Measure of Fit

For each output parameter, Results Analytics performs a regression analysis to measure how well the predicted model approximates the actual function at the data points used to construct the model. The analysis returns the following values:

$R^{2}$

An $R^{2}$ value of 1.00 indicates that the values of the predicted model and the values of the actual function are identical at all the data points. It is always possible to perfectly fit $N$ points using a polynomial with $N + 1$ coefficients. Therefore, a perfect value of the $R^{2}$ coefficient does not necessarily indicate that the model will match the actual function everywhere in the design space, unless the number of points used for analysis is considerably greater (3–10 times) than the number of polynomial coefficients.

$R^{2}$ Adjusted

$R^{2}$ adjusted is a modified value of $R^{2}$ that accounts for the number of parameters in your model relative to the number of data points. Results Analytics provides a value for $R^{2}$ adjusted to account for the value of $R^{2}$ increasing when you add parameters to the data set. The value of $R^{2}$ adjusted is always less than, or equal to, the value of $R^{2}$ .

Root Mean Square Error

The root mean square error is the standard deviation of the differences between the predicted and actual values and is a numerical measure of the difference between the predicted values and the actual values.

RMSE = \sqrt{\frac{\sum_{t = 1}^{n} {(\hat{Y} t - Y t)}^{2}}{n}}

You should apply different interpretations to $R^{2}$ and $R^{2}$ adjusted. You use $R^{2}$ as an indication of the measure of fit to the regression line. In contrast, you use $R^{2}$ adjusted to compare combinations of different parameters in your approximations. Some parameters are redundant and play no role in the approximation. Adding a redundant parameter will result in an increase in the value of $R^{2}$ , but will result in a decrease in the value of $R^{2}$ adjusted.