Y1 = 10.1, X1 = 15
Y2 = 25.0 , X2 = 236
Y3 = 32.0 , X3 = 520
Y4 = 35.4 , X4 = 660
Y5 = 55.7 , X5 = 2590

I'm positive there's a connection between Y and X, but I can't seem to figure it out. The closest I got to discovering a pattern was to raise Y to the power of 3.04+-0.05 and then dividing the result by X, the results were more and more accurate the closer to 3.04 I got,but still not nearly good enough.

Anyone have an idea?

Handy dandy Excel came up with this

y = -1E-05x^2 + 0.0455x + 11.449

or

x = 0.014y^3.022

Both are rather close.

-AntonK

What do these values correspond to? Is there a reason to believe they are correlated?

The values are the lengths and the corresponding weights of a kind of grown salmon after t months, counted from their birth, so it's safe to assume they're correlated. There simply has to be a way to express this correlation as a y(x) function.

AntonK, how did Excel come up with that function for you? I have, after much toil come up with a way to calculate which power Y has to be raised to in order for all values to have a common denominator, but it's far too big and complicated to implent in any calculator I have.
It's pretty close for most of the values, not close enough for Y3 to be the exakt function though I think.

I would expect a logarithmic or exponential relationship, but I am unsure of which. Which values correspond to length, which to weight, and what are the units (e.g. pounds ounces grams kilograms inches etc)

Rataxes,

Welcome to sciforums.

The values are the lengths and the corresponding weights of a kind of grown salmon after t months, counted from their birth, so it's safe to assume they're correlated. There simply has to be a way to express this correlation as a y(x) function.

You can't express the growth of a complex organism, like salmon, as one function.

It is likely that there are several functions in the salmons life cycle that determine its growth rate based on its genetic code and its environment.

Tom

Originally posted by ryans
I would expect a logarithmic or exponential relationship, but I am unsure of which. Which values correspond to length, which to weight, and what are the units (e.g. pounds ounces grams kilograms inches etc)
Y corresponds to the length in centimetres, X to weight in grams. Thanks for attempting to help :)

Originally posted by Prosoothus
Rataxes,

Welcome to sciforums.



You can't express the growth of a complex organism, like salmon, as one function.

It is likely that there are several functions in the salmons life cycle that determine its growth rate based on its genetic code and its environment.

Tom
Thanks!

I'd guess that environment isn't a factor since the this kind of salmon is grown in an isolated environment, rather than living in it's natural habitat. Genetic code would be a factor, yes, but perhaps whatever function was used to create the values I listed was based on the average values of thousands of grown salmons?

Regardless, I'm positive that these particular values are based on a function, even if it doesn't correspond 100% with the real length/weight correlation of salmons :)

I've done a few plots, but from a scientific point of view, there is not enough data to draw any conclusive results. In fact the results a bad. I can give you the relationship but I need more results and more parameters namely if you could supply these

The time the measurements were taken, more length and more weight data.

Is the data you gave me taken at equal time intervals?

The thing that i think will be important here is the ratio of the weight to the length, but to prove this I need more data.

Is this for some research?

I've found a rough relationship.

I approximated the fish volume as an ellipsoid and multiplied it by its density, which is approximately that of water. Divide this by the length of the fish, which is 2 times the length of the semi-major axis of the fish to get

W/L=(2*PI/3)d*h where d is the width of the fish and h is its height( viewed from side on) Since the ratio of d to h will remain the same as the fish grows, we get

d/h = C where C is a constant thus

d = C*h

and

W/L =(2*PI/3)C*h*h

W/L=C(2*PI/3)h^2

Thus the ratio of the fish weight to length is quadratic, which is acceptable on the fact that the ratio of the volume of a sphere to its radius is also quadratic. I call C the universal fish parameter, and it is unique for a unique shape of fish.

But this is as a function of the height of the fish. Hang five and I will generalise it further.

Wow, thanks for your efforts ryans! Eager to see if you can work it out. Though it does look almost too complex for the supposed difficulty level this task is on. Granted it's considered a difficult one for this course, but it's still only 11th grade math :)

This is for my final assignment in a math course I'm taking.

I was given seven Y and X values, I could probably get you the two final values later this evening (don't have access to my assignment papers at the moment) but 7 values isn't going to be enough if 5 wasn't, is it?

The correlation between the time t in months and the length is
y = 80(1-0.96^t)

So for Y1, t1 = 3.306
t2 = 9.179
t3 = 12.513
t4 = 14.313
t5 = 29.189

How did you get the weight values?

What country are you in?

Originally posted by ryans
How did you get the weight values?

What country are you in?

I live in Sweden.

Both the length and weight values were part of the assignment details.

I would like to know how, given the length values, you found the values of t?

Oh I'm sorry. The Y(t) function Y = 80 * (1-0.96^t) was also part of the assignment details.

Ok, here's the full table I was given:

Y1 = 10.1cm, X1 = 15g,,, t1 = 3.306 months
Y2 = 25.0cm, X2 = 236g,, t2 = 9.179 months
Y3 = 32.0cm, X3 = 520g,, t3 = 12.513 months
Y4 = 35.4cm, X4 = 660g,, t4 = 14.313 months
Y5 = 43.8cm, X5 = 1250g, t5 = 19.425 months
Y6 = 45.5cm, X6 = 1425g, t6 = 20.603 months
Y7 = 55.7cm, X7 = 2590g, t7 = 29.189 months

I wasn't actually given the values of t, I've just calculated them myself for the corresponding Y values, using the formula above.

I realize if you can't do much more with these numbers than with what you had before, but your effort is appreciated :)