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Math Help - Line of Best Fit

  1. #1
    Senior Member sakonpure6's Avatar
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    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.
    Line of Best Fit-untitled.png

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

    Thanks for your time
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  2. #2
    MHF Contributor

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    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!
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    Senior Member sakonpure6's Avatar
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    Re: Line of Best Fit

    thank you.
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  4. #4
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    Re: Line of Best Fit

    Quote Originally Posted by sakonpure6 View Post
    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.
    Click image for larger version. 

Name:	Untitled.png 
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Size:	10.8 KB 
ID:	27539

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

    Thanks for your time
    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 \begin{align*} y = A + B\log{(x)} \end{align*} might be appropriate. If we let \displaystyle \begin{align*} X = \log{(x)} \end{align*}, this gives \displaystyle \begin{align*} y = A + B\,X \end{align*}, a LINEAR function.

    So what you can do is to evaluate \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 \begin{align*} X \end{align*} and \displaystyle \begin{align*} y \end{align*}. Your model will then be much more accurate, and then it can be written in terms of \displaystyle \begin{align*} \log{(x)} \end{align*} again.
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