Combining Equations with Different Domains: A Mathematical Challenge

[kimori]

Please I need to combine these three equations to be one, though they have different domains, what can I do?
RxLevel = -0.87RxQual - 72
RxLevel = -0.013Dis - 58
RxLevel - -0.2MOP - 81
Where RxQual, Dis and MOP are variables

 

[chiro]

Please I need to combine these three equations to be one, though they have different domains, what can I do?
RxLevel = -0.87RxQual - 72
RxLevel = -0.013Dis - 58
RxLevel - -0.2MOP - 81
Where RxQual, Dis and MOP are variables

Hey kimori and welcome to the forums.

If you combine these equations into one single expression you won't actually get a function by just an implicit relationship. Functions that are explicit take a set of things and return a single output, so for a function you will usually take two of the three and return the one that is left over.

In terms of the relation just set them all equal and move all them to one side. In this case you have:

A = -0.87RxQual - 72, B = 0.013Dis - 58, C = -0.2MOP - 81. So when you have A = B = C you have A - B = 0, B - C = 0. Since 0 - 0 = 0, we have A - B - (B - C) = A - 2B + C = 0 - 0 = 0.

There are lots of different combinations, but this is one of them.

 

[haruspex]

Please I need to combine these three equations to be one, though they have different domains, what can I do?
RxLevel = -0.87RxQual - 72
RxLevel = -0.013Dis - 58
RxLevel - -0.2MOP - 81
Where RxQual, Dis and MOP are variables

Kimori, I get the feeling you mean RxQual, Dis and MOP to be independent variables, yet you provide equations which effectively make everything one variable. Could you explain the physical background to them to ensure we're understanding the issue correctly?

 

[kimori]

The issue is that I was doing a research and trying to establish how RxQual, Dis and MOP are affecting RxLevel. After the data collection of these three parameters using a drive test I wanted to develop a mathematical model which shows how there parameters are affecting RxLevel. I used MATLAB to formulate these three equations. Now I want to come up with a single equation which shows how these three parameters are affecting RxLevel at the same instantaneous time. All these parameters RxQual, Dis and MOP are also dependent parameters.

If it not clearly, please ask for mor elaboration

 

[haruspex]

I'll put the question more directly: when you say RxLevel = -0.87RxQual - 72, is that holding Dis and MOP constant (at what values?), or does varying RxQual cause Dis and MOP to vary in a fixed manner?

 

[kimori]

The fact is that when one parameter is analysed the others remain constant i.e., when RxLevel = -0.87RxQual - 72 the other parameters are regarded as being constant at all values and that is why I have come up with three different linear equations

 

[haruspex]

The fact is that when one parameter is analysed the others remain constant i.e., when RxLevel = -0.87RxQual - 72 the other parameters are regarded as being constant at all values and that is why I have come up with three different linear equations

OK, that's what I suspected. That means the three equations are not generally correct. Each one is only true for a specific pair of values of the other two independent variables (and I did ask what those values were).
For convenience, I'm going to abbreviate your variables as L, Q, D and M.
The general form of the relationship may be:
L = a*Q*D*M + b*Q*D + c*D*M + d*M*Q + e*Q + f*D + g*M + h
Suppose you obtained the equation L = α*Q + β with D fixed at D_Q and M fixed at M_Q. Then
a*D_Q*M_Q + b*D_Q + d*M_Q + e = α
c*D_Q*M_Q + f*D_Q + g*M_Q + h = β
Similarly for the other two equations you had. This gives a total of 6 equations, but you have 8 unknowns. So unfortunately you do not have enough data. You need to obtain a second equation for at least one of the independent variables using a different setting of the other two.

 

[Ratch]

kimori,

Please I need to combine these three equations to be one, though they have different domains, what can I do?
RxLevel = -0.87RxQual - 72
RxLevel = -0.013Dis - 58
RxLevel - -0.2MOP - 81
Where RxQual, Dis and MOP are variables

RxLevel = -0.87RxQual - 72
RxLevel = -0.013Dis - 58
RxLevel - -0.2MOP - 81
_______________________

3*RxLevel = (-0.87RxQual - 72)+(-0.013Dis - 58)+(-0.2MOP - 81)

And there you have it. One equation with all the variables. Just simplify.

