Littlebird
  • Littlebird
What does a natural logarithm regression equation look like?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Littlebird
  • Littlebird
1 Attachment
amistre64
  • amistre64
|dw:1377546986075:dw|
amistre64
  • amistre64
is this excel practice?

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amistre64
  • amistre64
ti83 also has a lnreg function
Littlebird
  • Littlebird
Not literally. I mean as an equation. I'm in calculus.
amistre64
  • amistre64
linear regression is such a pain that i dont think lnreg would be that any easier to calculate by hand
amistre64
  • amistre64
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amistre64
  • amistre64
i spose you could try out some approximation techniques ... it all depends on how "best dit" you want your line to be i spose
Littlebird
  • Littlebird
I used my calculator. My problem was that I had no idea how to start finding the equation. Thanks. :)
amistre64
  • amistre64
my ti83, fill List1 and List2 with the given points and use the LnReg function to evaluate between the L1, L2
ybarrap
  • ybarrap
Regression using natural logs is fairly straight-forward with a little linear algebra: $$ \begin{matrix} x & \ln x & Energy\\ 5 & \ln(5)=1.6 &7.8 \\ 10 & \ln(10)=2.3 & 27.8\\ 20& \ln(20)=3.0 & 31.6\\ 25& \ln(25)=3.2 &33.9 \end{matrix}\\ \text{Let A}= \begin{vmatrix} 1.6& 1 \\ 2.3& 1\\ 3.0& 1\\ 3.2 &1\\ \end{vmatrix}\\ \text{Let b}= \begin{vmatrix} 7.8 \\ 27.8\\ 31.6\\ 33.9\\ \end{vmatrix}\\ \text{Let x}= \begin{vmatrix} m \\ b\\ \end{vmatrix}\\ \text{Where m is the slope and b is the y-intercept of the regression line}\\ \text{So we need to solve the regression equation: }Ax=b.\\ \text{To do this we need to isolate the x: }\\ \left [ A^TA \right ]^{-1}\left [ A^TA \right ]x=\left [ A^TA \right ]^{-1}\left [ A^Tb \right ]\\ x=\left [ A^TA \right ]^{-1}\left [ A^Tb \right ]\\ x= \begin{vmatrix} m \\ b\\ \end{vmatrix}\\ \text{Solving for m and b, we find: }m=15.25669291\text{ and }b=-13.32314961 $$ So our regression equation is: \( y=15.3x-13.3\), where y is Energy and x is natural log of time (i.e x=5,6,..). These equations are easily solved using Excel (see attachment below).
Littlebird
  • Littlebird
That was amazing
ybarrap
  • ybarrap
Thanks, but let me know if you have any questions.

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