When marketing meets mathematics – the 4ps goes regression

If you start studying marketing, it is very likely that one of the first things you will encounter is the 4ps concept, also known as “The Marketing Mix”.

“Invented” in the early 1960’s by Dr. Edmund Jerome McCarthy, an American marketing professor and author;

This concept assists marketers in making strategic decisions related to the so-called marketing mix. According to Dr. McCarthy’s, there are four controllable variables to satisfy a company’s objectives on the one hand and to meet the needs of the targeted market on the other hand.

These variables are product, price, place, and promotion.

By carefully adjusting the feature sets of these variables, based on research, knowledge from experiences or simply by brainstorming a company can “create” a successful product.

In almost every general marketing textbook the 4ps are introduced as an analytical tool that enables you to pursue your marketing objectives.

Being a number person, I remember how excited I was when my own professor introduced the marketing mix to us – finally something where you can use numbers and maths, I thought.

How wrong I was! Just like in almost any other textbook, lecture, or scriptum, she presented them with lengthy and wordy descriptions, enhanced by nicely colored tables and endless case studies without a single sign of a number…

Don’t get me wrong. The 4ps (or today the 7ps, which is the Product, Price, Place, Promotion, Physical evidence, and Process) require no numbers to help you to develop your tactics.

And by no means you need to do a single calculation to exploit the concept’s power.

But back then, I just thought, wait – that’s it? 4 variables and no equation? 

So, after reading the whole chapter, I emailed my professor to tell her how puzzled I was (I studied via distance learning).

And then something wonderful happened. Alongside with her reply came some links to research papers about marketing mix modelling.

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It turned out that some marketers, marketing researchers and marketing analysts used linear regression – a statistical approach for modelling the relationship between a response (let’s say the number of sales) and one or more explanatory variables (in our case the 4ps!) – not only to find the best possible mixture of the 4 variables but also to predict changes in sales and other outcomes if you adjust the variables, and they called it “marketing mix modelling”. Apparently, all you needed to do was

  1. To brainstorm over applicable adjustments in your 4ps and then
  2. present these adjustments to your targeted audience (e.g., via a survey) to find out how they would affect the response variable (e.g., numbers of sales, customer loyalty etc.)
  3. Take the data you have gained from your surveys and feed it to your favorite data analytics tool (e.g., Excel) to eventually
  4. come up with a linear regression model

For the actual modelling part, you need some decent statistical and mathematical knowledge, so to not losing every single reader, I stick to the very basics in the hope you are not scared away:

Let’s assume you are the marketing manager of an internationally operating company (let’s call it “Intersell”) which targets b2b customers in the UK, North America, and Spain, and sells air cleaning office plants to small and middle-sized companies.

Let’s further say your survey included the following statements and the participants are then to assign one of the following numbers to each of the statements (this is called a Likert scale):

1 = I totally disagree

2 = I disagree

3 = I somewhat agree

4 = I agree

5 = I totally agree


P1 – Product

Our company prefers small plants rather than large ones

There is not enough space in our office rooms to provide every employer with an own plant

It is important that the plants do not need too much care. E.g., we can’t water them every day


P2 – Price

We need to pay in instalments

We are willing to pay a monthly fee for a watering service via the weekends

We are willing to pay higher prices for very robust plants


P3 – Place

An online shop with nice images and good descriptions is important for the purchasing decision

We don’t buy from single online shops. We would rather prefer Amazon business.

There should be an outlet if we decide to order large amounts of plants, so that one can actually see and touch the plants


P4 – Promotion

Organic rankings at Google are important. A company that does not rank at the first 5-6 positions are not trustworthy enough

Customer reviews are crucial

Free samples of the plants are important

You then conduct a few statistical tests such as multicollinearity test, heteroscedasticity test, F–test, t-test and so on to finally come up with (with the help of your favorite statistics tools such as Excel, SPSS or Python) a regression equation that looks like this one:



In this regression model (or equation) p1 is the product, p2 is the price, p3 is the place and p4 is the promotion.

Once you have your model you can do some very useful things.

To give you a quick example: The factors (0.199, 0.255, 0.143 and 0.145) tell the impact of the single Ps in your marketing mix.

In our (theoretical) example for an instant, the factor for p2 is the highest of all factors, right? From that you can see how important the price related features for the plants are, intersell wants to sell their b2b customers.

Apparently, they are as twice as important as place and promotion.

Again, I don’t want you to believe that the way you will encounter the 4ps concept is less worth it than looking at it from a numerical perspective.

Instead, I wanted you to realize that if you combine mathematics with marketing, you really can get some helpful and interesting insights that might prove beneficial, particularly if you are heading towards a career in digital marketing as I did.

By the way, I still have contact with my former professor who provided me with the links to the research papers.

Currently, we are discussing marketing decision making with the help of fuzzy logic. But this is a different story.

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