GB513 Unit 9 Multiple Regression Model Example

Store Size Drops Out: A Unit 9 Multiple Regression Model for Ranking Three Pet Supply Sites

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Purdue University Global

GB513: Business Analytics

Unit 9 Multiple Regression Model

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[Date]

The pet supply chain, its stores, the candidate sites and every figure are composite and illustrative; the methods cited are real.

The Site Selection Question

Pawsome Pet Supply operates 38 stores and plans to open one more next year. The real estate team has three candidate sites. The question is which site is likely to produce the highest monthly sales.

The Variables

Monthly sales, the response, in thousands of dollars, averaged over the last twelve months.

Population, residents within a fifteen-minute drive, in thousands. Included because more nearby households mean more potential customers.

Competitors, the number of pet supply stores within the same area. Included because competitors split demand.

Store size, selling floor area in thousands of square feet. Included because larger stores carry more products.

Suburban, coded 1 for suburban locations and 0 for urban. Included because suburban households tend to own more and larger pets.

Checking the Predictors

A correlation matrix shows that population and store size are strongly related, with a correlation of 0.83: the chain has built larger stores in more populous areas. David Levine and colleagues warn that when two predictors move together this closely, their separate effects become hard to estimate, a problem called multicollinearity (Levine et al., 2021). Population and competitors are only weakly related, at 0.30.

How the Data Were Prepared

Sales figures are twelve-month averages, which smooth seasonal swings such as the December holiday peak and spring flea and tick season. Population counts come from census estimates for each store's fifteen-minute drive-time area. Competitor counts were taken from a business directory and checked against online maps; a store counted only if it sold pet food and supplies, not a grocery store with a pet aisle. Two stores opened during the last year were excluded, because twelve months of sales were not yet available.

The Full Model

The full model, with all four predictors, has R squared of 0.904 and adjusted R squared of 0.893, with a standard error of about $14.2 thousand.

Population: coefficient 2.159, p-value below 0.001. Each additional thousand residents is associated with about $2,160 more monthly sales, holding the other predictors constant.

Competitors: coefficient negative 10.803, p-value below 0.001. Each additional competitor is associated with about $10,800 less monthly sales, holding the others constant.

Store size: coefficient negative 0.229, p-value 0.94. Once population and the other predictors are in the model, store size adds nothing.

Suburban: coefficient 17.999, p-value 0.0005. Suburban stores sell about $18,000 more a month than comparable urban stores.

Store size looked important on its own only because big stores sit in big markets; once population is in the model, size explains nothing extra.

The Reduced Model

Dropping store size gives a reduced model with population, competitors and suburban.

Fit: R squared 0.904, adjusted R squared 0.896, standard error about $13.97 thousand.

Equation: predicted monthly sales equal 83.635 plus 2.146 times population, minus 10.795 times competitors, plus 17.962 if suburban.

All three predictors are significant at the 0.001 level.

Comparing the Two Models

The reduced model fits as well as the full model, with the same R squared, a slightly higher adjusted R squared and a slightly smaller standard error. Adjusted R squared penalizes predictors that add little, so its rise confirms that store size was not helping (Anderson et al., 2020). The reduced model is simpler and should be preferred.

Ranking the Candidate Sites

Site A: 64,000 residents, 2 competitors, suburban. Predicted sales about $217,400 a month.

Site B: 78,000 residents, 4 competitors, urban. Predicted sales about $207,800 a month.

Site C: 52,000 residents, 1 competitor, suburban. Predicted sales about $202,400 a month.

Site A ranks first. Site B has the largest population, but its four competitors and urban location cost it more than its extra residents add.

Cautions

The predictions differ by only about $5,000 to $15,000 a month, which is close to the model's standard error of about $14,000, so the ranking is a guide rather than a certainty. The model also assumes the new store will perform like the existing 38, which may not hold in a new region. James Evans advises pairing a regression forecast with judgment about what it leaves out (Evans, 2020), here things like parking and visibility from the road.

What the Model Suggests Beyond the Site Choice

The coefficients carry a lesson for strategy as well as site selection. A competitor costs a store about $10,800 a month, roughly the sales gained from five thousand more residents. That means a site with fewer competitors can beat a larger market, as Site A does against Site B. It also suggests that when a competitor opens near an existing store, the chain should expect a loss of that size and plan marketing to defend the store.

Recommendation

Choose Site A, subject to a site visit confirming access and visibility, and track its first year of sales against the predicted $217,400 to check the model.

References

Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., & Cochran, J. J. (2020). Statistics for business and economics (14th ed.). Cengage.

Evans, J. R. (2020). Business analytics: Methods, models, and decisions (3rd ed.). Pearson.

Levine, D. M., Stephan, D. F., & Szabat, K. A. (2021). Statistics for managers using Microsoft Excel (9th ed.). Pearson.