Assignment 2 Guide: Exploring Categorical Relationships and Regression Models

Assignment 2 focuses on exploring the relationship between two categorical variables using the Z-test for independence (Topic 3), as well as analyzing how different independent variables influence a dependent variable through multiple regression modeling (Topic 4). Although this assignment is not compulsory, you are strongly encouraged to complete it. It will deepen your understanding of key statistical concepts and enhance your ability to apply these models in real-world contexts. Additionally, it provides valuable practice with statistical software, which is essential for your future career.

Scenario 1: Z test for independence 

A company is considering an organizational change involving the use of self-managed work teams. To assess the attitudes of employees of the company toward this change, a sample of 400 employees is selected and asked whether they favour the institution of self-managed work teams in the organization. Three responses are permitted: favour, neutral, or oppose. The results of the survey, cross-classified by type of job and attitude toward self-managed work teams, are summarized as follows:

1. At the 0.05 level of significance, is there evidence of a relationship between attitude toward self-managed work teams and type of job? 

The survey also asked respondents about their attitudes toward instituting a policy whereby an employee could take one additional vacation day per month without pay. The results, cross-classified by type of job, are as follows:

1. At the 0.05 level of significance, is there evidence of a relationship between attitude toward vacation time without pay and type of job?

NOTE:

• Clearly present all steps involved in the hypothesis testing to answer the question above.
• You may calculate the Z-test statistic manually or use PhSTAT for assistance.
• If you use PhSTAT, be sure to include its output in the appendix of your work.

Scenario 2: Multiple Regression Modelling 

A manager of boiler drums wants to use regression analysis to predict the number of worker-hours needed to erect the drums in future projects. Data for several randomly selected boilers have been collected. In addition to worker-hours (Y), the variables measured include boiler capacity, boiler design pressure, boiler type (Utility vs Industrial), and drum type (Mud vs Steam). 

1. Estimate and state the multiple regression equation to predict the number of worker-hours needed to erect boiler drum.
2. Interpret the estimated regression coefficients in (1).
3. Given the estimated regression equation, predict the number of worker-hours needed to erect an industrial-field, mud-drum boiler with a capacity of 100,000 pounds per hour and a design pressure of 1,000 pounds per square inch.
4. Given the estimated regression equation, predict the number of worker-hours needed to erect a utility-field, stream-drum boiler with a capacity of 550,000 pounds per per hour and a design pressure of 1,400 per square inch.
5. According to the estimated regression equation, what is the difference between the mean number of worker-hours required for erecting industrial and utility field boiler? And what is the difference between the mean number of worker-hours required for erecting boilers with steam drums and those with mud drums?
6. Compute and interpret the adjusted R². Is there any difference from R²? Explain.
7. Is there a significant relationship between worker-hours and the four independent variables at the 5% level of significance?
8. At the 5% level of significance, determine whether each independent variable contributes to the regression model.
9. Construct and interpret a 95% confidence interval estimate of the population slope for (a) the relationship between worker-hours and boiler capacity, and (b) the relationship between worker-hours and boiler design pressure.
10. Add an interaction term (Column G in Excel file, Boiler Capacity × Drum Type) to the model and at the 5% level of significance, determine whether it makes a significant contribution to the model?
11. On the basis of the result of (1) to (10), which model is most appropriate? Explain.
12. Prepare a brief report (maximum 300 words) for the manager outlining how boiler capacity, design pressure, boiler type (Utility vs. Industrial), drum type (Mud vs. Steam) and interaction term affect worker-hours. (Note: Your report in should be succinct, informative, and clearly linked to the scenario. Ensure that all findings are presented within the report, along with recommendations supported by your statistical analysis)

Assessment Criteria

Students should note the following information:

