level
from 95 to 90.

Step 4: Click ok
The results are contained in the attached Minitab Session file
d) Perform model reduction if possible.
As in (c) above.
e) Find out the fitted probability at a width of 25 cm.
stat > Regression > Binary Logistic Regression > Predict
Input 25 under width and click ok. The results attached