today we'll go through chapter 1 an introduction to quantitative analysis
now for quantitative analysis we need some input which is in the form of raw
data so using the raw data when we do the quantitative analysis the idea is to
get some useful information out of it information is something which can be
used or which can be implemented for some business benefit suppose you have
$100,000 with you you may want to make a decision like how would you invest this
money you could have so many options let's say you have two options one is
you put the money in a bank in the form of CD or in stocks nowadays actually CDs
not earning much return like the percentage interest you get is very very
low and if you have seen for last several months the stock market has been
doing really well but there's always a risk in stock markets that you could
lose lot of money whereas in CD it is much more safe so both have some benefit
some positives and some negatives to make a decision obviously some kind of
analysis is needed like how much return you can get or how much risk you have
and then once you get a proper information or insight from quantitative
analysis then you can use that for making a decision like what you should
do so when we are doing quantitative analysis you may come across two
different type of variables or factors one is quantitative and another is
qualitative quantitative obviously is something where you can convert that
information easily into a number like height length weight or profit loss of a
company so all those are quantitative variables and qualitative variables are
more subjective it could be opinions or ratings and so
on so if we are dealing with quantitative variables this process can
easily be automated the process of doing quantitative analysis
based on raw data and getting information can always be automated now
let's go through the general steps that are involved for doing quantitative
analysis first step is to define a problem those are the situations
defining a problem could be very very straightforward and sometimes it could
be tricky some problems are very complex one care one has to take is not to
confuse symptom for a problem so many times you may come across symptoms and
think that actually that is a problem like if I go to doctor and if I say that
I have a headache what doctor it is only a symptom so doctor may collect some
data they may check my temperature or blood pressure and ask me some questions
basically to understand what the real problem is so for the doctor headache is
not really a problem but it is a symptom so understanding
or defining a problem is always first step in any quantitative analysis next
step is to develop a model so that is step number two in quantitative analysis
math models are very common in popular and they have several advantages you can
easily manipulate math models to maybe optimize the parameters and so
on so it's not that expensive once we developed model you can always apply
different methods to optimize it let's take one example so let's say one of the
variables is number of TV ads that appear during a week on TV and
y-axis let's say is sales of a car like how many cars gets sold during that week
so in this case if we represent this variable TV ads by X so this X is
called decision variable it is also called controllable variable because
this is the variable on which we have control like we can control how many TV
ads to give and sales is something which is obviously not controllable not that
much controllable we do not have direct control over it and TV ads is also called
independent variable if you recall POM 212 business statistics so
X is your independent variable and sales in this case is the dependent variable
because it depends on how many TV ads are given so you could have a model
something like this like if you collect data you may get this kind of pattern
and this model can be optimized like you can always find what is the maximum
sales you can get and what is the number of TV ads that can give that value
because in this simple example you can see after this point as you increase
number of TV ads the sales are not increasing significantly so once we have
a model we need to get data or acquire data so this is the third step now
getting data is very very important and not only getting data but one has to get
quality data so data quality is very very critical in any analysis because if
data quality is not good no matter how sophisticated quantitative skills or
model you use it is not going to really help if the data quality is not good so there
is a computer terminology you may have come across which says garbage in and
garbage out so if data quality is not good then all
this process will not yield desired outcome so once you have good quality
data you can develop solutions so this is step number four now for finding
solutions there are so many ways we do it for example you can find optimal
values for the model so you can optimize a model and find optimal parameters that
will yield the desired outcome there are trial and error methods so if
the model is very complex for example you may want to try and find a solution
by trial and error so basically you try with something and it may not work out
then try something else so keep on trying till you get desired outcome
and another approach for finding solution is complete enumeration so
complete enumeration is basically like hundred-percent inspection
you try everything and if you have a model and if you are using a computer
then going through all possible solutions is not that difficult so once
a solution is developed obviously one has to test it see whether it works so
once you test the solution which is step number five you also analyze the solution
so analyzing solution which is step number six one of the common methods is
