Hi quick question: Does a line of best fit HAVE to be a straight line? because I have a set of data that look like they form a logarithmic function.

Attachment 27539

see, that does not look good. Any ideas or tips?!

Thanks for your time

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- Mar 15th 2013, 10:13 AMsakonpure6Line of Best Fit
Hi quick question: Does a line of best fit HAVE to be a straight line? because I have a set of data that look like they form a logarithmic function.

Attachment 27539

see, that does not look good. Any ideas or tips?!

Thanks for your time - Mar 15th 2013, 10:51 AMHallsofIvyRe: Line of Best Fit
Yes, a

**line**of best fit has to be a**line**which is just a short way of saying**straight**line. All lines are straight! - Mar 15th 2013, 11:05 AMsakonpure6Re: Line of Best Fit
:) thank you.

- Mar 15th 2013, 03:07 PMProve ItRe: Line of Best Fit
Yes, your line of best fit does have to be a line. HOWEVER, since your data looks logarithmic, then a logarithmic transformation to the data would be appropriate to make your data linear.

Note that the model $\displaystyle \displaystyle \begin{align*} y = A + B\log{(x)} \end{align*}$ might be appropriate. If we let $\displaystyle \displaystyle \begin{align*} X = \log{(x)} \end{align*}$, this gives $\displaystyle \displaystyle \begin{align*} y = A + B\,X \end{align*}$, a LINEAR function.

So what you can do is to evaluate $\displaystyle \displaystyle \begin{align*} X \end{align*}$ for each of your observed x values, and then do a least squares linear regression on the two sets $\displaystyle \displaystyle \begin{align*} X \end{align*}$ and $\displaystyle \displaystyle \begin{align*} y \end{align*}$. Your model will then be much more accurate, and then it can be written in terms of $\displaystyle \displaystyle \begin{align*} \log{(x)} \end{align*}$ again.