Ratch

 

[haruspex]

RxLevel = -0.87RxQual - 72
RxLevel = -0.013Dis - 58
RxLevel - -0.2MOP - 81
_______________________

3*RxLevel = (-0.87RxQual - 72)+(-0.013Dis - 58)+(-0.2MOP - 81)

And there you have it. One equation with all the variables. Just simplify.

Ratch

Really? So why not
4*RxLevel = 2*(-0.87RxQual - 72)+(-0.013Dis - 58)+(-0.2MOP - 81)
or
7*RxLevel = (-0.87RxQual - 72)+2*(-0.013Dis - 58)+4*(-0.2MOP - 81)
etc?

If you read back through the posts, I think we've established that the original statement of the problem is misleading.

 

[kimori]

I am becoming more confused as Batch comes with one simple equation 3*RxLevel = (-0.87RxQual - 72)+(-0.013Dis - 58)+(-0.2MOP - 81), which contains all three variables by just adding them up while haruspex puts it in a more complicated way by asking why not 4*RxLevel = 2*(-0.87RxQual - 72)+(-0.013Dis - 58)+(-0.2MOP - 81) or
7*RxLevel = (-0.87RxQual - 72)+2*(-0.013Dis - 58)+4*(-0.2MOP - 81) etc?
For me this is a total confusion.

Again, haruspex suggests another complicated way with a lot of constants such as a, b, d, e, etc., which I don't know how to go about in order to come up with a single expression which shows the linear relationship between RxLevel, RxQual, Dis and MOP at the same instance!

 

[cocopops12]

Is it valid to take linear combinations of the three equations above? since all the variables are linear, and RxLevel depends on 3 independent variables.

can we say:
RxLevel = C1(-0.87RxQual - 72) + C2(-0.013Dis - 58) + C3(-0.2MOP - 81)

?

 

[haruspex]

Is it valid to take linear combinations of the three equations above? since all the variables are linear, and RxLevel depends on 3 independent variables.

If, as appears, these are 3 independent variables, not even the three original equations are really correct. Each is only valid for specific values of the other two variables, and we don't even know what those values were (kimori may know).

can we say:
RxLevel = C1(-0.87RxQual - 72) + C2(-0.013Dis - 58) + C3(-0.2MOP - 81)
?

No. As I pointed out, the information provided is consistent with the full equation containing terms like constant * RxQual * Dis * MOP.
kimori, I'm sorry you don't like my answer, but it is the only way. You need the following additional information:
- for each of the three equations, what were the values of the other two independent variables?
- at least one more equation; e.g. if the RxQual equation you have is for Dis = Dis₀ and MOP = MOP₀, get another equation using different values for Dis and MOP.
If you can supply these I'll help you derive the full equation.

 

[cocopops12]

Thanks haruspex

so what i understand is that we need to know the domain of each independent variable and also some initial conditions to determine the constants?

 

[kimori]

haruspex, I am not ver good in mathematics and that is why may be either I do not understand what you want from me or we don't understand each other. I think it is better you give me your e-mail address so that I can send you the data in excel file format with detailed explanation as an attachment and tell you exactly what I was trying to do. In this way I think you will help me with the mathematical expression I need!

 

[haruspex]

it is better you give me your e-mail address so that I can send you the data in excel file format with detailed explanation as an attachment and tell you exactly what I was trying to do. In this way I think you will help me with the mathematical expression I need!

Done. Check your notifications.

 

[haruspex]

so what i understand is that we need to know the domain of each independent variable and also some initial conditions to determine the constants?

We need enough datapoints.
Given that the partial derivatives are all constants, there are 8 constants to be determined, as indicated. (With n independent variables there would be 2ⁿ.) The simplest would then be to take two values of each independent variable and find the value of the dependent variable for each of the 2ⁿ combinations of these values.

 

[kimori]

Done. Check your notifications.

Unfortunately, I have not seen it

 

[haruspex]

Unfortunately, I have not seen it

It was definitely sent. You're looking here: https://www.physicsforums.com/usercp.php ?
You should see that link at top right, just under the Quick Links pull-down and "Welcome, kimori".

 

[kimori]

haruspex, I have sent the data collected in your e-mail and in case more clarification is needs please let me be informed