sensitivity analysis what is done in sensitivity analysis is very simple you
try to change your model parameter slightly and see how the solution
changes because in real life your data could be slightly different or model
parameters may not be exactly same all the time there could be some variations
so basically you want to see how sensitive your model is to such small
variations that might occur in real practice so if your model or your
solution is very very sensitive to even small changes in the model then
obviously that's not a good situation to have because when we implement the
solution these small changes are bound to happen
so nothing is going to remain like as it is all the time there will be some
changes small changes here and there in the model parameters and if the solution
changes significantly in response to those small changes obviously it is not
a very good solution so sensitivity analysis helps to determine how robust
the model is so once the solution is analyzed then obviously it has to be
implemented so this is the last step step number seven so if all the previous
steps are done properly implementation could be very straightforward but
sometimes it could be tricky especially if it involves some changes to where the
things are done by people so people could develop a resistance to that
change and the reason could be that maybe the solution demands
different skill level and different technology which people are not comfortable with so
one has to take into account all those things before a solution is implemented
and one good way actually to address this is to involve those people who will
be implementing the solution from beginning so if they have a stake and
they have understanding what's going on from the beginning and if they are not
just brought into the picture only at step number seven so they may have a
better understanding and they may be more willing to help during
implementation of solutions so these seven steps are seven general steps that
you might come across during quantitative analysis and as we go
through various chapters in this course many of the things will be highlighted
from time to time
let me take one example of a model that is very common in business so you have
this model called profit equals revenue minus expenses p equals s times X
minus expenses include fixed costs F plus variable cost and control variable
X so in this model X is number of items sold S is the selling price per item
F is the fixed cost V is a variable cost so generally it is very common to
try and find out what will be a break-even point break-even point or BEP
is achieved for profit equals zero so basically in the above equation if we put P
equals zero and then solve for X so what you are going to get is zero equals so
if I open the brackets you have minus F and minus V times X so if I keep X
variables on one side and take other things on the other side so F comes this
side becomes positive and suppose X is common and then you have s minus V so
your equation basically looks like this F over s minus V equals x so this is the
break-even point you need at least X items to break-even and anything more
than that obviously is profitable so if you take example of the class size in a
university so class size is important because if the class size is too small
so obviously the class may be running at a loss for the university and to
figure out like what is the break-even point in terms of number of students
enrolled in the class is very useful but to find that value of x where there
is a break-even point we need all these values like F S and V so these are
called parameters this S F and V are the parameters of this model because we
need data on that before we can figure out break even point in terms of class size
so let's say s which is the selling price per item so based on the tuition
and all that let's say it is 300 dollars so I am just making up some numbers it may
not be accurate this is this for illustration suppose you want to find
fixed cost now to find fixed cost you have to see
what are the things or variables or factors that remain fixed from one
semester to other semester and it is not dependent on how many students are there
in the class so for example not every semester we change all the furniture in
the class or tables or chairs or the buildings so they remains fixed whether
we add one more student to the class or two more student to the class we are not
changing certain things with every student or every semester so building is
fixed furniture is fixed the technology used in class is fixed so let's say it
is about fifteen hundred dollars now variable cost V is something that
changes with every additional student so for example if I have 10 student in the
class and if I have to distribute handouts so I need to print them and
then bring to the class so there is some cost involved with that for every
additional student I will have to print additional hand out so that will increase
the cost so let's say for a class that type of cost is about 50 dollars per
student you will notice that getting these numbers are not straightforward
so acquiring this data is not very easy one has to go into lot of details in
figuring out how to include a particular expense and will it be part of the fixed
cost or variable cost or should it be s so once you have good quality data for s
F and V then finding the solution is not very difficult so you just apply the
formula so 1500 divided by 300 minus 50 so you get 6 which means for the
university class will run profitably only if the number of students in the class
are more than 6 so if they are exactly 6 then we break even if it is less than 6
so obviously the class will run at a loss
so administration can basically make a decision whether to run that class or
cancel the class because of low enrollment