This document provides an introduction to MATLAB for people working in marketing. It explains that MATLAB is useful for analyzing large or complex datasets, as it can handle data more efficiently than Excel. The document demonstrates how to use MATLAB through a example of modeling mobile app subscription prices and demand based on survey data. Key functions and operations in MATLAB like vectors, matrices, element referencing, basic math operations, plotting, and linear regression are covered. The example shows how to estimate a linear pricing model that fits the sample data well.

1. MATLAB for
Marketing People
Toshi Takeuchi

2. MATLAB = MATrix LABoratory
Why should you care?
Excel is super intuitive and useful if:
● The data fits the computer screen
● You can manipulate data manually
● Your analysis is relatively simple.
Excel can be a nightmare if:
● The data is too large to fit the computer
screen or manipulate directly
● Your analysis is complex and needs
debugging

3. You already use matrices and
vectors in Excel
This is a matrix
● has rows and columns
This is a vector
● only one row or column
They contain numbers
● numbers are in each cell

4. MATLAB also has rows and columns
like Excel
Functions
Functions
Data
Data
More focus on direct
data manipulation
More focus on manipulating
data via code

5. MATLAB and Excel = BFF
Import data
Export data

6. Before we start:
MATLAB user interface
Command Window: where you type your
command and run your code
Workspace:
where your data
lives as
variables
Editor, but we don’t use it in our
example here, to keep it simple.
Command
History, but
we don’t use
it in our
example here
Files, but we
don’t use it
our example
here.

7. Motivating Example: Price modeling
for a new mobile app
A small scale market research was done for a
new mobile phone app that recognizes music
playing in the background Learn more
After the service was demonstrated, we asked:
“How much are you willing to pay for a monthly subscription?”
Note: this was back in 2003 or 2004, when people still paid for such apps.

8. Creating the sample dataset in
MATLAB
Copy and Paste this:
>> Price = [0;100;200;300];
>> Responses = [304;336;215;145];
Two vectors are now in the Workspace
Double click

9. Data is stored as matrices/vectors in
MATLAB
A matrix with 3 rows, 2 columns
3x2 matrix
A column vector with 3 rows, 1 column
3x1 vector
A row vector with 1 row, 3 columns
1x3 vector
Numbers inside are called “elements”

10. Referencing elements/cells in
MATLAB and Excel
How to reference an element in a matrix “M”
How to reference a cell in Excel
Column 1
Row 2

11. Referencing elements in vectors in
MATLAB
Referencing an element in column vector V1
Referencing an element in row vector V2
You only need one
index for vectors
Indexing starts
with 1 for both
matrices and
vectors

12. Price modeling example
Find the responses for Price=100
Hint: vectors Price and Responses share the
same indexing
Print Price
>> Price
Index into Responses
>> Responses(2)
Answer: 336
It’s the
second
element
Variable contents are printed when variable names are entered without an ending semicolon.

13. What functions do you use in Excel
often?
Sum, Average, Count, Max, Min?
How do you do these in MATLAB?
First, create a new matrix:
>> M = [1, 2; 3, 4; 5, 6]
● Use [ ] to start and end the matrix or vector
● Use comma or space to separate elements
● Use semicolons to start a new row
● Content will be displayed when you enter this
without an ending semicolon.

14. Functions in MATLAB work on
columns and rows
Sum ≈ Sum
Average ≈ Mean
By columns By rows Both
By columns By rows Both

15. Functions in MATLAB work on
columns and rows (continued)
Max ≈ Max
Min ≈ Min
By columns By rows Both
By columns By rows Both

16. Functions in MATLAB work on
columns and rows (continued)
Count ≈ Size
Count ≈ Numel
Both Rows Columns
All elements
● size gives you the dimensions – the number
of rows and columns for matrices
● length does the same for vectors
● numel gives you the number of elements,
regardless of dimensions

17. Practical Advice:
Organize your data well
As in Pivot Tables in Excel, data organization
is a key in MATLAB and many other languages.
MATLAB functions operate on columns by
default, so:
● Each column should represent one label
● Each row should represent one sample
Data Label 1 Data Label 2 Data Label ..n
Data Sample 1
Data Sample 2
Data Sample...m

18. Price modeling example
Find total number of responses
How large was this survey, in terms of number
of responses?
You can just sum Responses
>> sum(Responses)
Answer: 1000
So it is a fairly decent size.

19. Using Matrices and Vectors
Matrix Addition/Subtraction
First, create new matrices:
>> A = [3,8;1,7;1,3];
>> B = [9,4;1,7;4,8];
How do you do A+B? By adding/subtracting
corresponding elements.
Just A+B or A-B in
MATLAB
The dimensions must match between two matrices.

20. Matrix Scalar Multiplication
/Division
How do you do A×3 or A÷3?
By multiplying/dividing each element.
3×A? same. Also A÷3 = A×1/3 = 1/3×A
Scalar = just a number,
≠ a matrix or vector
Just A*3
or A/3 in
MATLAB

21. Price modeling example
Convert responses to ratios
We want to express the responses in terms of
percentages to the total: “at price = x, y% of
people were willing to pay”.
You can just divide each element by the total.
>> shares = Responses/sum(Responses)
Store the result in a
new variable “shares”

22. Price modeling example
Estimate the subscriber demand
Assumption: we can use cumulative sum.
● If you are willing to pay 100, you will still use
the service at 90, 80, or any lower price.
● So at 90, we get both people who are willing
to pay 100 as well as 90, and so forth.
Price Share of responses Cumulative sum
0 0.304 0.145+0.215+0.336+0.304
100 0.336 0.145+0.215+0.336
200 0.215 0.145+0.215
300 0.145 0.145

23. Price modeling example (continued)
Estimate the subscriber demand
How to do it in MATLAB
1. cumsum sums it in a wrong order, so flip the
vector first with flipud
>> subscribers = cumsum(flipud(shares))
2. The result is sorted in wrong order, so flipud
again.
>> subscribers =flipud(subscribers)
3. The result is now stored in subscribers

24. Price modeling example (continued)
Plot the subscriber demand
plot takes vectors for x-axis and y-axis, so use
Price for x-axis and subscribers for y-axis.
>> plot(Price, subscribers)
We got a nice straight
line.
Our pricing model will
be a linear equation!

