Verifying the Credibility of Demand Estimates based on Regression

Analysis

Yuqian Chen

1,† a

Yiming Huang

2,† b

and Yuankai Wu

3,† c

Economics, University of Texas at Austin, Austin, U.S.A.

Business Analysis, City University of Hong Kong, Hong Kong SAR, People Republic of China

Data Science, University of Melbourne, Melbourne, Australia

†

These authors contributed equally

Keywords: 4P Theory, Regression Analysis, Prediction Analysis.

Abstract: We conduct pre-test research to analyze the credibility of the demand estimates, marketing expenses and price

of K-Pack in the future. In order to set up the experimental conditions, three prices 50 cents, 60 cents, 70

cents, and two advertising levels $3 million introduction plan and a $3.5 million plan have been introduced.

Further, two store locations, L1: K-Pack in the bakery section and L2 K-Pack in the breakfast food section

were used to collect data. A 4P marketing principle has been used to describe product, price, place and

promotion. ANOVA, F-test and regression analysis have been used to test the research hypothesis and to

examine the relationship among the research variables. It is identified from the study outcomes that price

and/or store volume will affect monthly average sales for the first month. Furthermore, the coefficient value

indicates that store volume positively predicts average sales, while price negatively predicts average sales,

indicating that price has a statistically significant effect on average sales while the store volume does not have

a statistically significant impact on average sales. Moreover, according to the results of the second month,

price and store volume are insignificant to explain the variation in average sales. Similarly, price and sales

are found to be insignificant in explaining variation in average sales of K-Pack. It is identified from 4P

marketing analysis that the company need to focus on product quality, affordable prices, store locations, and

promotional strategy to increase its sales in future. Overall, these results shed light on credibility of demand

estimates.

1 INTRODUCTION

The 4P theory came into the United States in the 1960s

with the marketing mix theory (E Jerome McCarthy

EIL, H. BORDEN 1960). In 1953, Neil Borden coined

the term “Marketing mix” in his inaugural address to

the American Institute of Marketing, which means that

market demand is more or less influenced to some

extent by so-called “Marketing variables” or

“Marketing elements”. In order to seek a certain

market response, enterprises should combine these

elements effectively to meet market demand and

obtain maximum profits.

The Marketing mix actually consists of dozens of

elements (Borden’s proposed Marketing mix

originally consists of 12 elements), which were

https://orcid.org/ 0000-0001-8536-1216

https://orcid.org/ 0000-0001-7087-8757

https://orcid.org/ 0000-0003-0910-3594

generally summarized by Jerome McCarthy in his

1960 book Basic Marketing into four categories:

Product, Price, Place and Promotion (also known as

4Ps) (NEIL, H. BORDEN 1953). In 1967, Philip

Kotler, in the first edition of his best-selling book

Marketing Management: Analysis, Planning and

Control, further confirmed the marketing mix method

with 4Ps as the core:

 Product: one should pay attention to the

functions of development, require products to

have unique selling points, and put the

functional demands of products in the first

place.

 Price: according to different market

positioning, develop different Price strategies,

product pricing is based on the brand strategy

Chen, Y., Huang, Y. and Wu, Y.

Verifying the Credibility of Demand Estimates based on Regression Analysis.

DOI: 10.5220/0011188800003440

In Proceedings of the International Conference on Big Data Economy and Digital Management (BDEDM 2022), pages 503-509

ISBN: 978-989-758-593-7

503

of the enterprise, pay attention to the gold

content of the brand.

 Distribution (Place): enterprises do not

directly face consumers, but focus on the

cultivation of distributors and the

establishment of sales networks. The contact

between enterprises and consumers is carried

out through distributors.

 Promotion: Enterprises concentrate on the

change of sales behavior to stimulate

consumers, promote consumption growth by

short-term behavior (e.g., discount, buy one

get one free, marketing atmosphere, etc.),

attract consumers of other brands or lead to

advanced consumption to promote sales

growth.

Moreover, regression analysis method, based on

the analysis of the market with the relationship

between independent variable and dependent variable,

establishes a regression equation between variables.

The regression equation is also known as the

prediction model, which can change to estimate the

dependent variable relationship characterized by

correlation according to the number of independent

variables in the prediction period. As a consequence,

the regression analysis prediction method is a kind of

important market forecasting methods (R.A Fisher

2005). When we forecast the future development

status and level of market phenomena, if one can find

the main factors affecting the market forecast objects

and obtain their quantitative data, it is feasible to

construct a high accuracy regression analysis and

prediction method to forecast. It is a concrete,

effective and practical method of market prediction.

The 4P marketing mix strategy is frequently

applied in numerous real lives start-up business plans.

