Linearizing Data to Fit an Equation - A Homework Guide

[rootX]

Homework Statement

(Data fittings)

for y = D/(x+C)
my book do:
y = (-1/C) *(xy) + (D/C)
I do:
1/y = (1/D)*x + C/D

so using y=Y and X = xy
book finds A and B in Ax+b =y
so, finds an equation that fits the data

It hints that my way is absurd. I really couldn't get what's wrong with using 1/y = ..

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

What exactly are you trying to do? Your formula is not absurd: if y= D/(x+C) then
1/y= (x+C)/D= (1/D)*x+ C/D. y= (-1/C)*(xy)+ (D/C) is also true. Which of those true statements works for whatever you are trying to do, depends on what you are trying to do! And you haven't told us what that is!

 

[rootX]

here's the question:
x, y
1,2
2,5
3,10
4,17
5,26

when using X = xy and Y = 1/y for y = D/(x+C) the least square fit is
y = -17.719403/(x-5.476617)

and when using X = x and Y = 1/y the least square fit is:
y = 1/(-0.106253x+0.4987330)

Determine which fit is best and Why one of the solutions is completely absurd

Since, the book has provided us the formula in the text, so it should be obvious that other one is absurd. I plotted both, and found the first one fits more accurately.

 

[TheoMcCloskey]

RootX - did you really plot out the results using the un-transformed equations? Plot out the original form using the C and D results from the first transformed model. I think you'll see something.

After that, to answer the 'absurd' question; what can you say about linear regression and the [hint] independent variables?