| Course | MST-7000 Managerial Statistics |
|---|---|
| Module | Module 7 |
| Paper type | Final project: observational statistical study with linear and multiple regression |
| Length | About 1,001 words, 6 pages |
| Format | APA 7 student paper |
| School | Thomas Edison State University |
| Program | MBA in Data Analytics |
| Updated | October 2026 |
Free sample paper for MST 7000 Module 7
Days, Damage and Assembly: An Observational Study of Delivery Satisfaction at an Online Furniture Retailer
Student Name
MBA in Data Analytics, Thomas Edison State University
MST-7000: Managerial Statistics
Mentor Name
Month Day, Year
Days, Damage and Assembly: An Observational Study of Delivery Satisfaction at an Online Furniture Retailer
Proposal Summary
The approved proposal stated the question, what aspects of delivery explain customers' satisfaction ratings, and the plan: draw a random sample of 150 orders delivered in the second quarter, link each to the customer's post-delivery survey rating on a 1 to 10 scale and to order records, and use regression to estimate how each factor relates to satisfaction. The study is non-trivial because the company spends heavily on faster delivery without knowing how much speed matters compared with other factors.
Data and Variables
Survey ratings were available for every sampled order because the sample was drawn from orders with completed surveys, a choice whose consequences are discussed under limitations.
| Variable | Type | Summary |
|---|---|---|
| Satisfaction rating (outcome) | 1 to 10 scale | Mean 6.99, SD 1.62 |
| Delivery days | Days from order to delivery | Mean 6.19 |
| Damaged | 1 if item arrived damaged, 0 if not | 12 orders damaged |
| Order value | Hundreds of dollars | Mean $784 |
| Assembly service | 1 if customer bought assembly, 0 if not | 63 orders |
Simple Regression
Anderson et al. (2011) present simple linear regression as estimating a line that relates one predictor to an outcome by least squares, with the coefficient of determination showing the share of variation explained. I ran Excel's Regression tool with satisfaction as the outcome and delivery days as the predictor.
Each additional day of delivery is associated with half a point lower satisfaction, and delivery time alone explains about 20 percent of the variation in ratings. Anscombe (1973) showed that very different data sets can share the same regression results, so I examined the scatter plot before trusting these numbers; it showed a steady downward pattern with no curve and no single order driving the line.
| Result | Value |
|---|---|
| Correlation, delivery days and satisfaction | negative 0.44 |
| Intercept | 10.10 |
| Slope for delivery days | negative 0.50 (SE 0.083), t = negative 6.01, p below 0.001 |
| R squared | 0.196 |
Multiple Regression
Delivery days may carry the effect of other factors, since slow deliveries are more often damaged ones. I added damage, order value and assembly service.
The F test shows that the model as a whole explains satisfaction better than chance. Together the four predictors explain about 41 percent of the variation in ratings, twice as much as delivery days alone.
| Predictor | Coefficient | Standard error | t | p |
|---|---|---|---|---|
| Intercept | 8.92 | 0.531 | 16.78 | below 0.001 |
| Delivery days | negative 0.40 | 0.074 | negative 5.41 | below 0.001 |
| Damaged | negative 2.42 | 0.386 | negative 6.27 | below 0.001 |
| Order value, per $100 | 0.07 | 0.026 | 2.63 | 0.010 |
| Assembly service | 0.51 | 0.212 | 2.40 | 0.018 |
| R squared 0.406; adjusted R squared 0.389; F = 24.75, p below 0.001; standard error of estimate 1.26 | | | | |
Interpreting the Coefficients
Each coefficient describes the association with satisfaction holding the other predictors constant. An extra day of delivery is associated with 0.40 points lower satisfaction, slightly less than the simple regression suggested, because part of the simple slope reflected damage. A damaged item is associated with 2.42 points lower satisfaction, equal to about six days of delay. Customers who bought assembly rated delivery about half a point higher, and larger orders were rated slightly higher, 0.07 points per $100.
Comparing Models
I also fit a model without order value. Its adjusted R squared fell from 0.389 to 0.365, so order value adds explanatory power even after allowing for the extra predictor, and I kept it. Adjusted R squared, unlike R squared, penalizes predictors that add little, which makes it the fairer comparison between models of different sizes. Rosenbaum (2002) notes that an observational study's conclusions are stronger when its design anticipates the main alternative explanations; comparing the simple and multiple models is one step in that direction, since it shows how the delivery-days slope changes once damage is accounted for.
Checking the Assumptions
Regression inference assumes a linear relationship, independent errors with constant variance and roughly normal residuals. The residual plot against predicted values showed no funnel shape, and a normal probability plot of residuals was close to a straight line, with slight bunching at the top because ratings cannot exceed 10. Correlations among predictors were all below 0.3, so multicollinearity is not a concern. Because ratings are bounded at 1 and 10, predictions near the ends of the scale should be treated with care.