For example, McDonald’s Corporation’s marketing

mix (4Ps) involves various approaches that meet

business concerns in different fast food restaurant

markets around the world, the company’s corporate

standards for productivity are implemented in the

management of each company-owned and franchised

location. In this article, we will review the progress

made in the last few years (George S. Spasis,

Konstantinos Z. Vasileiou. 2006, Muhammad

Hasbullah Hadi Bahador 2019, Baker, Saren, M. eds.,

2016, Resnick, Cheng, Simpson, Lourenço, 2016,

Ferrell, Hartline, 2012, GbolagadeAdewale, Oyewale,

2013, Lamb, Hair, McDaniel, 2011, Eason, Noble,

Sneddon 1955, J. Clerk Maxwell 1892, Jacobs Bean

1963, Yorozu, Hirano, Oka, Tagawa 1982, Young

1989).

The rest part of the paper is organized as follows.

The Sec. 2 will introduce the data origination and

processing as well as regression models. The Sec. 3

presents the results of the regressions for four months

separately. Subsequently, the Sec. 4 demonstrates the

explanation of results as well as lists the limitations.

Eventually, a brief summary is given in Sec. 5.

2 DATA & METHOD

This data here is collected by Mary, the marketing

director of SMARTFOOD during a four-month test

market study at 24 grocery stores in four different

cities. The data consisted of average sale per month

for 4 months (24 each) from store audits of the stores

in each city. The mean average sales of each of the

four months at the time of data collection were 161,

255, 278, 280, respectively.

The original data obtained from the market study

were already treated for missing values and screened

for outliers. In the current study, the descriptive

statistics for all the variables were examined to make

sure they fell within acceptable range and skewness

is one such statistic that was carefully looked at.

Histograms were obtained for all the variables whose

skewness statistic was greater than 1 to have a

pictorial view of the distribution of the variables.

Information about the independent variables and how

they were measured is provided in Table 1.

Table 1: Summary of the independent variables with sample

means and standard deviation.

Variables Scale M SD

Price 60 8.34

Advertising

3 million 0

3.5 million 1

Location

Backery 1

Breakfast 0

Store

Volume

49 5.61

The dependent variable in this study was Average

Sales per Month and it was measured by a four-month

market study test. Sales of K-Pack were measured

using store audits from a panel of stores in each city.

The independent variables were price and store

volume. The dummy variables considered in the

present study are advertising, location of K-Pack

within each store, and city index. These variables that

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504

were based on recommendations from previous

research were selected for use in this study.

Marketing mix variables were: price, advertising, and

location of K-Pack within each store. The price,

measured the price of a single piece of K-Pack. The

variable, advertising, measured the money that spend

on advertising. Store location measured the place that

K-Pack put in the store. To be specific, there are three

prices: 50 cents, 60 cents, 70 cents; two levels of

advertising: a simulation of a $3 million introduction

plan and a $3.5 million plan; and two store locations:

K-Pack in the bakery section versus K-Pack in the

breakfast food section. Location measured as 1 if K-

Pack in the bakery section, 0 if K-Pack in the

breakfast food section. Prices and location were to be

varied across stores within a city while advertising

was varied across cities. Advertising was in the form

of spot TV ads. Advertisement levels were selected

that would simulate on a local basis the impact of

national ads at the level of $3 million and $3.5

million. Advertising measured as 1 if the impact of

national ads at the level of $3.5 million, 0 if the

impact of national ads at the level of $3 million.

3 RESULTS

To investigate if price and volume interact with each

other in determining sales, the following results are

presented accordingly. In detail, the multiple linear

regression model is applied to address the issues with

the p-values for the regression weights. In other

words, a regression model is to be developed for

predicting sales. This regression model is then to be

used for determining the right marketing mix. The

price should be treated using dummy variables, which

are advertising and location. The results of the first

month regression statistics and analysis are displayed.

Table 2: Regression statistics.

Regression Statistics

Multiple R 0.577

R Square 0.333

Adjusted R Square 0.270

Standard Error 52.244

Observations 24

Table 3: ANOVA result.

ANOVA df SS MS F Significant F

Regression

Analysis

2 28670.5 14335.25 5.252 0.014

Residual 21 57319.13 2729.482

Total 23 85989.63

Table 4: Regression analysis output.

