GB701 Unit 8 Regression Model Report Example

From No Difference to 1.6 Days: A Unit 8 Regression Model Report on Portal Use and Quote Conversion

[Student Name]

Purdue University Global

GB701: Business Statistics

Unit 8 Regression Model Report

[Instructor Name]

[Date]

The distributor, its accounts and every figure are composite and illustrative; the methods and sources cited are real.

Choosing Predictors Before Fitting

The model was specified in the Unit 4 memo before any account was coded. The outcome is quote-to-order time in days. Five predictors were chosen for reasons stated in advance.

Portal use, coded 1 for accounts requesting at least half of their quotes through the portal, is the predictor of interest.

Special-order account, coded 1 for accounts whose quoted lines are mostly non-stock items, is included because Units 2 and 3 showed these accounts convert far more slowly.

Heavily revised quotes, the number of the account's quotes in the year that went through three or more revision rounds, is included because revisions delay orders and may differ by channel.

Tenure, in years as a customer, is included because longer relationships may involve faster approvals.

Annual purchases, in hundreds of thousands of dollars, is included because larger customers may have procurement departments that move differently.

Credit limit was considered and dropped before fitting, because it correlates at .97 with annual purchases in the sample and would add collinearity without new information.

The Model

An ordinary least squares regression of quote-to-order time on the five predictors gives R-squared of .254, adjusted R-squared of .236, F of 14.29 on 5 and 210 degrees of freedom with p below .001, and a residual standard error of 4.04 days.

Reading Coefficients in Days

Intercept, 6.80 days. The predicted conversion time for a stock-order account that does not use the portal, has no heavily revised quotes, and has zero tenure and purchases. The last two conditions are outside the data, so the intercept has no practical meaning on its own.

Portal use, -1.63 days, 95 percent CI -2.85 to -0.41, p = .009. Among accounts with the same order type, revision count, tenure and purchases, portal users convert quotes about 1.6 days sooner on average.

Special-order account, 3.44 days, CI 2.01 to 4.87, p below .001. Holding the other predictors constant, special-order accounts take about three and a half days longer.

Heavily revised quotes, 0.93 days per quote, CI 0.49 to 1.37, p below .001. Each additional heavily revised quote in the year is associated with nearly a day more in average conversion time.

Tenure, 0.00 days per year, CI -0.07 to 0.07, p = .99. No association once the other predictors are included.

Annual purchases, -0.10 days per $100,000, CI -0.28 to 0.09, p = .32. A small and uncertain association. Following the reporting rule adopted in Unit 6, each p value above sits beside an interval in days, so that a reader judges size as well as significance.

Why Adjustment Changed the Answer

Unit 7 found essentially no difference between portal users and others. The regression finds a difference of 1.63 days. The two results are consistent once the mix of accounts is considered. In the sample, portal use correlates at .35 with being a special-order account, and portal users are far more common among special-order customers than among stock customers, as Unit 7 reported. Special-order accounts convert about three and a half days more slowly. In the unadjusted comparison, the portal group's faster conversion within each type was hidden by its larger share of slow special-order accounts. Once order type is held constant, the association appears. Gelman and Hill (2007) describe this pattern, an association masked by a variable related to both the predictor and the outcome, as the reason regression adjustment is used in observational data.

Portal users looked no faster because they were disproportionately the accounts that are slow for other reasons.

How Much the Model Explains

The five predictors explain about a quarter of the variation in conversion time across accounts. Order type and revision count do most of the work; together their standardized coefficients are about twice that of portal use. Removing portal use from the model lowers R-squared from .254 to .229, an f-squared of .033 for portal use alone, small by the benchmarks Cohen (1988) proposed and slightly below the .04 the Unit 4 power analysis assumed. Three-quarters of the variation remains unexplained, which is typical for account-level business outcomes and a reminder that individual accounts will differ widely from the model's predictions.

Association, Stated Carefully

The regression estimates an association between portal use and faster conversion among accounts that are similar on the measured predictors. It does not show that the portal causes faster conversion. Customers chose whether to use the portal, and the customers who chose it may differ on traits nobody coded, such as how organized their purchasing departments are. The finding supports a pilot in which the sales team encourages portal use among a set of accounts and compares their conversion times with similar accounts, which would come closer to a causal answer. Even a simple design, encouraging portal use in randomly chosen territories, would separate the portal's contribution from the kind of customer who chooses it.

What the Result Would Mean If It Holds

If the association survives diagnostics and later replication, its practical meaning is modest but real. A conversion time 1.6 days shorter on each portal account, if it held for every such account, would shorten the cash cycle on the share of sales those accounts generate, and it would free sales staff from chasing quotes by email. But the estimate's interval runs from under half a day to nearly three days, so the plausible benefit spans a range from trivial to substantial. That range is itself useful to the vice president of sales: it says a portal campaign is worth piloting, not worth rolling out on the strength of this study alone. The distinction between an estimate worth testing further and an estimate worth acting on is one the business has rarely drawn, and the regression makes it possible to draw it.

Handed On to Diagnostics

The coefficients and intervals above assume the model's conditions hold: linear relationships, independent errors with constant variance, approximately normal residuals and no single accounts driving the result. Unit 9 checks each of these and reports what was found and what was done, before any of these figures is carried into a results section. Fox (2016) recommends treating diagnostics as part of the model, not as an afterthought, and the results above are provisional until they are complete.

References

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.

Fox, J. (2016). Applied regression analysis and generalized linear models (3rd ed.). SAGE.

Gelman, A., & Hill, J. (2007). Data analysis using regression and multilevel/hierarchical models. Cambridge University Press.