Regression problem: 2 unknowns, Log or nonlog?

[syntax_this]

Dear every -and anybody who expresses interest in this post,

I've browsed this forum a fair bit now, without any luck in finding a response to my query. I apologize in advance if I have posted this in the wrong section, but I didn't know where else it would fit best in.

My problem is the following:

I am replicating "a recipe" from a research paper. I have to basically create some curves, which are used to evaluate other things (It's an Index, basically). Not important - lets focus on the math!

The curves are generated from the following expression, serving as a benchmark curve (as stated in the recipe):

X = b*m^(r-c)

Where the known variables are 'X' and 'r'
Constant is denoted by 'c'
b and m are unknown coefficients.

The dataset consists of two variables, 'X' and 'r', and are both continous numbers of type float.

Other curves are produced by changing the constant manually acoording to other criteria, which isn't the focus of this post.

The benchmark curve is "created by linked data points together through a log regression" according to the recipe, however - I am completely lost on where to start when dealing with two unknown coefficients. I am also confused by the call for 'log regression', as I was under the impression this only applied to binary variables.

I have Excel and STATA at my disposal.

Any help would be much appreciated. Feel free to ask questions!

/A fellow student of the world

 

[Deleted member 4993]

Dear every -and anybody who expresses interest in this post,

I've browsed this forum a fair bit now, without any luck in finding a response to my query. I apologize in advance if I have posted this in the wrong section, but I didn't know where else it would fit best in.

My problem is the following:

I am replicating "a recipe" from a research paper. I have to basically create some curves, which are used to evaluate other things (It's an Index, basically). Not important - lets focus on the math!

The curves are generated from the following expression, serving as a benchmark curve (as stated in the recipe):

X = b*m^(r-c)

Where the known variables are 'X' and 'r'
Constant is denoted by 'c'
b and m are unknown coefficients.

The dataset consists of two variables, 'X' and 'r', and are both continous numbers of type float.

Other curves are produced by changing the constant manually acoording to other criteria, which isn't the focus of this post.

The benchmark curve is "created by linked data points together through a log regression" according to the recipe, however - I am completely lost on where to start when dealing with two unknown coefficients. I am also confused by the call for 'log regression', as I was under the impression this only applied to binary variables.

I have Excel and STATA at my disposal.

Any help would be much appreciated. Feel free to ask questions!

/A fellow student of the world

Linearize the equation using Log:

X = b*m^(r-c)

Log(X) = Log(m) * r + [Log(b) - c * Log(m)]

Your new variables would be

Dependant variable = Log(X)

and the independant variable remains the same (r).

 

[syntax_this]

Linearize the equation using Log:

X = b*m^(r-c)

Log(X) = Log(m) * r + [Log(b) - c * Log(m)]

Your new variables would be

Dependant variable = Log(X)

and the independant variable remains the same (r).

Thanks for the fast reply, and I also tried this path, but it didn't work for me for the following reasons (which I should have originally, stated, sorry!). If I have misunderstood something, I'll be most grateful if you can help me understand. This is where I'm "stuck":

1. A 'standard' curve (for comparative reasons) will be created using known values for X and r, where X=0 and where r is 0<r<1.
Im thinking log(0) will give me problems?

2. The curves are illustrated in an example and look like "ISO curves", something like this: http://structfire.com/images/Iso834.png

3. The coefficients b and m are not known, they are to be obtained through the regression.

I hope my question is comprehensable, and please don't hesitate to ask clarifying questions if needed.

Thanks,

/Fellow student

 

[syntax_this]

Curious Canuck here:

if X=0, then b and/or m = 0 : right?

if r=c, then m^(r-c) = 1 : right?

Solving X = b*m^(r-c):
r-c = LOG(X/b) / LOG(m)
So if X=0, then you'll always end up with LOG(0) : right?

Not important, but why is your equation not shown this way:
X = bm^r / m^c

An example:
if X=2, b=8, m=3, c=2, then
r = LOG(X/b) / LOG(m) + c
r=.73814...

Thanks for your reply.

The equation is not made by me, I am merely trying to replicate it.

Regarding your comment "If X=0, you'll always end up with LOG(0)", that's what I also fear.

That being said, do you have any proposals as to how this equation can be regressed to generate said curves? I am kind of stuck...