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Goodbelly Marketing: Analysis and Recommendations Cody Wild & Luba Gloukhov October 7, 2014

List of Tables 1 2 3 4 5 6 7

Univariate Summary Statistics . . . . . . . . . . . . . . . . . . . . . Breakdown of Observations By Occurance of Marketing Techniques Estimated Revenue Benefit of Marketing Technique By Region . . . Region Abbreviations and Names . . . . . . . . . . . . . . . . . . . Summary of Units Sold and Price By Region . . . . . . . . . . . . . Breakdown of Observations When Endcap == 1 . . . . . . . . . . . Breakdown of Observations for Endcap == 0 . . . . . . . . . . . .

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List of Figures 1 2 3 4 5 6 7 8 9 10 11 12

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Units Sold vs. Date (Model A1) . . . . . . . . . . . . . . . . . Residual Distribution (Model B5) . . . . . . . . . . . . . . . . Residual vs. Fitted Values (Model B5) . . . . . . . . . . . . . Increase Due to Endcap in Areas With and Without Sales Rep Distribution of Units Sold . . . . . . . . . . . . . . . . . . . . Distribution of Average Retail Price . . . . . . . . . . . . . . Distribution of Revenue . . . . . . . . . . . . . . . . . . . . . Distribution of Total Units Sold Per Store . . . . . . . . . . . Model C2: Residual Distribution . . . . . . . . . . . . . . . . Model C2: Residuals vs Fitted values . . . . . . . . . . . . . . Model C2: Residuals vs Average Retail Price . . . . . . . . . . Impact of Demo on Revenue (given Endcap = 0) . . . . . . .

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Executive Summary

Understood most generally, this report supports continuation of both endcap and demonstration programs, since both can be associated with powerful and significant boosts to sales and consequently revenue. Where the endcap campaign is successful, it is linked to with increases between $1, 850 and $2, 050 in weekly store revenue. The success of this campaign, however, is strongly influenced by the presence of a regional sales representative interfacing with the store. In regions without a sales representative, the effect of an endcap was essentially nonexistent. In the short term, this result 1

suggests that endcaps should be curtailed in stores without a sales representative, and expanded in stores with one. In the long term, more research should be done to determine factors underlying the presence of a sales representative are driving this dynamic. Demonstrations are more consistently beneficial, leading toaverage revenue boosts of $430 in the week they are conducted, and $300 in the 5 weeks thereafter. This addresses and assuages one of the fears laid out in our briefing: that the benefits of a demonstration recede quickly. In fact,our analysis suggests that the positive effects of a demo continue at 75% of initial strength for up to five weeks after they are conducted. Although definitive judgments on continuation would require cost information, based on the available data, we believe marketing funds have by and large been spent effectively in the past, and, incorporating this report’s insights as well as additional research, can be deployed even more effectively in future.

2

Introduction

2.1

Problem Statement

Given the financial exigencies imposed by the recession and consequent market constriction in 2008, the question of whether Goodbelly’s current marketing projects are leading to justifiably large returns is of particular relevance. With that as a backdrop, this report investigates whether, and to what degree, two specific marketing campaigns targeting Goodbelly sales at Whole Foods have been successful. The first of these campaigns involved the use of marketing funds to set up two parallel incentive structures. One of these incentivized sales representatives to convince more Whole Foods stores to present Goodbelly products at the ends of aisles. The other incentivized Whole Foods stores to create the most decorative endcaps to attract customers. The second marketing campaign paid for part-time individuals to set up a demonstration stand in the Whole Foods and offer samples to customers.

2.2

Data Description

The dataset provided for this analysis includes 1,386 observations, each of which represents information for a given store, for each of the eleven weeks between May 4 and July 13 of 2010, across 12 variables: • Date - Date corresponding to first day of the week • Region - Two-digit code corresponding to geographic region

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• Store - Name of individual Whole Foods store • U nits.Sold - Goodbelly units sold during the week • Average.Retail.P rice - Average price of Goodbelly products • Sales.Rep - Binary variable set to 1 if a regional, rather than national, sales rep was responsible for the store and 0 otherwise 1

A full list of abbreviations and corresponding region names can be found in the Appendix.

2

• Endcap - Binary variable set to 1 if the store had a Goodbelly endcap installed during the week, and 0 otherwise • Demo - Binary variable set to 1 if the store conducted a demo during this week, 0 otherwise • Demo1.3 - Binary variable set to 1 if the store conducted a demo during the 1-3 weeks prior to this week, 0 otherwise • Demo4.5 - Binary variable set to 1 if the store conducted a demo during the 4-5 weeks prior to this week, 0 otherwise • N atural - Number of natural food stores located within five miles of this Whole Foods store • F itness - Number of fitness centers located within five miles of this Whole Foods store • **Revenue - Not included in the initial dataset, this variable, set equal to U nits.Sold ∗ Average.Retail.P rice was created for ease of analysis

Table 1: Univariate Summary Statistics Variable Min Median Mean U nits.Sold 47.6 236.7 253.8 Average.Retail.P rice 2.9 4.1 4.1 Revenue 204.2 967.3 1041.0 [H] Endcap 0 0 .038 Demo 0 0 .058 Demo1.3 0 0 .157 Demo4.5 0 0 .076

Max 1041 6.3 4252.0 1 1 1 1

Both U nits.Sold and Revenue follow unimodal and right-skewed distributions. Average.Retail.P rice follows a bimodal right-skewed distribution. Histograms of both of these continuous variables can be found in Appendix 1. As shown in the above table, Demos were occured in 5.8% of the observations within this dataset. The mean values for Demo1.3 and Demo4.5 are somewhat higher, at 15.7% and 7.6% respectively, accounting both for presence of multiple weeks within these intervals and for demos that occured during the weeks prior to the window covered by the dataset. Demos appeared at some point in the time spanning the data set in 69 of the 126 stores. Endcaps appeared in just 12 of the 126 stores.

