Math Is Fun Forum

python

Member

Registered: 2009-10-27

Posts: 6

Representation of Graph in Equation

Hello Math Gurus,

I am trying to find if there is a way to represent a graph into equation. Not the other way.
Here is my problem, i trying to look for a proper mathematical equation which represents the sales graph Sales vs Geographic area coverage(i cannot say more)!! but this is how it looks, The graph moves upwards along the zero Y axis with '0' X co-ordinates and slowly at some point along the (0,y) co-ordinate starts to drop down as x co-ordinates increases .. as it drops down to a point and then it is y = mx + c straight line. The factor by which the graph relates initially is time and some constant or variable which determines the changes before the curve follows straight line with increasing slope.

The example is this .. (0,0), (0,4),(0,6),(0,8),(2,7), (4,6),(5,5),(7,9),(9,12),(12,14),(14,14),(16,16),(20,20) ... Anything close to it

The challenge is to make a pattern atleast close to the represented initial grpah before it has constant slope or something close.

Note: I am not particular about y=mx+c with something etc, Any thing which resembles this even remotely will be my formula to present the data.
Please any equation which even remotely resembles the this pattern, i am interested.  I will add to the equation some variables which closely resembles this.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Representation of Graph in Equation

Hi python;

I can fit to that set of points but without knowing the underlying law that created them I would caution you about using the equation to extrapolate. You can use it for interpolation but it will be rough at best.

I have made a very, very rough sketch of what intervals I will try to fit for. Let me know if that is OK for your needs.

Last edited by bobbym (2009-10-28 03:13:14)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

python

Member

Registered: 2009-10-27

Posts: 6

Re: Representation of Graph in Equation

Hi bobbym
Thank you. However my upload of spread sheet did not go through here yesterday. It did not throw an error.
I have made that graph already as attached.
Regards to the question, The curve before it becomes predictable stright line with definite slope is observed data over the time and experience of sales and also expected sales.
I am more interested to see if there is any mathematical equation that fits (close and approximate is really OK). If there is a mathematical equation then it will be really useful for some prediction and can say to management with head high a nice way of presenting it.

Can you help me with a equation.

Regards

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Representation of Graph in Equation

Hi python;

I provided the graph to see If the interval between the 2 points I have marked is acceptable.

Do you want to fit an equation for all the points or just the ones between the 2 points I have marked " here "  and  " To here "? In other words I think you want an equation for the interval (0,8) to (12,14).

Once I know what points you are interested in having an equation for then we can talk about what you intend to use for.

Last edited by bobbym (2009-10-28 10:53:33)

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

python

Member

Registered: 2009-10-27

Posts: 6

Re: Representation of Graph in Equation

Hi bobbym.

Thank you very much. Apologies for for not getting your question right.

I observe in my sales report that for many small products, i research in our marketting the trend follows more or less with some variation ofcourse the graph i you have drawn or i enclosed.
So i want to use the equation whcih gives me the probability of sales and gives a far more opportunity to present risks and strategies. So i would like to have the equation which presents entire path (ofcourse need not be accurate at all). Is it possible ..

Please advice.

Thanks in Advance.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Representation of Graph in Equation

Hi python;

I will find the simplest polynomial fit to that data. Here is the problem with what you are trying to do.

Take a look at the second picture it is a freehand sketch of your data points from A to B. The problem is, do you see the peacock of lines after your last point B? These are all possible future outcomes. We do not know what the next month's value will be. Any fit I give you will only choose one of them as it's prediction. It might predict sales are going up but that may be incorrect. Prediction past B based on previous points is not possible and the surest way to get into trouble.

Take a look at the first picture. Does it look familiar? It looks like your model. It was made by flipping a coin and keeping track of it's total number of heads versus tails. It is called a random or drunkards walk. Certainly I could fit an equation to those points too. But would you use that equation to determine what the next flip of the coin will be? Certainly not.

The process of predicting past given data points is called extrapolation. It is never recommended except when the underlying law of the data points is known or surmised. This law is usually a differential equation. I cannot even guess at what the underlying law of your data is as it might even be a random phenomena. That's what picture A is suggesting.

If you are want to predict points between your data set this process is called interpolation and it is much more realiable. So, please inform me of what kind of prediction you expect my model to make, interpolation or extrapolation.