25. Linear Equation Review
y = αx + β where α = slope, β = intercept
Example: α = -0.25, β = 1
Calculate y for x =
>> y = -0.25*x+1
Hard-coding parameter values like α and β in
your code makes it less flexible, however.

26. Using Matrices and Vectors
Matrix Vector Multiplication
First, create a new vector:
>> B = [2;3];
How do you do A×B? Go row by row with A:
Row 1: 3×2+8×3=6+24=30
Row 2: 1×2+7×3=2+21=23
Row 3: 1×2+3×3=2+ 9=11
It’s simple in MATLAB

27. Matrix Vector Multiplication
(continued)
Pay attention to the dimensions!
3x2 matrix 2x1 vector 3x1 vector
4x3 matrix 3x1 vector 4x1 vector
m x n matrix × n x 1 vector = m x 1 vector
Questions:
1. What do you get if
you multiply 5x2
matrix with 2x1
vector?
2. What happens when
you multiply 7x3
matrix with 4x1
vector?
Answers:
1.5x1 vector
2.Dimension mismatch error
“n” must match.

28. Linear Equation Revisited
Apply Matrix Vector Multiplication
y = αx + β where α = -0.25, β = 1
Calculate y for x = , p =
Add Intercept , then do >> y = x*p
This column
was added to
represent the
intercept
1×-0.25+1×1=0.75
2×-0.25+1×1=0.50
3×-0.25+1×1=0.25
Parameters
are now a
variable, too!
x: became 3x2 matrix
p: 2x1 matrix
● Now the dimensions match!
● Multiplying intercept by 1
doesn’t change the value

29. Linear Equation
How to do this in MATLAB
To add the intercept term to x:
1. ones(3,1) creates a 3x1 vector of 1’s – same
as [1;1;1]
2. Concatenate it with x using [x ones(3,1)]
3. Now you are ready to apply multiplication
>> y = [x ones(3,1)]*p
This makes the code more general and run faster.

30. Using Matrices and Vectors
Matrix Matrix Multiplication
First, create a new matrix:
>> B = [2,1;3,4];
How do you do A×B? Break it down to matrix
vector combinations:
First
Then
In MATLAB,
same as
before
>> A*B

31. Matrix Matrix Multiplication
(continued)
Pay attention to the dimensions!
3x2 matrix 2x2 vector 3x2 vector
2x3 matrix 3x2 vector 2x2 vector
m x n matrix × n x o matrix = m x o matrix
Questions:
1. What do you get if
you multiply 5x2
matrix with 2x3
vector?
2. What happens when
you multiply 5x3
matrix with 2x3
matrix?
Answers:
1.5x3 matrix
2.Dimension mismatch error
“n” must match.

32. Linear Equation Revisited
Apply Matrix Matrix Multiplication
y = αx + β, but now we have multiple possible
parameters.
No problem! Use matrix matrix multiplication.
P =
The code is still x*p, but it is
now really flexible :)
Intercept term added

33. Transpose
You now know the dimensions matter in matrix
calculations
Multiply a 3x2 matrix with another 3x2 matrix?
This won’t work, unless you can flip the second
one into 2x3 matrix.
This flipping is called “transpose”, and you will
use this trick a lot in MATLAB.
Transpose of A is AT
,or A' in MATLAB

34. Price modeling example
Estimate parameters from the data
You can apply linear regression to estimate the
parameters α and β, using polyfit (n=1 for
linear).
>> [p_fit, Stats] = polyfit(Price,subscribers,1)
α = -0.0029
β = 0.9854
Pricing Model: y = -0.0029x+0.9584

35. Price modeling example
Plot the estimate against the data
Compare the estimate to the data
>> y_fit =[Price ones(4,1)]*p_fit'
>> plot(Price,subscribers)
>> hold on
>> plot(Price,y_fit,'r')
>> hold off
The estimate fits well with the data! So our
pricing model is fairly decent.

36. The next step
Now you understand why you want to use
matrices and vectors for large datasets.
To actually learn how to use MATLAB, it is
easier if you watch tutorial videos.
For tutorial videos for beginners, go to
www.youtube.com/user/MATLAB
Enjoy!

37. Appendix I
Summary of the code used
Price modeling example
>> Price = [0;100;200;300];
>> Responses = [304;336;215;145];
>> shares = Responses/sum(Responses);
>> subscribers = cumsum(flipud(shares));
>> subscribers = flipud(subscribers);
>> plot(Price,subscribers)
>> [p_fit, Stats] = polyfit(Price,subscribers,1);
>> y_fit =[Price ones(4,1)]*p_fit';
>> hold on
>> plot(Price,y_fit,'r')
>> hold off

38. Appendix II
An optional assignment
Figure out the revenue-maximizing price from
this pricing model with MATLAB
Hints
Revenue curve should look
like this.
You need more data points
to plot a smooth curve
Type >> 1:10 in MATLAB and see what
happens.