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Table 2: Breakdown of Observations By Occurance of Marketing Techniques Demo Demo1.3 Demo4.5 Endcap n Units.Sold Average.Retail.Price 0 0 0 0 992 213.27 ± 57.03 4.09 ± 0.44 1 28 497.78 ± 257.91 4.11 ± 0.53 1 0 82 304.88 ± 57.88 4.25 ± 0.53 1 3 443.86 ± 244.68 3.71 ± 0.88 1 0 0 171 308.53 ± 47.38 4.09 ± 0.52 1 14 662.26 ± 229.49 3.72 ± 0.47 1 0 15 366.30 ± 70.76 4.31 ± 0.40 1 0 N aN ± N A N aN ± N A 1 0 0 0 57 334.21 ± 55.51 4.19 ± 0.45 1 5 710.74 ± 238.72 4.00 ± 0.43 1 0 2 394.86 ± 47.37 4.63 ± 0.85 1 0 N aN ± N A N aN ± N A 1 0 0 12 427.50 ± 38.52 4.39 ± 0.50 1 2 905.95 ± 28.49 3.50 ± 0.32 1 0 2 532.47 ± 34.05 4.22 ± 0.53 1 1 1041.20 ± NA 4.08 ± N A All 1386 253.82 ± 111.00 4.11 ± 0.46

3

Model Construction

3.1

Initial Exploration

Before examining models that directly addressed the effect of Goodbelly’s marketing, our team started with more basic models that we hoped would reveal patterns in the data. Since the data was structured as a time series, our first exploratory model, Model A1, regressed U nits.Sold against Date. Although this Simple Linear Regression had low explanatory power, with an Ra2 at just over .05, the fact that Date was a highly significant variable, with p < 2e−16 , communicated the fact that the data contained a chronological trend, with Units Sold increasing as observations moved forward in time. Since the response under consideration in this analysis is connected to customer purchasing decisions, basic familiarity with economic theory suggested that Average.Retail.P rice may explain variation in units sold, with customers buying less at higher prices. Despite this intuition, Model A2, which regressed U nits.Sold against both Date and P rice 2 , found the effect P rice to not be significantly different from zero, with p = .32. Given this lack of significance of P rice as an explanatory variable here, and further given the similarity in the distributions of U nits.Sold and Revenue, our team decided to continue the process of model construction removing P rice as an explanatory variable and using Revenue, rather than U nits.Sold, as the dependant variable. This decision was motivated by the fact that, ultimately, the question of whether these marketing programs are cost-effective is determined by whether the revenue they bring in is greater than the cost they incur. Therefore, modeling Revenue as the dependant variable is more directly in line with the questions under consideration in this report. 2

For the sake of brevity, P rice is used here to refer to Average.Retail.P rice

4

Figure 1: Units Sold vs. Date (Model A1)

It was at this point, with Model A3, that the explanatory variables of interest, the indicators of the presence of each marketing technique during a given observation, were added into the regression. With this addition, the explanatory power of our model increased almost tenfold, growing from an Ra2 = .054 to Ra2 = .523. All of the marketing variables (i.e. Demo, Demo1.3, Demo4.5, and Endcap) have positive and significant coefficients in this model: the first concrete sign of a notable benefit associated with these marketing strategies. Notably, once these indicators are added into the model, Date ceases to be significant at α = .05, suggesting that the upward chronological trend observed in more simplistic models and graphics is largely explained by the greater presence of marketing efforts as time goes on. Now that the most general explanatory variables - Date and P rice - as well as the targeted explanatory variables have been incorporated, the next step was to include information that differentiates stores from one another. On the most aggregate level, stores are distinguished from one another by their geographical location, which Model A4 incorporated by adding Region as an explanatory variable3 . This model was a substantial improvement on its predecessor, with a jump of 15% in terms of absolute explanatory power, from Ra2 = .523 to Ra2 = .668 Given this as a solid core of a model, our team continued to build upwards with the variables on hand, which now distinguish individual stores within region. Models A5 and A6, which add F itness and N atural respectively to the baseline established by A4, find neither to add significant predictive value, with p values of .56 and .58. In Model A7, which adds Sales.Rep, we see that while it doesn’t add substantial predictive power - a change of only .001 in Ra2 , it is significantly different from zero, and thus was kept in subsequent models moving forward.

3.2

Regional Interaction Models

Prior to adding any interaction terms, the benchmarked current best model is specified as follows: Revenue = β0 + β1 Region + β2 Endcap + β3 Demo + β4 Demo1.3 + β5 Demo4.5 + β6Sales.Rep 3

In interpreting output from models involving Region, be aware that the zero-level of Region, and therefore the one chosen by R to be removed and incorporated into the intercept to ensure invertibility, was consciously chosen to be New England (NE), since that region exhibited revenue closest to the average level revenue across all regions.

