Expert: Paul Klarreich - 4/16/2007

Question
I am looking at the length-weight relationship in a population of fish, the equation for this is:

W =aL^b where W = weight, a = intercept, L =length and b = slope.

(I think I should be using Loge (base of natural logarithms)

I just don't understand what to do with my data to get it to transform into a logarithm. Is it simply a matter of transforming the length and weight data and then plotting it on a graph? For example, INV 20.0.  

Answer
Questioner:   Emma
Category:  Advanced Math
 
Subject:  Logarithmic transformation
Question:  I am looking at the length-weight relationship in a population of fish, the equation for this is:

W =aL^b where W = weight, a = intercept, L =length and b = slope.

(I think I should be using Loge (base of natural logarithms)

I just don't understand what to do with my data to get it to transform into a logarithm. Is it simply a matter of transforming the length and weight data and then plotting it on a graph? For example, INV 20.0.  
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Hi, Emma,

I'm not sure what you are trying to do, either.  But it sounds as if:

W and L are the variables, and
a and b  are constants.

In that case, you don't have a logarithmic (or exponential) relationship.

HOWEVER, if you are trying to determine values of a and b from a set of pairs (L,W) then what you have is:

W = a L^b
W/a = L^b  

log W/a = b log L

log W - log a = b log L
log W = b log L + log a

(and it makes no difference whether these are natural logarithms or common logarithms)

I think the next step is to take the measurements (you actually caught and measured these fish?  Yuk!) and plot these ordered pairs:

(log L1, log W1)
(log L2, log W2)
(log L3, log W3)
etc.

These should lie on a straight line, and you obtain:

b is the slope of the line
log a is the intercept.

I think you can handle the rest.