| Course | GB701 Business Statistics |
|---|---|
| Unit | Unit 9 |
| Paper type | Assumption diagnostics memo |
| Length | About 830 words, 6 pages double-spaced |
| Format | APA 7 student paper |
| School | Purdue University Global |
| Program | MBA |
| Updated | October 2026 |
Free sample paper for GB701 Unit 9
What Was Checked, What Failed, What Was Done: A Unit 9 Assumption Diagnostics Memo for the Quote Conversion Model
[Student Name]
Purdue University Global
GB701: Business Statistics
Unit 9 Assumption Diagnostics Memo
[Instructor Name]
[Date]
The distributor, its accounts and every figure are composite and illustrative; the methods and sources cited are real.
Memo
TO: Doctoral mentor FROM: DBA candidate SUBJECT: Diagnostics for the quote conversion regression and the model carried forward
Summary Table
Collinearity. Check: variance inflation factors. Result: 1.01 to 1.41. Response: none needed.
Linearity. Check: residual plots against each predictor; a squared tenure term. Result: no curvature; squared term p = .141. Response: none needed.
Constant variance. Check: residuals against fitted values; residual spread by thirds of fitted values; Koenker's form of the Breusch-Pagan test. Result: spread widens from 3.43 to 3.98 to 4.52 days; test statistic 7.89 on 5 degrees of freedom, p = .162. Response: heteroscedasticity-consistent standard errors as the primary inference.
Normality of residuals. Check: normal Q-Q plot; Shapiro-Wilk test. Result: W = .945, p below .001; residual skewness 0.90. Response: rely on the sample size for coefficient inference; log-outcome model as a sensitivity check.
Influential cases. Check: Cook's distance. Result: 15 accounts above 4/n; largest 0.055. Response: refit without them as a sensitivity check.
Collinearity, Cleared Quickly
Variance inflation factors range from 1.01 for annual purchases to 1.41 for special-order status. None approaches the levels at which collinearity inflates standard errors materially. Credit limit, which would have been highly collinear with purchases, was excluded before fitting.
Linearity
Plots of residuals against tenure, purchases and the revision count show no curvature. Adding squared tenure, the predictor most likely to have a nonlinear relationship, does not improve the model, p = .141.
The Fan in the Residual Plot
The residuals-against-fitted plot widens to the right: accounts predicted to convert slowly vary more around their predictions than accounts predicted to convert quickly. Splitting the fitted values into thirds, the residual standard deviation rises from 3.43 to 3.98 to 4.52 days. The studentized version of the Breusch-Pagan test that Koenker (1981) proposed, which does not assume normal errors, is not significant, p = .162. The test has limited power in a sample this size, and the plot shows a consistent pattern, so the memo treats the fan as real but modest.
Because nonconstant variance affects standard errors rather than coefficients, the response is to use heteroscedasticity-consistent standard errors. Long and Ervin (2000) recommend the HC3 version for samples under about 250, and it is adopted here as the primary inference. With HC3 standard errors, the portal coefficient's interval is -2.80 to -0.46 days, p = .007, nearly the same as the ordinary interval.
The fan changed how uncertainty is reported, not what the model says.
Normality, Handled Honestly
The residuals are right-skewed, skewness 0.90, and the Shapiro-Wilk test rejects normality, W = .945, p below .001. The Q-Q plot shows the departure is in the upper tail: a few accounts converted much more slowly than predicted. With 216 accounts and five predictors, the sampling distribution of the coefficients is close to normal even when the residuals are not, so inference on the coefficients remains reasonable. As a sensitivity check, the model was refit with the logarithm of conversion time as the outcome. The portal coefficient becomes -0.195 on the log scale, about 17.7 percent faster conversion, consistent in direction and size with the 1.63-day estimate at the sample's mean of about 8.4 days.
Fifteen Influential Accounts
Fifteen accounts have Cook's distance above the common screening threshold of 4 divided by n, about 0.019. The largest is 0.055, far below the value of 1 that Cook (1977) suggested as a sign of a single case dominating the fit. The fifteen were reviewed by hand; all are genuine accounts with correctly coded data, most of them special-order customers with unusually long conversion times. Refitting without them changes the portal coefficient from -1.63 to -1.66 days. No single account, or small group of accounts, drives the result.
What the Diagnostics Did Not Check
Two conditions cannot be checked from the residuals. The model assumes accounts are independent, which may not hold for accounts that share a parent company or a purchasing agent; the sample includes a handful of such pairs, and they will be flagged in the limitations. And no diagnostic can show whether an unmeasured variable, such as the customer's own approval process, confounds the portal association. No residual plot can reveal that problem; only the study design could have addressed it.
Two Remedies, One Primary Model
The model carried forward to the results section is the Unit 8 ordinary least squares model with HC3 standard errors. Two sensitivity analyses accompany it: the log-outcome model and the model without influential cases. Both agree with the primary model on the direction and approximate size of the portal association. Reporting one primary model, chosen before the sensitivity analyses were run, avoids the temptation to present whichever version looks best.