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Given that the field of possibly fruitful single variables has been considered, we now move on to interaction terms, which would lead to the effects of one variable varying according to the levels of another. Starting again from the most macro view of possible differentiation, we considered Region as a possible category by which effects of a marketing technique might differ. Based on this, we constructed Model B1, which adds a Region ∗ Endcap interaction term to the base model above. The addition of this interaction boosted our model’s Ra2 value, which had plateaued at roughly .67 in Models A4-A7, up to .78. It should be noted that a majority of the levels of Region have NA coefficients for their interaction with Endcap. This is because only five regions ever experience an endcap: Florida, Mid-Atlantic, Northern California, Pacific Northwest, and Rocky Mountain. Since only these five regions experience endcaps, R defines interaction coefficients for only four of them, leaving the last to be encompassed in the value of the uninteracted Endcap coefficient. In this case, that region is Rocky Mountain, meaning that the the effect of Endcap in the Rocky Mountain region is 1573, with all other coefficients expressed in relative terms to that one. Although this will be explored in considerably more depth in later sections, it is worth noticing at this juncture the stark divide between the effect of an Endcap on Revenue in NC, PN, and RM - where it is in the range of $1400-$2050 - and FL and MA, where it is between −100 and 30. Since the success of Region’s addition suggested that Endcap may vary significantly based on geographical area, Model B2 moved from a more aggregated geographical breakdown to a more minute one, adding an interaction term between Store and Endcap. Although the nominal R2 increased by .02 once this interaction was added, the Ra2 increased by far less, with a change of .002. Given that information, our team elected to continue model construction without a breakdown by individual store, on the basis of a few rationales. First, and most straightforwardly, this small boost in explanatory power was completely out of proportion to the the increase in complexity triggered by this interaction’s addition, which grew our coefficient vector from 20 to over 200. Secondly, we opted to continue without Store-level interactions because we believe that, all else equal, a more general model is a more powerful, as it carries more easily abstractable insights, and is less likely to overfit to this specific dataset. Moving back to the starting point of a single interaction between Region and Endcap, Model B3 takes the Region interaction and applies it to the Demo variable. In this case, however, the interaction between Region and Demo is insignificant, with p-values on individual coefficients ranging from .23 to .92, and a coefficient of partial determination with a p-value of .83. So, while Endcap appears to vary greatly and significantly by Region, there isn’t support, at any reasonable level of significance, for the hypothesis that Demo does likewise. While Model B3 provided strong evidence that the effect of a Demo on revenue doesn’t vary by region, Model B4 adddresses the question of whether the effect of a Demo could vary depending on whether previous Demos had occured at the same store. To address this, it incorporates interactions between Demo:Demo1.3, Demo1.3:Demo4.5, and Demo:Demo4.5. Out of these, only the foremost was significant at α = .05, with the partial effect of a Demo heightened when it was preceded by another Demo in the prior 1-3 weeks. After consideration of these various interactions as possible additions to our model, our benchmark model is Model B5, specified as follows: Revenue = β0 + β1 Region + β2 Endcap + β3 Demo + β4 Demo1.3 + β5 Demo4.5 + β6 Region ∗ Endcap + β7 Demo ∗ Demo1.3 + β7 Sales.Rep Given that this is under consideration as a potential final model, tests of the underlying assumptions of homoskedasticity and normality of error terms are now necessary. The Breusch-Pagan 6

test, returned a p-value of .11 on this model, which gives us insufficient evidence to reject the null hypothesis of homoskedastic error. However, the Shapiro-Wilk normality test returned a p-value .f .007, leading us to reject the null hypothesis of normality at α = .05. Figure 2: Residual Distribution (Model B5)

Figure 3: Residual vs. Fitted Values (Model B5)

Since neither the metric of homoskedasticity nor that of normality is ideal, a BoxCox estimation was performed to determine whether a Y transformation may be useful in correcting some of these deficiencies. This estimation returned a value of .75, leading us to Model B6, which is identical in its parameters to B5, but with a transformed performed on Y. As a result of this transformation, Ra2 decreases slightly, from .785 to .75. However, there are also strong compensatory changes on the metrics of homoskedasticity and normality, with Breusch-Pagan and Shapiro-Wilk tests returning p-values of .91 and .54 respectively. One minor note is that in this transformed model, Demo:Demo1.3, which had previously been borderline significant, now ceases to be significant at any reasonable level, with a p-value of .211. With all Demo:Demo interactions removed 7

