Line of Best Fit

• Mar 15th 2013, 10:13 AM
sakonpure6
Line 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?!

• Mar 15th 2013, 10:51 AM
HallsofIvy
Re: 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 AM
sakonpure6
Re: Line of Best Fit
:) thank you.
• Mar 15th 2013, 03:07 PM
Prove It
Re: Line of Best Fit
Quote:

Originally Posted by sakonpure6
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?!

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.