Last edited by bobbym (2009-10-29 05:36:53)

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

python

Member

Registered: 2009-10-27

Posts: 6

Re: Representation of Graph in Equation

Hi Bobbym,
Thank you so much. You are very knowledgeable, you just refreshed to the point i hear the words extrapolation and interpolation. I see immense usages of your help to me.
I am fundamentally, an Software engineering and acting up as a conduit between technical and sales. I am really glad i asked you this question. Honestly i like the idea of uncertainity and very useful in the risk analysis. I see many advantages here. Since i am not a salesman but merely presenting a trend in sales (Actually bit more complex and i made as simpler as i could to avoid confusion to experts like you, who would want to help me). I saw your profile now and since you too come from Engineering background, here are more details. [A complex data of bugs found in a product to that time sales, and phase of the project, feature additions etc are considered to understand the impact of issues found vs testing time and impact on sales at that time]. I am surprised, that both the options chart A and Chart B(with peacock) possibilities are very much possible and sure have seen in my experience. That would be really great if i can somehow manage to make a mathematical equation from the data with variables input from you to use it as relevant. I am finding this very exciting as i could use either one to present the quality of product, possible sales figure for hardcore sales personnal etc.

I have a question here, the possible path it takes on the second chart, is based on a variable parameter ? if so that is vital for me because that could be quality, design gap etc etc.
then i see your chart as blessing because you have given me a variables with any change in them can change the outcome. Can i know the equation.

Thank you so much, this is incidentally second time i am relying on maths to resolve issues. The last time i had polyphonic sound with so many notes, not playable on phone because of MIPS issue, i had sought help of other team member who uses Matlab who gave me a algorithm .. i plotted a graph .. removed the notes in between the graphs to make least possible points on the graph . presto .. it played on the phone... i completed the feature.  This time too thanks to you i could see real help.

I have another question here: Regarding the first chart, which is close to graph i presented, is there a possibility to know a factor, which determines the prediction of next point in the graph please.

Thanks a ton.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Representation of Graph in Equation

Hi python;

Here is the equation. It is very close to the best possible quadratic in the least square sense.

You are very knowledgeable,

No, just rather experienced. These sort questions came up all the time in my livelihood.

I saw your profile now and since you too come from Engineering background, here are more details.

Nope, please don't get angry but physicists and engineers give me hives.

I am finding this very exciting as i could use either one to present the quality of product, possible sales figure for hardcore sales personnal etc.

I enjoy working on it too, but I have to be frank. I would use the equation in a sales presentation to a rival. Or to people who are just interested in a fancy graph. I would never, never, never bet my own dough on it. You are exceeding the capabilities of math ! Having tons of data about the past does not mean that you can predict the future.

i plotted a graph .. removed the notes in between the graphs to make least possible points on the graph . presto .. it played on the phone... i completed the feature.

Good solution!

I have another question here: Regarding the first chart, which is close to graph i presented, is there a possibility to know a factor, which determines the prediction of next point in the graph please.

Absolutely not! The next data point for that chart depends on whether a true coin comes up heads or tails on the next flip. I can give a probability, I cannot predict what the next flip will be. If your data points are random also then spotting trends is impossible.

Last edited by bobbym (2009-10-30 07:54:40)

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

python

Member

Registered: 2009-10-27

Posts: 6

Re: Representation of Graph in Equation

Thanks a ton bobbym,

It's a great help to me.. could i ask you what are things i need to know to come to this all differential equation ?  how to learn it .can i start to learn all again now.. the things i learnt are gone!!
So can i understand with these assumption. Please correct me.
In the equation .. y = .010218 x^2 + .579087 x + 4.42272, the constant 4.42272 would determine one of the those peacock paths. If so in my case that would be constant, in my case (could be quality, etc). 

Thanks a ton.

python

Member

Registered: 2009-10-27

Posts: 6

Re: Representation of Graph in Equation

Hi Bobbym.

Sorry to quote you as engineer, i am not sure i read that some where that you are chemical engineer .. must have read half asleep.. apologies.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Representation of Graph in Equation

Hi python;

It's a great help to me.. could i ask you what are things i need to know to come to this all differential equation ?  how to learn it .can i start to learn all again now.. the things i learnt are gone!!

The tools you need are a good understanding of algebra,analytical geometry and calculus. I don't know what the D.E. that would model your problem is. I probably do not know enough about your field to even find it.

The constant 4.42 is probably the least responsible term for any of those paths. The other two terms are going to drown it out. Anyway, the model I have provided is going to continually increase. This may not actually reflect future conditions as I have warned.

Sorry to quote you as engineer, i am not sure i read that some where that you are chemical engineer .. must have read half asleep.. apologies.

No apologies necessary, Chemistry was my first passion, sorry to be mysterious, but knowing my occupations would lead to a lot of people asking me the kind of questions I don't want to answer.

Last edited by bobbym (2009-10-29 22:16:44)

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.