from the current model, this implies that the effect of a Demo at any given point in time is not significantly different from the effect of that Demo given that prior Demos have been performed. In simpler terms, the effect of susbsequent Demos is simply additive rather than both additive and multiplicative. The adoption of this transformation, as well as the removal of the Demo:Demo1.3 interaction, leads to Model B7, as specified here: Revenue.75 = β0 + β1 Region + β2 Endcap + β3 Demo + β4 Demo1.3 + β5 Demo4.5 + β6 Region ∗ Endcap + β7 Sales.Rep This model was a strong candidate in many ways. It balanced parsimony and explanatory power, incorporated only minimal transformation, exhibited had no obvious deficiencies in the way of nonconstant error variance of non-normally-distributed error terms. However, there remained one fundamental problem with this model: the most compelling and unexpected story it told was one that we had no clear way of explaining. This story is the divergence previously mentioned, between the strikingly large benefit associated with an Endcap promotion in three regions that had experienced Endcaps - NC, RM, PN - and the nonexistent or even negative effect in the other two - FL and MA. Model B7 succeeded at identifying this divergence, but it didn’t clarify what factors made these two groups of regions different from one another. This leaves us without a position of strength from which to answer the question: among the six regions were Endcaps have not previously been employed, where are they likelier to behave like the successful group (Group 1), and where are they likelier to behave like the unsuccessful one (Group 2)? In an attempt to determine the key factor distinguishing these groups of regions, the data was subsetted to only include these five regions, and a binary indicator variable was created, set to 1 if the observation belonged to a region in Group 1, and set to 0 if it belonged to a region in Group 2. We then ran a logistic regression with this Indicator (ecSuccess), and variables we thought could be characteristic of regions - F itness, N atural, Average.Retail.P rice, andSales.Rep - as explanatory variables. The output of this regression isn’t included, because when it was run, it in fact failed to converge, warning of a likely error due to ”an essentially perfect fit”. This unexpected result triggered another round of examining our data, which resulted in an elegant and, ultimately, logically consistent realization: among stores that had experienced Endcaps, Sales.Rep, which indicated whether the store interacted with a regional sales representative or just a national one, was a perfect predictor of whether a store belonged to a Group 1 Region or a Group 2 Region. In other words, out of the Endcap stores, all observations in the unsuccessful regions of MA and FL lacked a regional Sales Rep, while all observations in the successful regions of NC, PN, and RM had one.

3.3

Sales Rep Interaction Models

Given this realization, it occured to us that since the categorization of a region into a successful or unsuccessful group depended on Sales.Rep, the ideal interaction may be not between Region and Endcap but between Sales.Rep and Endcap. This interaction is demonstrated visually by the figure below. This led to C1, the first in our final set of models, which switched out the two aforementioned interactions. As we had hoped, this new interaction term was significant, with a R2 of roughly .77, at par with the prior best model. However, this new model did have clear problems, as expressed by Breusch-Pagan and Shapiro-Wilk test yielding p values of < 2.2e−16 and .0018 respectively. 8

Figure 4: Increase Due to Endcap in Areas With and Without Sales Rep

A Box-Cox estimation was performed on Model C1, but it didn’t generate a useful result, with a suggested lambda parameter of one. At this point, we reviewed the list of variables that had previously been excluded from the model, to see if reincorporating them at this point might correct this problem. After several unsuccessful attempts, we found one that worked: switching the dependant variable back to U nits.Sold and reintegrating Average.Retail.P rice as an explanatory variable. This resulted in our final model, Model C2.

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4

Final Model: Implications

Model C2, our final recommended model, is specified as: U nits.Sold = β0 + β1 Sales.Rep + β2 Region + β3 Average.Retail.P rice + β4 Endcap + β5 Demo + β6 Demo1.3 + β7 Demo4.5 + β8 Sales.Rep ∗ Endcap When this model is run, it generates the following coefficients and t-values: Estimate Std. Error t value Pr(>|t|) (Intercept) 290.4688 18.4468 15.746 < 2e-16 *** Demo 106.4176 5.7614 18.471 < 2e-16 *** Demo1.3 72.6323 3.8370 18.929 < 2e-16 *** Demo4.5 72.5876 5.1404 14.121 < 2e-16 *** Endcap -1.1611 12.4999 -0.093 0.9260 RegionFL -13.2980 10.5617 -1.259 0.2082 RegionMA -12.6337 9.9816 -1.266 0.2058 RegionMW 7.6899 6.6410 1.158 0.2471 RegionNA -19.2996 9.9375 -1.942 0.0523 . RegionNC 7.1791 6.9733 1.030 0.3034 RegionPN 0.2981 7.5342 0.040 0.9684 RegionRM 1.7499 7.3517 0.238 0.8119 RegionSO -15.7381 10.7988 -1.457 0.1452 RegionSP 7.9846 7.0766 1.128 0.2594 RegionSW -20.8752 10.6241 -1.965 0.0496 * Sales.Rep 39.4663 10.5825 3.729 0.0002 *** Average.Retail.Price -21.7311 3.7075 -5.861 5.74e-09 *** Endcap:Sales.Rep 457.4982 15.3309 29.842 < 2e-16 *** --Multiple R-squared:

0.8071,Adjusted R-squared:

0.8047

While the R2 value for this model is essentially identical to that of Model C1, this model minimizes the problems posed by heteroskedasticity and nonnormality, with Breusch-Pagan and ShapiroWilk p-values of .26 and .73 respectively. The coefficient on Endcap when Sales.Rep == 0 isn’t significantly different from zero - a result that aligns with previous findings of Endcap having a marginal or even negative effect within these regions. By contrast, when Sales.Rep == 1, the coefficient on Endcap is a highly significant 457.5. The effect of Demo on U nits.Sold is more consistent, as interaction terms both between Demo and Region and between Demo turned out not to be significant. When a Demo is conducted in the week of observation, that fact is associated with a 106.4 increase in volume of U nits.Sold. When a Demo has been conducted further in the past, either by 1-3 or 4-5 weeks, that fact is associated with 72.6 increase in U nits.Sold for both cases. The coefficient on P rice, which in prior models had lacked significance, fits the expectations of economic theory by being significant and negative in this model. This suggest that, in prior models, high correlation between P rice and a variable not yet in the model was a source of endogeneity and thus bias in our estimates. 10