Coefficients

Standard

Error

t Stat

P-

value

Lower

95%

Upper

95%

Lower

90.0%

Upper

90.0%

Intercept 254.232 106.739 2.38 0.026 32.255 476.21 70.560 437.903

Price -4.413 1.391 -3.172 0.004 -7.305 -1.520 -6.806 -2.019

Store Volume 3.541 2.068 1.713 0.101 -0.7586 7.8414 -0.0166 7.099

In the Tables 2-4, the regression statistics,

standard errors and p-values for all the predictors are

given. The results of the first month shows that 27%

of the variance in average sales can be accounted for

by price and store volume, F (2,21) =5.252. The

probability that the null hypothesis in our regression

model cannot be rejected is 1.4%. Looking at the first

month unique individual contributions of the

predictors, store volume (t=1.713, p=0.101)

positively predicts average sales, while price (t=-

3.172, p=0.004) negatively predicts average sales.

This suggests that price has a statistically significant

effect on average sales. Besides, unlike what we

hypothesized, store volume does not contribute to

average sales. The results of the second month

regression statistics and analysis are displayed in the

following.

Verifying the Credibility of Demand Estimates based on Regression Analysis

505

Table 5: Regression statistics.

Regression Statistics

Multiple R 0.101

R Square 0.0102

Adjusted R Square -0.084

Standard Error 59.553

Observations 24

Table 6: ANOVA Results.

ANOVA df SS MS F

Significance

Regression

Anal

sis

2 764.112 382.056 0.107 0.898

Residual 21 74478.846 3546.611

Total 23 75242.95

Table 7: Regression Analysis Output.

Coefficient

Standard

Error

t Stat

P-

value

Lower

95%

Upper

95%

Lower

90.0%

Upper

90.0%

Intercept 199.662 121.672

1.64

0.115 -53.369 452.693 -9.704 409.029

Price 0.217 1.585

0.13

0.892 -3.079 3.514 -2.511 2.945

Store

Volume

0.87 2.357

0.36

0.715 -4.0313 5.772 -3.185 4.926

In the Tables 5-7, the results of the second month

shows that the explanation towards response is pretty

low or negligible, which means insignificance of

price and store volume, F(2,21)=0.107. The

probability that the null hypothesis in our regression

model cannot be rejected is 89.8%. The results of the

second month unique individual contributions of the

predictors shows that both price (t=0.137, p=0.892)

and store volume (t=0.369, p=0.715) positively

predicts average sales. This suggests that unlike what

we hypothesized, both price and store volume do not

have a statistically significant contribution to average

sales. The results of the second month regression

statistics and analysis are displayed.

Table 8: Regression statistics.

Regression Statistics

Multiple R 0.381

R Square 0.146

Adjusted R Square 0.065

Standard Error 62.283

Observations 24

Table 9: ANOVA Results.

ANOVA df SS MS F Significance F

Regression

Analysis

2 13914.542 6957.271 1.793 0.191

Residual 21 81463.082 3879.194

Total 23 95377.625

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Table 10: Regression analysis output.

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 90.0% Upper 90.0%

Intercept 222.179 127.249 1.746 0.095 -42.451 486.808 3.215 441.142

Price -2.370 1.658 -1.429’ 0.168 -5.819 1.078 -5.223 0.483

Store Volume 4.087 2.465 1.658 0.112 -1.038 9.213 -0.154 8.239

In the Tables 8-10, the results of the third month

shows that 6.5% of the variance in average sales can

be accounted for by price and store volume,

F(2,21)=1.793. The probability that the null

hypothesis in our regression model cannot be rejected

is 19.1%. According to the third month unique

individual contributions of the predictors, store

volume (t=1.658, p=0.112) positively predicts

average sales, while price (t=-1.429, p=0.168)

negatively predicts average sales. This suggests that

unlike what we hypothesized, both price and store

volume do not have a statistically significant

contribution to average sales. The results of the

second month regression statistics and analysis are

displayed.

Table 11: Regression statistics.

Regression Statistics

Multiple R 0.321

R Square 0.103

Adjusted R Square 0.0179

Standard Error 62.661

Observations 24

Table 12: ANOVA results.

ANOVA df SS MS F Significance F

Regression

Analysis

2 9502.837 4751.418 1.210 0.318

Residual 21 82454.121 3926.386

Total 23 91956.958

Table 13: Regression analysis output.

Coefficients

Standard

Erro

t Stat P-value

Lower

95%

Upper

95%

Lower

90.0%

Upper

90.0%

Intercept 306.232 128.021 2.392 0.026 39.998 572.466 85.941 526.523

Price -2.441 1.668

1.463

0.158 -5.911 1.028 -5.312 0.429

Store Volume 2.476 2.479 0.998 0.329 -2.681 7.634 -1.791 6.744

In the Tables 11-13, the results of the forth month

shows that 1.79% of the variance in average sales can

be accounted for by price and store volume,

F(2,21)=1.21. The probability that the null hypothesis

in our regression model cannot be rejected is 31.8%.