What an Observational Study Cannot Show
This is an observational study: delivery days, damage and assembly were not assigned by the researcher. Freedman (1991) argued that regression on observational data cannot by itself establish cause, because unmeasured factors may drive both predictors and outcomes. Customers who choose assembly may differ from those who do not, for instance in age or in how much they value service, and that difference, not assembly itself, may raise their ratings. The sample also includes only customers who completed surveys, and very dissatisfied customers may respond at different rates. The coefficients describe associations in this sample; they suggest where to act, and a randomized test, such as offering free assembly to a random half of orders, would show whether assembly causes higher satisfaction.
Findings for Management
Damage is the factor most strongly associated with low satisfaction, and one damaged delivery is associated with as large a drop as six extra days. The company's planned spending on faster delivery should therefore be weighed against spending on packaging and on carrier B for fragile items, as the Module 5 memo recommended. Delivery speed still matters: cutting average delivery from 6.2 to 5.2 days would be associated with a 0.4 point rise in average satisfaction. The assembly result justifies a randomized test of a free-assembly offer, which could be run for one quarter at modest cost.
Conclusion
The study used simple and multiple regression on 150 orders to show that delivery time, damage, order value and assembly service together explain about 41 percent of variation in delivery satisfaction, with damage the strongest factor. The observational design limits causal claims, and the findings point to two tests the company can run next.
References
Anderson, D. R., Sweeney, D. J., & Williams, T. A. (2011). Essentials of modern business statistics with Microsoft Excel (5th ed.). South-Western Cengage Learning.
Anscombe, F. J. (1973). Graphs in statistical analysis. The American Statistician, 27(1), 17-21. https://doi.org/10.1080/00031305.1973.10478966
Freedman, D. A. (1991). Statistical models and shoe leather. Sociological Methodology, 21, 291-313. https://doi.org/10.2307/270939
Rosenbaum, P. R. (2002). Observational studies (2nd ed.). Springer.
Reading the MST 7000 Module 7 assignment instructions
The MST-7000 final project, worth 35 percent of the grade, is an original observational statistical study that is non-trivial in nature. A proposal of 200 to 300 words is due by week 5 and must be approved by your mentor, and the full requirements are in the course's Final Project area. Expect to pose a business question, gather or obtain real data, choose methods from the course, run the analysis in Excel, interpret the results and discuss the study's limits. Many students use regression, from Module 7, but the method should fit the question you proposed. Write the study as a report: question, data, method, results, interpretation, limitations and findings for management. Include the Excel output as an appendix and the key figures in tables within the text.
How this MST 7000 Module 7 example is built
The study summarizes the approved proposal and describes the data and variables in a table. A simple regression section reports the slope, correlation and R squared, and checks the scatter plot with research support. A multiple regression section adds three predictors in a full coefficient table and interprets each coefficient holding the others constant. Sections check assumptions and explain what an observational design cannot show, drawing on research on regression and causation. Findings for management and a conclusion follow. A model comparison section uses adjusted R squared to decide whether order value belongs in the model, and research on observational design explains why comparing models helps. The findings translate the coefficients into decisions about delivery speed, packaging and a test of free assembly.
Where the marks sit in the MST 7000 Module 7 rubric
The final study is graded on a clear and non-trivial question, appropriate data and methods, correct analysis, accurate interpretation and honest discussion of limitations. Studies that interpret multiple regression coefficients as holding other variables constant, and explain how they differ from the simple slope, show command of the method. Checking assumptions with residual plots demonstrates rigor. Explaining why observational data cannot establish cause, and proposing a test that could, shows the judgment this course sets out to develop. Comparing models with adjusted R squared, rather than R squared alone, shows understanding of model fit. Findings written in managers' units, such as satisfaction points per day, demonstrate the purpose of the study.
Common MST 7000 Module 7 mistakes, and how to avoid them
Students lose points by choosing trivial questions, by running regressions without checking assumptions, by interpreting coefficients as causal effects or by reporting R squared without explaining it. Others submit the ToolPak output with little interpretation. Propose a question that matters to a business. Plot the data first. Interpret each coefficient in words and units. Discuss what the design cannot show. Compare at least two models and explain which you kept. Turn the coefficients into recommendations in units a manager understands. Keep the proposal and the final study aligned, and explain any change of plan in a sentence. A free first sample on your own MST-7000 final project is available on request.
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MST 7000 Module 7 questions, answered
Where can I find a free MST 7000 Module 7 sample paper?
An observational regression study of delivery satisfaction at a furniture retailer is the final project above.
What does R squared measure?
How much of the outcome's variation the regression's predictors account for, as a share.
How is a multiple regression coefficient interpreted?
As the shift in the outcome that goes with a one-unit rise in that predictor while the other predictors stay fixed.
Why can't an observational study prove cause?
Because predictors were not assigned, unmeasured factors may drive both the predictors and the outcome.
What must the MST-7000 final project proposal include?
A 200 to 300 word description of the planned observational study, submitted by week 5 for mentor approval.