• Your answers to assignment must be set out neatly and concisely, and should be accompanied by any associated workings, in the form of calculations or computer printouts, so that, if necessary, your answers can be verified. If you provide your workings then we can also give you partial credit for answers that are incorrect.
• A value alone will not count as a solution to a question. It is the student’s responsibility to communicate to the marker their understanding of how their numerical result was produced.
• If a formula is being used to answer a question, the formula should be presented, then the values should be entered into the formula and finally the value of the calculation presented.
• If you use Excel/PHStat output to aid you in your assignment work, the presentation of the Excel/PHStat display will not be accepted as the sole answer to the question. Students must display their understanding of the formula and calculations that have been used to produce the output.
• Detailed referencing of formulae in your assignment is not required. A general reference to the text and the unit notes at the end of your assignment will be sufficient in QM162/262.
• Assignments in QM162/262 are not classified as compulsory. So, if you miss an assignment you will not automatically receive an NI grade. However, you will lose the 15% weighting associated with each assignment, that could potentially affect your overall performance.
• The use of Generative Artificial Intelligence (e.g., MS copilot, ChatGPT, Grammarly and other AI grammar checkers, etc.) is notpermitted in this unit under any circumstances. Students suspected of using generative AI will be referred to the academic integrity team for potential breaches of the Student Academic Integrity Policy.

Grading Scheme

Marking of assignment questions will be on the basis of logical structure and method (70%), accuracy of results (20%) and presentation (10%). The following is an indicative expectations and descriptions of marks obtained in assessments.

Assessment Summary and Guidance Report

Assessment Criteria

• Logical structure and method (70%)

• Accuracy of results (20%)

• Presentation and clarity (10%)

Step-by-Step Guidance

 1: Understanding Scenario 1 (Z-Test for Independence)

• The mentor guided the student to formulate null and alternative hypotheses for both survey data sets.

• Step-by-step calculation of expected frequencies, test statistic, and comparison with the critical value at 0.05 significance was explained.

• Interpretation emphasized whether job type and attitudes are dependent or independent.

2: Approach to Scenario 2 (Regression Modelling)

• The mentor first explained the regression model framework: dependent variable (worker-hours) and independent variables (capacity, pressure, type, drum).

• Guidance was given on estimating coefficients using Excel’s Data Analysis Toolpak, checking significance (t-tests, p-values), and interpreting the meaning of coefficients.

• Predictions for specific industrial/utility and mud/steam drum scenarios were demonstrated.

• Mentor ensured the student understood the calculation of adjusted R⊃2;, its difference from R⊃2;, and how it affects model quality.

 3: Advanced Analysis

• Mentor instructed the student to compute confidence intervals for slopes, ensuring clear explanation of formula use and interpretation.

• For the interaction term (Capacity × Drum Type), mentor explained its inclusion in the regression equation, significance testing, and impact on model selection.

4: Preparing the Managerial Report

• Mentor guided the student to write a concise, 300-word report, highlighting how each factor (capacity, design pressure, type, drum, interaction) influences worker-hours.

• Recommendations were linked to practical decision-making, making the report suitable for non-technical stakeholders.

Final Outcome and Learning Objectives Covered

By following this guided process:

• The student successfully demonstrated hypothesis testing skills (Z-test for independence).

• Applied multiple regression modelling techniques to real-world data.

• Learned to interpret coefficients, evaluate model fit, test significance, and construct confidence intervals.

• Developed the ability to translate statistical findings into actionable managerial insights through the written report.

Learning Objectives Achieved:

• Strengthened understanding of categorical data analysis and hypothesis testing.

• Gained practical skills in regression modelling, prediction, and model evaluation.

• Enhanced ability to use statistical software (Excel/PhSTAT) for applied research.

• Improved academic writing, presentation of data, and communication of results to professional audiences.

Access Your Assignment Help with Confidence

Looking for guidance on similar tasks? You can download the available sample solution to understand the right structure, formatting, and approach to tackling your assignment. However, please remember that the sample is meant strictly for reference purposes only. Submitting it as your own work may lead to plagiarism concerns.

If you need a fresh, plagiarism-free, and custom-written assignment solution tailored to your topic and requirements, our team of professional academic writers is here to help. With years of expertise across multiple subjects, we ensure:

• 100% original and well-researched content

• Customized solutions matching your assignment guidelines

• Proper formatting, citations, and academic standards

• Timely delivery to meet urgent deadlines

• Reliable support from subject-matter experts

Plagiarism Disclaimer: The sample provided is for study and reference use only. We strongly recommend ordering a custom solution if you wish to submit it as part of your coursework.

Take the smarter route today — learn from the sample, but secure your grades with a fresh solution crafted exclusively for you.