Although Region adds relatively little predictive power to this model, its inclusion helped stem problems of heteroskedasticity and nonnormality that were present otherwise, and so it was included for its normalizing effect. The table below summarizes the average estimated revenue boosts associated with each of the marketing techniques in each Region, using P rice = the average P rice in that region and Sales.Rep set equal to 1 if there are stores within that region who interface with a regional rather than national sales representative. Revenue benefit values which lie within the range of the dataset (i.e. where we have observations for that combination of Region and Sales.Rep) are are indicated with ∗∗ . Table 3: Estimated Revenue Benefit of Marketing Technique By Region Region Sales.Rep meanPrice n Endcap Demo Demo1.3 Demo4.5 ∗∗ NE 0 $4.33 30 $2.69 $462.69 $318.00∗∗ $323.13∗∗ NE 1 $4.09 80 $1860.84 $437.15∗∗ $300.45∗∗ $305.29∗∗ FL 0 $4.15 88 $2.57∗∗ $443.05 $304.50 $309.41∗∗ MA 0 $3.61 209 $2.24∗∗ $385.80∗∗ $265.15∗∗ $269.43∗∗ MW 1 $3.94 176 $1789.96 $420.50∗∗ $289.00∗∗ $293.66∗∗ NA 0 $4.13 143 $2.57 $441.40 $303.37 $308.25 ∗∗ ∗∗ ∗∗ NC 1 $4.53 165 $2058.67 $483.62 $332.39 $337.74∗∗ ∗∗ ∗∗ ∗∗ PN 1 $4.05 99 $1841.52 $432.61 $297.33 $302.12∗∗ RM 1 $4.40 110 $2001.14∗∗ $470.11∗∗ $323.10∗∗ $328.30∗∗ SO 1 $3.80 77 $2.36 $405.61 $278.77 $283.26 ∗∗ ∗∗ SP 1 $4.40 132 $1999.50 $469.72 $322.83 $328.04∗∗ SW 0 $4.20 77 $2.60 $448.18 $308.03 $312.99

5

Recommendations

Based on the results of our final model, we can provide an analytically sound answer to the questions posed in our problem statement: namely, whether marketing techniques undertaken by Goodbelly resulted in substantial and long-lived increases in sales. Within this data, in-store demonstrations were shown to have a consistent, positive, and significant effect that didn’t vary significantly between regions or as a result of an additional demonstration having taken place during a prior week. This positive effect was predictably highest, with an average boost of 106 units sold and $430 in increased revenue, when the demonstration had occured that week. The effect then tapered to 72.6 additional units sold in the week after the demonstration, and stayed elevated at this level for at least five weeks thereafter. This result has a few key implications for future marketing decisions. Firstly, this analysis contradicts, at least in regards to the five weeks following a demonstration, the worry that effects of marketing are short-lived, as the positive effect continues at 75% strength for up to five weeks, and potentially longer. Secondly, since no interactions between this week’s demonstration and prior weeks demonstrations were ultimately found to be significant, our results suggest that, in order to operate most cost-effectively and allow the impact of a demo to take full effect, repeat demos in the same store should be spaced at least five weeks apart. The campaign of constructing decorative endcaps had a stronger positive effect on sales, but a less universal one. In stores and in regions with a regional sales representative, endcaps were associated with an average estimated sales boost of 457.5 units, translating to $1860 − $2050 in 11

additional revenue. However, in stores without a sales representative, that boost was essentially nonexistent. On the most basic level, this result would strongly recommends that the endcap campaign be continued in regions - NC, PN, RM - where it has found success, and minimized or eliminated in regions - MA and FL - where it has not. Projecting slightly further from the results of this analysis, this result suggests that the expansion of endcaps into new stores and regions is likeliest to lead to strong positive results in areas with a regional sales representative. By this criteria, Midwest, New England, and South Pacific would be ideal expansion targes. However, it is worth taking a moment to examine why it is that the presence of a sales representative is associated with such a strong positive effect. Maybe regional sales representatives have a deeper body of knowledge about their particular region, and are better able to target endcap installation to stores where they suspect it will be successful. Perhaps the closer connections that are formed between regional representatives and store employees motivate stores to construct endcaps that are more well-decorated and located more prominently within the store. It could even be that the same criteria that determines whether a regional sales representative is appointed is determinative of whether an endcap campaign is successful. The primary takeaway here is that while this report finds an association here, if Goodbelly wants to understand on a deeper level the causal mechanics at work here, further research would be necessary. This could potentially take the form of interviewing both regional and national sales representatives to ascertain the time spent on their endcap campaigns or more qualitative information about the endcaps themselves, such as their location within the store. It should be noted that, since information pertaining to the costs of each technique, all of these recommendations are made on the basis of increased revenue alone, rather than a more clear-cut cost-benefit analysis. However, given this caveat, if the revenue increases estimated by this report do indeed outstrip costs, then we recommend continuing or expanding all demonstration campaigns and a subset of endcap campaigns, and hope that this analysis can lead to more confident and ultimately successful decision-making by Goodbelly.

