C207 Task 2 Regression Pricing Analysis Example

Setting Net Price at a Regional Wholesale Bakery: A Regression Analysis of 36 Months of Case Volume, Price and Trade Promotion

[Candidate Name]

School of Business, Western Governors University

C207 Data-Driven Decision Making

Task 2 Performance Assessment

[Course Instructor]

August 11, 2026

Model document written by our desk. The company, the data set and every figure in it are composites built for teaching; no real organization, customer or employee is described.

Decision Problem and Data Set

Lakeshore Provisions Company is a composite regional wholesale bakery that ships fresh bread and rolls to 62 grocery stores across three metropolitan markets. Over the past 24 months its delivered variable cost has risen from $11.55 to $12.40 per case, which cut contribution margin from $6.95 to $6.10 at the current average net price of $18.50. Leadership brought one question to the analytics desk: should the company raise net price, hold price and spend more on trade promotion, or cut price to defend volume? The answer had to come from the company's own shipment history rather than from category habit, because the three options move the same two levers in opposite directions and intuition cannot rank them.

The supplied data set holds 36 monthly observations, January 2023 through December 2025, pulled from the order to cash system and reconciled to the general ledger to within 0.3 percent. Each month carries four fields: cases shipped, average net price per case after trade allowances, trade promotion spend, and delivered variable cost per case. Mean monthly volume is 20,900 cases with a standard deviation of 2,240. Mean net price is $18.50 with an observed range of $17.10 to $19.80, and mean promotion spend is $6,000 with a range of $2,900 to $10,400. Three months carried an accrual that was reversed in the following month; those entries were corrected before any model was fitted, and no values were missing.

Three techniques were weighed before one was chosen. A weighted decision matrix scores management preference across criteria, which suits a qualitative choice but is circular here, since the weights would encode the very answer the company wants tested. A break-even calculation is quick, but it takes a volume response as an input, and the volume response is exactly what nobody knows. Regression was chosen because it estimates the volume response to price and to promotion from behavior the company has already observed, and because it reports how much confidence the estimate deserves.

Method and Model Results

The model is ordinary least squares with cases shipped per month as the dependent variable and two predictors, average net price per case and monthly trade promotion spend, fitted on all 36 observations. The fitted equation is Cases = 48,430 - 1,540(Price) + 0.16(Promotion). Model fit is R-squared = .78, adjusted R-squared = .77, F(2, 33) = 58.5, p < .001. The price coefficient is -1,540 cases per dollar with a standard error of 214, t = -7.20, p < .001. The promotion coefficient is 0.16 cases per promotion dollar with a standard error of 0.05, t = 3.20, p = .003. Residual standard error is 1,060 cases per month.

Read in business terms, each $1.00 added to average net price is associated with 1,540 fewer cases shipped in a month. At the mean price of $18.50 and mean volume of 20,900 cases that is a price elasticity of -1.36, so demand in this category is elastic and volume does react. Promotion works, but barely. Each promotion dollar buys 0.16 additional cases, which at a contribution margin of $6.10 per case returns about 98 cents, so the last dollar of promotion does not pay for itself. Elastic demand and a promotion lever already spent to its break-even are the two facts that shape everything below.

Diagnostics were run before the model was used for anything. The residual plot showed no funnel and the Breusch-Pagan test returned p = .21, so constant variance holds. Durbin-Watson is 1.87, so the monthly residuals are not serially correlated. Variance inflation is 1.24 for both predictors, so price and promotion are not entangled. One observation, February 2024, carries a standardized residual of -3.1 and coincides with an ice storm that closed 11 of the 62 stores for six days; it was kept, because dropping it moved the price coefficient only from -1,540 to -1,481, under 4 percent. Adding quarterly indicators raised adjusted R-squared from .77 to .79 and left the price coefficient within 3 percent, so the simpler model carries the decision.

Assumptions and the Three Options Compared

Five assumptions carry the figures below, and each one is a place the answer could break. Delivered variable cost holds at $12.40 through the forecast year, supported by a flour contract fixed through next June and a labor rate set by the current agreement. Competitor shelf prices do not move, which is the largest known gap, because the data set carries no competitor price field. The price response is linear across the observed range of $17.10 to $19.80, and every price tested below sits inside that range, so none of these forecasts is an extrapolation. Store count stays at 62. Finally, 22 percent of variance between months is unexplained, so a single month can miss its forecast without the model being wrong.