The results of the fourth month unique individual

contributions of the predictors shows that store

volume (t=0.998, p=0.329) positively predicts

average sales, while price (t=1.463, p=0.158)

negatively predicts average sales. In this case,

different from what we hypothesized, both price and

store volume do not have a statistically significant

contribution to average sales.

4 DISCUSSION

A multiple linear regression analysis has been used in

the study to predict monthly average sales, by using

the price and store volume of K-Pack. It was

hypothesized based on secondary research that price

and store volume significantly affect average sales. In

this regard, four regression models have been

performed for four different months. It is identified

from the results that the first regression model was

significant at a 10% significance level as the p-value

associated with the F-statistic is less than 0.05. The

Verifying the Credibility of Demand Estimates based on Regression Analysis

507

R-square value indicates that price and store volume

explained only 27% variation in the average sales of

K-Pack and 73% of the variation remained

unexplained. Hence, there may be other factors (e.g.,

physical environment, store location, promotional

expenses, the attitude of staff, and number of

alternatives) that might explain variation in average

sales of K-Packs and all these factors ought to be

taken into consideration for a good regression model.

Further, the coefficient value indicates that store

volume positively affects the average sales, while

price negatively predicts average sales. It implies that

increasing the price of K-Pack would decrease its

sales while increasing the store volume increase its

sales. This p-value corresponding to price is less than

0.10, while it is greater than 0.10 for store volume,

hence it can be inferred price has a statistically

significant effect on average sales, while store

volume does not contribute to average sales.

With regard to the second month’s data and

analysis, it is identified that price and store volume

does not explain a significant proportion of variation

in the average sales of K-Pack. Further, the

significant F-value is also greater than 0.10, hence the

regression model is insignificant at a 10%

significance level. The coefficient values of the

second-month price and store volume are found out

to be positive, which means that increasing the price

and store volume in the second month led to an

increase in the sales of K-Pack. However, the p-

values indicated that both the variables are

insignificant at a 10% significance level as the p-

value of both the coefficient is greater than 0.10.

The value of the third month’s estimate shows that

price and store volume explain only a 6.45% variation

in the average sales of K-Packs, while both of the

variables are statistically insignificant to predict the

average sales of K-Packs as the p-value for the

corresponding coefficients is greater than 0.10.

Similarly, it is also found for the fourth month’s

estimate that both price and store volume does not

statistically significant to explain variation in average

sales as the p-value for the model and coefficients is

greater than 0.10. The reason may be small sample

size, due to which it does not represent the

characteristics of population accurately.

In the case of advantages by using marketing-mix,

the 4P Marketing mix analysis does simplify and

combine the 4P into one, which makes the marketing

easier to operate and control. Moreover, the

marketing mix strategy allows the company to

implement its marketing plan based on its current

resources and its customer needs.

Nevertheless, the marketing-mix strategy does not

count the qualitative issue, such as employee’s

behavior and contingency can be occurred, e.g.,

accidentally adding too much carbohydrate due to a

machine breaking down. Last but not least, it is time-

consuming and requires a lot of funds to invest in the

short run, in order to plan a proper strategy design,

analysis and efficient innovative bakery machines for

producing low-carbohydrate food.

Back-of-envelope calculation uses estimated or

rounded numbers to develop a ballpark figure

quickly. The 4P marketing-mix method is definitely

more accurate compared to back-of-envelope

calculation, whereas it required a much longer time

for planning.

Lastly, in the case of qualitative issues, one can

ask the customers to do a simple and straightforward

online survey with coupons provided for SMART

FOOD’s product, in order to collect customers’

comments and thus develop another method to avoid

these problems.

5 CONCLUSIONS

In summary, to predict monthly average sales based

on the price and store volume of K-Pack, the

credibility of the demand estimates, marketing

expenses and price of K-Pack in the future. According

to the findings, price and store volume significantly

affect the monthly average sales. It is also identified

that store volume positively affects the average sales,

while price negatively predicts average sales. It

implies that the CEO of the SMARTFOOD company

should make K-Pack affordable prices by setting

reasonable prices. In addition, the CEO of the

company also need to think about expanding the store

price in order to increase the average sales of the

company. However, the study results also reflected

that only price is found out to be a significant

predictor of the average sales for the first month. For

the other three months, price and store volume does

not affect the average sales. Nevertheless, the results

of the study may be affected by several random

causes and external factors, e.g., salesman attitude,

discounts, number of alternatives, which might have

impacts on the average sales of the company. The

findings of the research also reflected that the CEO of

the SMARTFOOD company needs to focus on

improving the product quality, promotional strategy,

price, and store locations to increase its sales

in future.

In brief, these results offer a guideline for marketing

director of SMARTFOOD company to test the

credibility of the demand estimates of K-Packs.

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