6 6.1

Appendix Univariate Statistics Table 4: Region Abbreviations and Names Abbreviation Name NE New England FL Florida MA Mid Atlantic MW Midwest NA North Atlantic NC North California PN Pacific Northwest RM Rocky Mountain SO South SP South Pacific SW Southwest

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Figure 5: Distribution of Units Sold

Figure 6: Distribution of Average Retail Price

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Figure 7: Distribution of Revenue

Figure 8: Distribution of Total Units Sold Per Store

14

6.2

Model Specification & Output Model A1 (Date SLR) U nits.Sold = β0 + β1 Date lm(formula = Units.Sold ~ Date, data = gbData) Residuals: Min 1Q -239.15 -59.45

Median -14.32

3Q 38.88

Max 770.94

Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -17090.576 1934.447 -8.835 F) 91338349 9133835 198.2805 < 2e-16 *** 21652374 21652374 470.0373 < 2e-16 *** 19032981 19032981 413.1746 < 2e-16 *** 7225538 7225538 156.8545 < 2e-16 *** 60823921 60823921 1320.3869 < 2e-16 *** 21645750 188224 4.0860 < 2e-16 *** 18230088 4557522 98.9363 < 2e-16 *** 803136 114734 2.4907 0.01528 * 57351206 46065

Model B3 (B1 + Region:Demo Interaction) Revenue = β0 + β1 Region + β2 Endcap + β3 Demo + β4 Demo1.3 + β5 Demo4.5 + β6 Region ∗ Endcap + β8 Region ∗ Demo + β7 Sales.Rep lm(formula = Revenue ~ Region + Demo + Demo1.3 + Demo4.5 + Endcap + 20

Region * Endcap + Demo * Region + Sales.Rep, data = gbData) Residuals: Min 1Q -678.40 -148.33

Median -3.63

3Q 135.76

Max 883.78

Coefficients: (10 not defined because of singularities) Estimate Std. Error t value Pr(>|t|) (Intercept) 846.028 39.700 21.311 < 2e-16 *** RegionFL -74.648 46.650 -1.600 0.109791 RegionMA -135.086 42.512 -3.178 0.001518 ** RegionMW 6.454 30.381 0.212 0.831791 RegionNA -100.029 43.612 -2.294 0.021964 * RegionNC 116.347 30.996 3.754 0.000182 *** RegionPN 15.798 34.845 0.453 0.650342 RegionRM 61.191 33.800 1.810 0.070458 . RegionSO -116.859 46.705 -2.502 0.012463 * RegionSP 94.353 32.130 2.937 0.003374 ** RegionSW -99.219 46.705 -2.124 0.033817 * Demo 441.396 91.736 4.812 1.66e-06 *** Demo1.3 288.567 17.020 16.955 < 2e-16 *** Demo4.5 310.970 22.785 13.648 < 2e-16 *** Endcap 1573.435 110.209 14.277 < 2e-16 *** Sales.Rep 132.113 46.895 2.817 0.004915 ** RegionFL:Endcap -1549.231 130.350 -11.885 < 2e-16 *** RegionMA:Endcap -1670.111 142.159 -11.748 < 2e-16 *** RegionMW:Endcap NA NA NA NA RegionNA:Endcap NA NA NA NA RegionNC:Endcap 476.420 124.825 3.817 0.000141 *** RegionPN:Endcap -159.159 126.302 -1.260 0.207834 RegionRM:Endcap NA NA NA NA RegionSO:Endcap NA NA NA NA RegionSP:Endcap NA NA NA NA RegionSW:Endcap NA NA NA NA RegionFL:Demo NA NA NA NA RegionMA:Demo -10.569 112.004 -0.094 0.924835 RegionMW:Demo 18.031 107.049 0.168 0.866268 RegionNA:Demo NA NA NA NA RegionNC:Demo 19.998 117.956 0.170 0.865398 RegionPN:Demo 148.704 125.202 1.188 0.235153 RegionRM:Demo 42.249 108.858 0.388 0.697994 RegionSO:Demo NA NA NA NA RegionSP:Demo 68.583 111.279 0.616 0.537788 RegionSW:Demo NA NA NA NA --Residual standard error: 215.9 on 1360 degrees of freedom 21

Multiple R-squared: 0.7874,Adjusted R-squared: 0.7835 F-statistic: 201.5 on 25 and 1360 DF, p-value: < 2.2e-16 Model B4 (B1 : Demo/Demo Interactions) Revenue = β0 + β1 Region + β2 Endcap + β3 Demo + β4 Demo1.3 + β5 Demo4.5 +β6 Region∗Endcap+β7 Demo∗Demo1.3+Demo1.3∗Demo4.5+Demo∗Demo4.5+β7 Sales.Rep lm(formula = Revenue ~ Region + Demo + Demo1.3 + Demo4.5 + Endcap + Region * Endcap + Demo * Demo1.3 + Demo1.3 * Demo4.5 + Demo * Demo4.5 + Sales.Rep, data = gbData) Residuals: Min 1Q -679.03 -149.14

Median -5.51

3Q 135.62

Max 882.60

Coefficients: (6 not defined because Estimate Std. Error (Intercept) 846.479 39.669 RegionFL -75.097 46.573 RegionMA -135.224 42.291 RegionMW 5.895 29.105 RegionNA -100.480 43.562 RegionNC 116.688 29.969 RegionPN 18.954 33.980 RegionRM 61.579 32.120 RegionSO -117.310 46.642 RegionSP 100.923 30.680 RegionSW -99.670 46.642 Demo 443.985 28.766 Demo1.3 282.093 18.337 Demo4.5 310.871 25.160 Endcap 1531.290 112.207 Sales.Rep 132.849 46.315 RegionFL:Endcap -1507.089 131.910 RegionMA:Endcap -1627.203 144.128 RegionMW:Endcap NA NA RegionNA:Endcap NA NA RegionNC:Endcap 519.498 126.706 RegionPN:Endcap -90.004 126.495 RegionRM:Endcap NA NA RegionSO:Endcap NA NA RegionSP:Endcap NA NA RegionSW:Endcap NA NA Demo:Demo1.3 127.918 63.508 Demo1.3:Demo4.5 -58.548 60.823 Demo:Demo4.5 145.612 110.244 22

