Logarithmic Regression: Different correlation from 3 different calculators

[CR Haeger]

Thanks - this post made me dig into Minitab and TI36X Pro a bit deeper.

Minitab blog suggests that the standard error, S be used in place of r or r^2 for nonlinear regressions. I believe the formula for S is

S = √(Σ(Y-Y')^2/(n-2)) where n is number of response Ys and 2 comes from 2 coefficients being "consumed" in the a +b*ln(x) regression. So for your data n-2 = 14.

Inputting your data into Minitab resulted in S of 8144 (Y units).

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TI36X Pro does not seem to offer S up directly but here is a workaround.
- Enter and regress the x, y data (in L1, L2) using LNReg
- Make sure to store the regression equation into f(x) using RegEQ-->f(x): YES
- 2nd quit to Home screen
- In data table, add this formula to L3 column: L3=abs(L2-f(L1)) which is absolute residuals. Even after this formula entered, always visit data to refresh L3 after running a regression.
- 2nd quit to Home screen
- Compute 1-variable stats on L3. Scroll down to 6:Σ(x^2) = 928584397 which I believe is SSE. MSE would be SSE/14 in this case
- Press enter to put Σx^2 onto the home screen
- You can build √(Σx^2/14) from this which gives 8144.2

I usually use L3 if I want to compute residuals on any regression.