Question

What does a natural logarithm regression equation look like?

Answer 1

is this excel practice?

Answer 2

ti83 also has a lnreg function

Answer 3

Not literally. I mean as an equation. I'm in calculus.

Answer 4

linear regression is such a pain that i dont think lnreg would be that any easier to calculate by hand

Answer 5

i spose you could try out some approximation techniques ... it all depends on how "best dit" you want your line to be i spose

Answer 6

I used my calculator. My problem was that I had no idea how to start finding the equation. Thanks. :)

Answer 7

my ti83, fill List1 and List2 with the given points

and use the LnReg function to evaluate between the L1, L2

Answer 8

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).

Answer 9

That was amazing

Answer 10

Thanks, but let me know if you have any questions.