of singularities) t value Pr(>|t|) 21.339 < 2e-16 *** -1.612 0.107093 -3.197 0.001418 ** 0.203 0.839528 -2.307 0.021227 * 3.894 0.000104 *** 0.558 0.577072 1.917 0.055427 . -2.515 0.012013 * 3.290 0.001029 ** -2.137 0.032781 * 15.435 < 2e-16 *** 15.383 < 2e-16 *** 12.356 < 2e-16 *** 13.647 < 2e-16 *** 2.868 0.004189 ** -11.425 < 2e-16 *** -11.290 < 2e-16 *** NA NA NA NA 4.100 4.38e-05 *** -0.712 0.476882 NA NA NA NA NA NA NA NA 2.014 0.044186 * -0.963 0.335919 1.321 0.186785

--Residual standard error: 215.3 on 1363 degrees of freedom Multiple R-squared: 0.7881,Adjusted R-squared: 0.7847 F-statistic: 230.4 on 22 and 1363 DF, p-value: < 2.2e-16 Model B5 (B1 + Demo:Demo1.3 Interaction) Revenue = β0 + β1 Region + β2 Endcap + β3 Demo + β4 Demo1.3 + β5 Demo4.5 + β6 Region ∗ Endcap + β7 Demo ∗ Demo1.3 + β7 Sales.Rep lm(formula = Revenue ~ Region + Demo + Demo1.3 + Demo4.5 + Endcap + Region * Endcap + Demo * Demo1.3 + Sales.Rep, data = gbData) Residuals: Min 1Q -678.14 -148.91

Median -2.61

3Q 135.85

Max 881.66

Coefficients: (6 not defined because Estimate Std. Error (Intercept) 847.529 39.594 RegionFL -76.052 46.525 RegionMA -135.528 42.283 RegionMW 4.063 29.071 RegionNA -101.530 43.495 RegionNC 115.068 29.921 RegionPN 18.268 33.973 RegionRM 62.904 32.052 RegionSO -118.360 46.579 RegionSP 100.991 30.656 RegionSW -100.720 46.579 Demo 448.034 28.507 Demo1.3 277.345 17.615 Demo4.5 307.204 22.686 Endcap 1549.236 110.293 Sales.Rep 132.734 46.314 RegionFL:Endcap -1525.130 130.319 RegionMA:Endcap -1642.973 142.147 RegionMW:Endcap NA NA RegionNA:Endcap NA NA RegionNC:Endcap 503.161 124.928 RegionPN:Endcap -108.683 124.331 RegionRM:Endcap NA NA RegionSO:Endcap NA NA RegionSP:Endcap NA NA RegionSW:Endcap NA NA Demo:Demo1.3 143.276 62.069 23

of singularities) t value Pr(>|t|) 21.405 < 2e-16 *** -1.635 0.102352 -3.205 0.001381 ** 0.140 0.888878 -2.334 0.019725 * 3.846 0.000126 *** 0.538 0.590857 1.963 0.049900 * -2.541 0.011162 * 3.294 0.001012 ** -2.162 0.030765 * 15.716 < 2e-16 *** 15.745 < 2e-16 *** 13.541 < 2e-16 *** 14.047 < 2e-16 *** 2.866 0.004221 ** -11.703 < 2e-16 *** -11.558 < 2e-16 *** NA NA NA NA 4.028 5.94e-05 *** -0.874 0.382195 NA NA NA NA NA NA NA NA 2.308 0.021128 *

--Residual standard error: 215.3 on 1365 degrees of freedom Multiple R-squared: 0.7878,Adjusted R-squared: 0.7847 F-statistic: 253.3 on 20 and 1365 DF, p-value: < 2.2e-16 studentized Breusch-Pagan test data: test BP = 35.2751, df = 26, p-value = 0.1058

Shapiro-Wilk normality test data: test$residuals W = 0.9969, p-value = 0.006932 Model B6 (B5 With Y 0 = Y .75 Transform) Revenue.75 = β0 + β1 Region + β2 Endcap + β3 Demo + β4 Demo1.3 + β5 Demo4.5 + β6 Region ∗ Endcap + β7 Demo ∗ Demo1.3 + β7 Sales.Rep lm(formula = Revenue^0.75 ~ Region + Demo + Demo1.3 + Demo4.5 + Endcap + Region * Endcap + Demo * Demo1.3 + Sales.Rep, data = gbData) Residuals: Min 1Q -101.968 -19.252