The three options are compared at the promotion level the company runs today, $6,000 per month. The baseline is 20,900 cases at $6.10 of contribution, or $127,490, less promotion, for $121,490 a month. Option 1 raises net price 4 percent to $19.24: predicted volume is 19,760 cases at $6.84 of contribution, or $135,158, less promotion, for $129,158, a gain of $7,668 a month. Option 2 holds price and adds $3,000 of promotion: predicted volume is 21,380 cases at $6.10, or $130,418, less $9,000 of promotion, for $121,418, which is $72 a month worse than doing nothing. Option 3 cuts price 4 percent to $17.76: predicted volume is 22,040 cases at $5.36, or $118,134, less promotion, for $112,134, a loss of $9,356 a month.

Two sensitivity tests were run against Option 1, because a single forecast is not a defense. The first is break-even: at $19.24 the company holds its current contribution as long as monthly volume stays above 18,639 cases. Volume can fall 2,261 cases, or 10.8 percent, before the price increase stops paying, and the model predicts a fall of 1,140 cases, or 5.5 percent. The second is the 95 percent confidence interval on the price coefficient, which runs from -1,975 to -1,105. Priced across that whole interval, the increase still adds between $5,469 and $9,873 a month, so the recommendation does not depend on the estimate landing exactly where it did.

Recommendation and How It Will Be Checked

One recommendation follows from the analysis. Raise average net price 4 percent, from $18.50 to $19.24 per case, at the start of the next quarter, and hold trade promotion spend at $6,000 per month. The forecast is an added $7,668 of monthly contribution, roughly $92,016 over twelve months, and the gain stays positive across the full confidence interval on the price response, between $5,469 and $9,873 a month. Promotion is not increased, because the marginal promotion dollar returns 98 cents of contribution. Price is not cut, because elastic demand does not rescue a contribution margin worth only 33 percent of price; Option 3 gives away $9,356 a month to buy 1,140 cases.

Implementation carries three controls. Announce the new list price 60 days ahead with the ingredient cost letter attached, so buyers see the reason before they see the invoice. Hold trade terms unchanged for two quarters, because an increase that is quietly refunded through allowances is not an increase, and the model reads net price rather than list price. Set a stop rule before launch: if shipped volume over the first 60 days runs more than 8 percent below the same 60 days a year earlier, adjusted for store count, leadership reviews the increase instead of waiting for the quarter to close. Eight percent sits inside the 10.8 percent break-even, which leaves room to act while the decision is still reversible.

Two conditions would overturn this recommendation, and both are measurable. The first is competitor response: the data set has no competitor price field, so a matched cut by the two national bakeries would fall outside the model. Finance should add a monthly shelf price field for the two largest competitors and refit once six observations exist. The second is input cost: if delivered cost falls back toward $11.55, contribution margin widens, each lost case costs more, and the case for a price increase weakens rather than strengthens. Tracking should compare cases shipped, realized net price after allowances, and contribution per case against forecast, remembering that residual standard error is 1,060 cases, so one month inside about 2,100 cases of forecast proves nothing either way.

References

Albright, S. C., & Winston, W. L. (2020). Business analytics: Data analysis and decision making (7th ed.). Cengage Learning.

Davenport, T. H., & Harris, J. G. (2017). Competing on analytics: The new science of winning (Updated ed.). Harvard Business Review Press.

Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2019). Multivariate data analysis (8th ed.). Cengage Learning.

Kahneman, D., Lovallo, D., & Sibony, O. (2011). Before you make that big decision. Harvard Business Review, 89(6), 50-60. https://hbr.org/2011/06/before-you-make-that-big-decision

Provost, F., & Fawcett, T. (2013). Data science for business: What you need to know about data mining and data-analytic thinking. O'Reilly Media.

U.S. Bureau of Labor Statistics. (2025). Producer price index industry data: Flour milling. U.S. Department of Labor. https://www.bls.gov/ppi/