QNT 375 Week 4 Analyzing Patterns and Trends Example

Who Cancels and Why: Patterns, Trends and Predictions in a Car Wash Chain's Membership Data

[Student Name]

University of Phoenix

QNT/375: Business Data Analytics

Week 4 Assignment

[Instructor Name]

[Date]

Summit Shine Car Wash, its locations, members, data and results are composites written for a model paper.

Weeks 1 through 3 framed the cancellation problem for Summit Shine, designed data collection and checked data quality. This paper analyzes the cleaned data: 12 months of records for about 80,000 members, current and canceled, with adjusted wash counts, corrected wait times, competitor distances and 640 survey responses.

Trends Over Time

Monthly cancellations averaged 6.1 percent in the first quarter of the study period, 6.9 percent in the second, 7.8 percent in the third and 8.4 percent in the fourth. New sign-ups were flat at about 4,800 a month. A seasonal pattern appears in past years too: cancellations rise in late spring when road salt disappears. But this year's rise exceeds the usual seasonal increase by about 1.5 points and began in winter, when cancellations normally fall.

Patterns by Group

Cross-tabulations compare cancellation rates across groups over the study year:

By tenure: members in their first six months canceled at 11.2 percent a month; members of more than two years at 4.3 percent.

By plan: the $25 basic plan at 9.6 percent; the $45 premium plan at 5.8 percent.

By recent washing: members whose washes fell by half or more over the prior two months at 17.5 percent; others at 6.2 percent.

By competitor proximity: members whose home site is within two miles of a competitor site at 9.7 percent after the openings; others at 7.1 percent.

By wait time: home sites with average weekend waits above 15 minutes at 8.9 percent; others at 7.4 percent.

Testing the Competitor's Effect

Comparing groups after the openings does not show cause, since nearby and distant locations differed before. A difference-in-differences comparison helps. Before the openings, cancellation rates at the seven nearby locations averaged 6.4 percent, against 6.0 percent at the fifteen distant ones. After the openings, nearby locations averaged 9.5 percent and distant ones 7.5 percent. Nearby locations rose 3.1 points and distant ones 1.5 points, so the competitor is associated with about 1.6 additional points at nearby sites, after accounting for the chain-wide rise. Angrist and Pischke (2009) explain that this comparison supports a causal reading only if, absent the openings, the two sets of locations would have moved in step; monthly rates in the year before the openings moved closely together, which supports the assumption.

The competitor explains part of the rise near its new sites, but cancellations also rose where it never opened.

Testing the Hypotheses Together

Logistic regression estimates how several factors relate to the probability of canceling in a given month while holding the others constant (Hosmer et al., 2013). A model with tenure, plan, change in washing, competitor proximity, wait time, price increase exposure and month showed:

H1 supported: members whose washing fell by half or more had roughly triple the odds of leaving, the strongest effect in the model.

H2 supported: proximity to a competitor raised the odds by about 40 percent.

H3 weakly supported: long waits raised the odds by about 15 percent, with wide uncertainty.

H4 supported: members on the basic plan exposed to the price increase had about 25 percent higher odds of canceling than basic members not yet exposed.

Checking for Seasonal Effects

Because cancellations normally rise in late spring, the regression includes a variable for each month, so the effects of usage, competitors and price are estimated after removing the usual seasonal pattern. Without this control, which costs nothing to add and is standard practice, the price increase, which took effect in spring, would appear larger than it is, since part of the spring rise happens every year.

Survey Reasons

Survey responses from canceled members help interpret these results. The most common main reasons were "I wasn't using it enough" at 31 percent, price at 24 percent, a closer or cheaper car wash at 19 percent, waits at 11 percent and moving at 9 percent.

Predicting Who Will Cancel

Neslin et al. (2006) studied churn prediction models submitted to a tournament and found that modeling choices made meaningful differences in predictive accuracy and that more accurate models could produce substantially greater profit from retention campaigns. Summit Shine's model was built on the first eight months and tested on the last four. Ranking current members by predicted risk, the top 20 percent of scores contained 46 percent of members who canceled the following month, more than double what random selection would capture.

Interpreting the Odds

Odds ratios can mislead readers unfamiliar with them, so the report translates them into probabilities. For a typical basic plan member, the model predicts about an 8 percent chance of canceling next month. If that member's washing has dropped by half, the predicted chance rises to about 21 percent. If the member also lives near a competitor site, it rises to about 27 percent. Expressing results this way lets managers see the size of each effect for a real member rather than as an abstract ratio.

Checking the Model's Fit

The model's predicted cancellation rates matched actual rates closely across groups of members sorted by risk, except in the very highest-risk group, where it slightly overpredicted. That pattern suggests the model ranks members well but that its exact probabilities should be treated as estimates. Since the decision depends on ranking, which members to contact first, this limitation matters little.

What the Evidence Supports

Falling usage is the strongest warning sign, but it may reflect many causes, from changing commutes to dissatisfaction.

The competitor likely caused a measurable share of the rise at nearby sites.

The price increase raised cancellation among basic plan members.

Waits matter less than managers believed.

Conclusion

The analysis turns a single rising number into a set of patterns: usage declines, competitor proximity and the price increase on the basic plan all relate to cancellation, and a difference-in-differences comparison supports a causal role for the competitor. A predictive model can rank members by risk with useful accuracy. Week 5 will turn these findings into recommendations and present them to decision makers.

References

Angrist, J. D., & Pischke, J.-S. (2009). Mostly harmless econometrics: An empiricist's companion. Princeton University Press.

Hosmer, D. W., Lemeshow, S., & Sturdivant, R. X. (2013). Applied logistic regression (3rd ed.). Wiley.

Neslin, S. A., Gupta, S., Kamakura, W., Lu, J., & Mason, C. H. (2006). Defection detection: Measuring and understanding the predictive accuracy of customer churn models. Journal of Marketing Research, 43(2), 204-211. https://doi.org/10.1509/jmkr.43.2.204