Median 0.226

3Q 18.607

Max 108.774

Coefficients: (6 not defined because of singularities) Estimate Std. Error t value Pr(>|t|) (Intercept) 156.5346 5.2827 29.631 < 2e-16 *** RegionFL -10.9843 6.2074 -1.770 0.077028 . RegionMA -18.5830 5.6415 -3.294 0.001013 ** RegionMW 0.4917 3.8788 0.127 0.899139 RegionNA -14.8584 5.8032 -2.560 0.010563 * RegionNC 14.7704 3.9922 3.700 0.000224 *** RegionPN 2.4013 4.5328 0.530 0.596361 RegionRM 8.0439 4.2764 1.881 0.060188 . RegionSO -17.1849 6.2147 -2.765 0.005766 ** RegionSP 12.9378 4.0901 3.163 0.001595 ** RegionSW -14.8376 6.2147 -2.387 0.017099 * Demo 56.5647 3.8035 14.872 < 2e-16 *** Demo1.3 35.9593 2.3503 15.300 < 2e-16 *** Demo4.5 38.8173 3.0268 12.824 < 2e-16 *** Endcap 170.9696 14.7156 11.618 < 2e-16 *** Sales.Rep 18.1382 6.1793 2.935 0.003388 ** RegionFL:Endcap -167.5761 17.3875 -9.638 < 2e-16 *** 24

RegionMA:Endcap -180.4750 18.9656 -9.516 < 2e-16 *** RegionMW:Endcap NA NA NA NA RegionNA:Endcap NA NA NA NA RegionNC:Endcap 56.5342 16.6682 3.392 0.000714 *** RegionPN:Endcap -7.5310 16.5885 -0.454 0.649908 RegionRM:Endcap NA NA NA NA RegionSO:Endcap NA NA NA NA RegionSP:Endcap NA NA NA NA RegionSW:Endcap NA NA NA NA Demo:Demo1.3 10.3542 8.2814 1.250 0.211403 --Residual standard error: 28.72 on 1365 degrees of freedom Multiple R-squared: 0.7534,Adjusted R-squared: 0.7498 F-statistic: 208.5 on 20 and 1365 DF, p-value: < 2.2e-16

studentized Breusch-Pagan test data: test BP = 16.8634, df = 26, p-value = 0.9132

Shapiro-Wilk normality test data: test$residuals W = 0.9989, p-value = 0.5397 Model B7 (B6 - Demo:Demo1.3) Revenue.75 = β0 + β1 Region + β2 Endcap + β3 Demo + β4 Demo1.3 + β5 Demo4.5 + β6 Region ∗ Endcap + β7 Sales.Rep lm(formula = Revenue^0.75 ~ Region + Demo + Demo1.3 + Demo4.5 + Endcap + Region * Endcap + Sales.Rep, data = gbData) Residuals: Min 1Q Median -101.852 -19.374 -0.111

3Q Max 18.657 109.131

Coefficients: (6 not defined because of singularities) Estimate Std. Error t value Pr(>|t|) (Intercept) 156.4244 5.2831 29.609 < 2e-16 *** RegionFL -10.8812 6.2082 -1.753 0.079875 . RegionMA -18.7376 5.6414 -3.321 0.000919 *** RegionMW 0.7329 3.8748 0.189 0.850010 RegionNA -14.7481 5.8037 -2.541 0.011159 * RegionNC 14.9972 3.9889 3.760 0.000177 *** RegionPN 2.7203 4.5266 0.601 0.547957 25

RegionRM 8.1731 4.2761 1.911 0.056167 . RegionSO -17.0746 6.2154 -2.747 0.006090 ** RegionSP 12.8824 4.0907 3.149 0.001673 ** RegionSW -14.7274 6.2154 -2.370 0.017950 * Demo 58.7430 3.3818 17.370 < 2e-16 *** Demo1.3 36.7875 2.2554 16.311 < 2e-16 *** Demo4.5 39.0925 3.0194 12.947 < 2e-16 *** Endcap 172.7580 14.6489 11.793 < 2e-16 *** Sales.Rep 17.8919 6.1775 2.896 0.003836 ** RegionFL:Endcap -169.3573 17.3326 -9.771 < 2e-16 *** RegionMA:Endcap -182.8674 18.8727 -9.690 < 2e-16 *** RegionMW:Endcap NA NA NA NA RegionNA:Endcap NA NA NA NA RegionNC:Endcap 54.5464 16.5956 3.287 0.001039 ** RegionPN:Endcap -9.1429 16.5418 -0.553 0.580549 RegionRM:Endcap NA NA NA NA RegionSO:Endcap NA NA NA NA RegionSP:Endcap NA NA NA NA RegionSW:Endcap NA NA NA NA --Residual standard error: 28.73 on 1366 degrees of freedom Multiple R-squared: 0.7531,Adjusted R-squared: 0.7497 F-statistic: 219.3 on 19 and 1366 DF, p-value: < 2.2e-16 studentized Breusch-Pagan test data: test BP = 17.1345, df = 25, p-value = 0.8769 Shapiro-Wilk normality test data: test$residuals W = 0.9988, p-value = 0.4771

Model C1 Revenue = β0 +β1 Sales.Rep+β2 Endcap+β3 Demo+β4 Demo1.3+β5 Demo4.5+β6 Sales.Rep∗Endcap lm(formula = Revenue ~ Demo + Demo1.3 + Demo4.5 + Endcap + Sales.Rep * Endcap + Sales.Rep, data = gbData) Residuals: Min 1Q -940.18 -152.37

Median -9.58

3Q 143.23

Max 827.31

Coefficients: Estimate Std. Error t value Pr(>|t|) 26

(Intercept) 740.043 Demo 453.726 Demo1.3 275.410 Demo4.5 331.758 Endcap -9.924 Sales.Rep 294.568 Endcap:Sales.Rep 1736.923 ---

9.229 26.151 17.199 23.104 55.406 12.993 67.450

80.190 17.350 16.013 14.359 -0.179 22.672 25.751