References
Cook, R. D. (1977). Detection of influential observation in linear regression. Technometrics, 19(1), 15-18. https://doi.org/10.1080/00401706.1977.10489493
Koenker, R. (1981). A note on studentizing a test for heteroscedasticity. Journal of Econometrics, 17(1), 107-112. https://doi.org/10.1016/0304-4076(81)90062-2
Long, J. S., & Ervin, L. H. (2000). Using heteroscedasticity consistent standard errors in the linear regression model. The American Statistician, 54(3), 217-224. https://doi.org/10.1080/00031305.2000.10474549
GB701 Unit 9 instructions, in plain terms
The ninth GB701 assignment asks you to check your regression's assumptions and report the results in a memo. Summarize every check in a table: the assumption, the method, the result and your response. Then discuss each in turn, collinearity, linearity, constant variance, normality and influential cases, using both plots and tests where appropriate. Where an assumption fails, choose a response matched to the problem and explain how it changes inference. Review influential cases by hand. State any conditions the diagnostics cannot check. Close by naming one primary model and the sensitivity analyses that accompany it, chosen before seeing their results. About five pages with four figures and APA 7 citations is common.
Inside the GB701 Unit 9 example
The memo opens with a five-row summary table. Collinearity clears with variance inflation factors from 1.01 to 1.41. Linearity passes, with squared tenure at p of .141. The residual fan is described from the plot and by thirds, Koenker's test is reported as not significant, and HC3 errors are adopted following Long and Ervin; the highlighted sentence says the fan changed the reporting, not the model. Normality fails, and a log model gives about 17.7 percent faster conversion. Fifteen influential accounts, reviewed by hand against Cook's guidance, barely move the estimate. A section names what residuals cannot reveal, and the primary model with two sensitivity analyses closes the memo.
GB701 Unit 9 rubric: what earns full points
Points in the GB701 diagnostics memo follow from reporting failures as clearly as passes. A summary table of every check earns credit for transparency. Using plots alongside tests, and recognizing when a test has limited power, shows judgment. Responses matched to each problem, such as robust standard errors for nonconstant variance, carry heavy weight because they fix what is wrong without overcorrecting. Reviewing influential cases by hand rather than deleting them shows care. Naming conditions the diagnostics cannot test demonstrates honesty. One primary model chosen in advance, with sensitivity analyses, completes the memo, along with clear figures and APA 7 citations. Because GB701 Unit 10 will report only the primary model in full, the memo is also judged on whether its choice of primary model is stated plainly enough to be carried forward without ambiguity.
Common GB701 Unit 9 mistakes, and how to avoid them
GB701 diagnostics memos often report only the checks that passed. Others run every test and remedy at once and present whichever model looks best. A common error is deleting influential cases from the primary analysis without checking whether they are errors. Writers frequently treat a non-significant test as proof an assumption holds, ignoring a clear pattern in the plot. Normality failures are often answered with transformations that change the question being asked. Report every check in a table, look at plots as well as tests, match each remedy to its problem, review influential cases by hand, say what cannot be checked and commit to one primary model. Send your model for a free custom diagnostics memo.
Get a GB701 Unit 9 example written to your instructions
Send the model output or data, the checks the assignment requires and the Unit 9 rubric. Once the custom diagnostics memo is done, inside 24-48h, every check has been run, each failure reported in plain terms and every remedy tied to the inference it protects. Your first sample is free. The paper above is an original model document written by our desk, not a submitted student paper and not an official Purdue University Global document.
More GB701 papers and MBA samples
- GB701 Unit 1: Discussion Board Post
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- GB701 Unit 5: Confidence Interval Exercise
- GB701 Unit 6: Seminar Reflection
- GB701 Unit 7: Hypothesis Test Writeup
- GB701 Unit 8: Regression Model Report
- GB701 Unit 10: Results Section Draft
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GB701 Unit 9 questions, answered
Which normality test should a GB701 diagnostics memo use?
Shapiro-Wilk is widely used and appears in most statistical software, but at larger sample sizes it flags departures too small to matter. Pair it with a Q-Q plot and a statement of what the regression's inferences actually depend on. For coefficient tests with a few hundred cases, the plot and the reasoning usually carry more weight than the p-value.
Are robust standard errors enough to fix heteroscedasticity?
For inference about coefficients, heteroscedasticity-consistent errors such as HC3 generally suffice, and R, Stata and SPSS extensions all provide them. They do not repair prediction intervals, and they do not address a misspecified model. If the fan pattern suggests a scale problem, adding a transformed outcome as a sensitivity check is worth the extra page.
Should influential cases be removed?
Rarely from the primary analysis, unless they are errors. Report them, check whether each reflects a data problem, and refit without them as a sensitivity analysis. If conclusions hold either way, say so; if they change, the influential accounts become a finding worth discussing, since they may represent a distinct kind of customer.
Where can I find a free GB701 Unit 9 sample paper?
This page holds a full GB701 Unit 9 assumption diagnostics memo with a summary table, residual and influence checks, HC3 standard errors, a log-model sensitivity check and one primary model.
Why use robust standard errors when the heteroscedasticity test is not significant?
The test has limited power at this sample size, the plot shows a consistent fan, and robust errors cost little when variance is constant, so they are a safe default.