Logarithmic Regression: Different correlation from 3 different calculators

06092015, 03:09 PM
Post: #1




Logarithmic Regression: Different correlation from 3 different calculators
I need a sanity check here. I'm running a logarithmic regression on some data, and I'm getting very slightly different correlation coefficients (r, not r^2) from three different calculators.
HP 48SX: 0.968372745387 TI36X Pro: 0.96835943144 TI89 Stats flash app: 0.968372745387 TI89 custom function: 0.968372683432 Notice the 48SX and TI89 stats app match up, so I'm inclined to believe those are the most accurate. The 36X Pro may have lower internal precision, or it's using a different faster/less accurate method to produce the result. The custom function I made for the TI89 (since the built in stat commands don't calculate correlation for logarithmic, exponential, or power regression for some reason) is also a little bit off. I used the formula shown about halfway down this page: http://brownmath.com/ti83/regres89.htm sum((x[i]meanx)*(y[i]meany),i,1,n)/((n1)*sx*sy) Where sx and sy are sample standard deviations of the x and y lists respectively. Also, the x list has been transformed with LN prior to any calculations. I have a feeling taking the sum of products is making it lose precision somewhere. And if that's the case, is there a better approach? I tried the zscore method given on that same page, basically moving the standard deviations into the products within the sum, but I end up with a repeating decimal that looks a bit fishy. This is the data I'm looking at. Note that a logarithmic fit is NOT correct for this particular data, I'm just testing the correlation calculation. 1999, 8456 2000, 14959 2001, 13516 2002, 11298 2003, 11109 2004, 15256 2005, 29316 2006, 46038 2007, 51726 2008, 56686 2009, 58372 2010, 68426 2011, 70760 2012, 77238 2013, 100836 2014, 95461 

06092015, 07:36 PM
(This post was last modified: 06092015 07:38 PM by CR Haeger.)
Post: #2




RE: Logarithmic Regression: Different correlation from 3 different calculators
I wonder if your r and r^2 values change slightly if you run the regression on normalized X, Y data?
Also, I think that calculating r for non linear regressions may require separate calculations of SSE and SST, then using r = sqrt(1  SSE/SST) . 

06092015, 07:45 PM
(This post was last modified: 06092015 07:53 PM by Dave Britten.)
Post: #3




RE: Logarithmic Regression: Different correlation from 3 different calculators
(06092015 07:36 PM)CR Haeger Wrote: I wonder if your r and r^2 values change slightly if you run the regression on normalized X, Y data? Yeah, I'm not enough of a statistician to know if there's a problem with my calculation method that's causing inaccuracy, or if I'm supposed to be using a different formula entirely. I know a lot of the HPs with accumulated stats just transform x and/or y on the fly as you enter them, so I'm not sure what else I'd have to do. I'll have to crack open my old stats 215 textbook later and see what it says about curve fitting. EDIT: Running a linear regression on a list of transformed ln(x) values gives me the same value for r as doing logarithmic regression on the original x values, at least with the 36X Pro. So I assume the formula is the same, but something must be clobbering numeric accuracy along the way. Hmm... 

06092015, 08:51 PM
(This post was last modified: 06092015 08:53 PM by CR Haeger.)
Post: #4




RE: Logarithmic Regression: Different correlation from 3 different calculators
OK. By normalized, I meant:
x_n = [2.0*(x  x_min)/(x_max  x_min)]  1.0 // changes x data to go from 1.0 > +1.0 do the same with y data then run the regression. 

06092015, 09:37 PM
Post: #5




RE: Logarithmic Regression: Different correlation from 3 different calculators
Just another data point for you  my Casio fx9750GII gives 0.96837274.
It shows the regression results in a 10 character space, and I can't figure out how to get any more digits out of it. Also, I'm sure you've checked this, but it took me three tries to get all the numbers entered correctly (and that's with the list display). When I had transposed the 2 and 7 in 58372, I got 0.96835999, pretty close to your TI36X number. And a question  I'm really weak in my stats knowledge, but is there any possible reason why more that 2 or maybe 3 significant figures for this value would matter? Of course, playing with numbers is its own fun. 

06092015, 10:00 PM
Post: #6




RE: Logarithmic Regression: Different correlation from 3 different calculators
(06092015 09:37 PM)groundbeef Wrote: Just another data point for you  my Casio fx9750GII gives 0.96837274. Yeah, I've checked and rechecked the data several times to make sure everything is entered properly. If you want to get a few more digits out of it, this works on my fx9860g Slim: 1. Evaluate r (from the Catalog) in Run mode. 2. Subtract the most significant digits from And and multiply by powers of 10 as needed. With that method, the Casio gives me 0.968372745386438, even more digits than the TI or HP. And in this particular case, you're right, I'm still getting more than enough accurate digits to draw a reasonable conclusion (i.e. that log regression isn't appropriate for this data). My fear is that the way I'm calculating correlation could have even worse accuracy with other datasets. If it were off in the hundredths place, that would be a bigger problem. 

06092015, 10:38 PM
Post: #7




RE: Logarithmic Regression: Different correlation from 3 different calculators  
06092015, 10:53 PM
Post: #8




RE: Logarithmic Regression: Different correlation from 3 different calculators
(06092015 10:00 PM)Dave Britten Wrote: 1. Evaluate r (from the Catalog) in Run mode.That's what I missed. I did LogReg, and it just gave me the same screen as stats mode. (06092015 10:00 PM)Dave Britten Wrote: With that method, the Casio gives me 0.968372745386438, even more digits than the TI or HP.Mine too. I have a TI84 Plus I can try for giggles. I went through the computation in steps with excel, so I could see intermediate results. Most of the numbers involved in sums span about 3 orders of magnitude. 4 in a couple of cases. But it looks like you lose more digits than that. The spreadsheet gives 0.968372745386560. I get .968516807361777 for a linear regression (casio). Comparing that might point toward or away from the log calculation. 

06092015, 11:16 PM
Post: #9




RE: Logarithmic Regression: Different correlation from 3 different calculators
I tried my TI84, and when I retrieved the r value, I realized that you can also pull out all of the sums. It's a little tedious, but if you can retrieve them from the 36X, I'll post mine for comparison.
The r value was .96837274538717, but I think we've already established the outlier. 

06092015, 11:26 PM
Post: #10




RE: Logarithmic Regression: Different correlation from 3 different calculators
r and r^2 may not be valid for nonlinear models per Minitab


06102015, 12:12 AM
Post: #11




RE: Logarithmic Regression: Different correlation from 3 different calculators
(06092015 10:38 PM)Paul Dale Wrote:(06092015 10:00 PM)Dave Britten Wrote: that log regression isn't appropriate for this data Oh, I was mostly referring to the fact that you get a TINY bit higher correlation with plain linear regression. This is actually some data from our ERP system showing growth of one of the larger tables in rows by year. (06092015 11:26 PM)CR Haeger Wrote: r and r^2 may not be valid for nonlinear models per Minitab Interesting, I'll read that over. Maybe coefficient of determination would be a better choice. 

06102015, 03:28 PM
(This post was last modified: 06102015 06:30 PM by CR Haeger.)
Post: #12




RE: Logarithmic Regression: Different correlation from 3 different calculators
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(YY')^2/(n2)) 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 n2 = 14. Inputting your data into Minitab resulted in S of 8144 (Y units).  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(L2f(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 1variable 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. 

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