Expert: Paul Klarreich - 4/17/2007

Question
PLEASE READ ALL OF THE INFORMATION I'VE PROVIDED - I'M NOT ASKING YOU TO DO MY HOMEWORK, I'M ASKING YOU TO HELP ME UNDERSTAND WHAT MY LECTURER WANTS FROM ME.

The relationship between total length, L, and total weight , W, for nearly all species of fish is expressed by the equation:

W equals aL^b

Values of W usually have been calculated logarithmic (base 10) equivalent:

log W equals log a plus b multiplied by log L

A graph of log W against log L forms a stright line with a slope of b and a Yaxis (log W) intercept of log a. Invariably, b is close to 3.0 for all species.   

I have been asked to: 'plot the length-weight relationship, pooling all the data available and calculate the length-weight relationship (equation above), apllying a suitable data transformation'.

I have plotted the length-weight relationship (raw data without any kind of transformation).

I smy lecturer simply asking me to transform my length data, and the weight data, into logarithmic data and then plotting it? I.e. does he want me to get the LOG10 of all the numbers I have?

Or am I being asked to do an actual calculation before I can plot the data?  

Answer
Questioner:   Emma
Category:  Advanced Math

Hi, Emma,

>> I'll see what I can do, but see comments:
 
Subject:  Logarithms - I need help understanding what is being asked of me
Question:  PLEASE READ ALL OF THE INFORMATION I'VE PROVIDED - I'M NOT ASKING YOU TO DO MY HOMEWORK, I'M ASKING YOU TO HELP ME UNDERSTAND WHAT MY LECTURER WANTS FROM ME.

>> You don't have to shout -- I can read what you wrote even when it is not in capital letters.  Writing in capitals is the online equivalent of shouting and is considered (by me, at least) bad manners.  

...................................
The relationship between total length, L, and total weight , W, for nearly all species of fish is expressed by the equation:

W equals aL^b

>> Yes, you wrote that.

Values of W usually have been calculated logarithmic (base 10) equivalent:

log W equals log a plus b multiplied by log L

>> Yes, that was part of my answer:

log W = log a + b log L

A graph of log W against log L forms a stright line with a slope of b and a Yaxis (log W) intercept of log a.

>> Yes, that was the whole point.

Invariably, b is close to 3.0 for all species.   

>> Well, I wouldn't know about that.

I have been asked to: 'plot the length-weight relationship, pooling all the data available and calculate the length-weight relationship (equation above), apllying a suitable data transformation'.

I have plotted the length-weight relationship (raw data without any kind of transformation).

Is my lecturer simply asking me to transform my length data, and the weight data, into logarithmic data and then plotting it? I.e. does he want me to get the LOG10 of all the numbers I have?

Or am I being asked to do an actual calculation before I can plot the data?   
.....................................
OK, here is what I think you will do.  You will write a table:

>> Warning: use a fixed size font, like Courier, to view this.

Column A         Column B        Column C        Column D
Values of L      Log(L)          Values of W     Log(W)
---------------+---------------+---------------+---------------+
    L1        |   Log(L1)     |      W1       |  Log(W1)      |
    L2        |   Log(L2)     |      W2       |  Log(W2)      |
    L3        |   Log(L3)     |      W3       |  Log(W3)      |
    L4        |   Log(L4)     |      W4       |  Log(W4)      |
etc
---------------+---------------+---------------+---------------+

Now take some ordinary graph paper.  Plot the points that correspond to the values in columns B and D.  Those are the ones that should produce a straight line graph.

Your alternative is to go to a specialty technical shop and purchase something called  log-log graph paper.  Then you can plot the values in columns A and C -- the raw data -- and get a straight line graph.  Since you probably don't know where to get this stuff (neither do I) you will have to do what I suggested -- graph the values in B and D.