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What are the measures that can be used to determine the fit of a model?
Three statistics are used in Ordinary Least Squares (OLS) regression to evaluate model fit: R-squared, the overall F-test, and the Root Mean Square Error (RMSE). All three are based on two sums of squares: Sum of Squares Total (SST) and Sum of Squares Error (SSE).
What variable is predicted in model fitting?
Y variable
Regression models predict a value of the Y variable, given known values of the X variables. Prediction within the range of values in the data set used for model-fitting is known informally as interpolation.
Which is the best measure of the fit of a model?
Lower values of RMSE indicate better fit. RMSE is a good measure of how accurately the model predicts the response, and it is the most important criterion for fit if the main purpose of the model is prediction. The best measure of model fit depends on the researcher’s objectives, and more than one are often useful.
Is it possible that all the goodness of fit measures indicate that?
Conversely, it is also possible that all the goodness of fit measures indicate that a particular fit is the best one. However, if your goal is to extract fitted coefficients that have physical meaning, but your model does not reflect the physics of the data, the resulting coefficients are useless.
How to calculate the fit of a regression model?
An alternative to this is the normalized RMS, which would compare the 2 ppm to the variation of the measurement data. So, even with a mean value of 2000 ppm, if the concentration varies around this level with +/- 10 ppm, a fit with an RMS of 2 ppm explains most of the variation.
Is it possible that none of your fits are the best?
Note that it is possible that none of your fits can be considered the best one. In this case, it might be that you need to select a different model. Conversely, it is also possible that all the goodness of fit measures indicate that a particular fit is the best one.