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Coefficient of Determination or Root mean square Error?

Coefficient of Determination or Root mean square Error?

Coefficient of Determination or Root mean square Error?

I am currently using ANSYS to model the behaviour of cardiovascular tissue.

I've input experimental data (non linear behaviour) and ANSYS has fitted a polynomial non-linear model to the data.

ANSYS  outputs two statistical measures of how well the calculated curve fits the experiemntal points....namely the root mean square error (as a percentage) and the coefficient of determination.

My problem is this.....ANSYS does a good job fitting the data...but the stats have confused me somewhat. Oone of the results states that the coefficient of determination is 0.999 (correct me if I'm wrong but this means a good fit), but the corresponding RMS error is given as 87% (which is bad & before anyone suggests..I've double checked the decimal points).

Anybody have an explaination for this?? How can both measures be soo far removed from another or am I missing the point?

Look forward to hearing from one of you,


Joe Daly

RE: Coefficient of Determination or Root mean square Error?

Let's start with the RMS error.  87% can sound bad, but only if it is compared to another regresion analysis that provides a better fit.  You can have a close fit and a high RMS error if you have significant scatter in your data.

Have you plotted the 95% confidence intervals?  Does all the data fit within this band?  If not you may need to try another regression fit.

Often with incresing variance towards one end of the data the use of Weibull or exponential regression works better.

The 0.999 on the coefficeint of determiniation indicates a good fit of the sample mean to the regressed mean.  It does not indicate a good fit to the intire data set.

Again start with a dot plot and box plots to see if you have any significant outliers and if the data has any specific trends.  Then try several different regressions to see how the data fits eachof them.

If you have already done this and still have the best fit, start checking for other data indicators (two populations, changes in how the results were collected, etc.)  

RE: Coefficient of Determination or Root mean square Error?

How many data points are we talking about here?  Is it something that you can easily share?

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