Regression assessment criteria

In this section, we will describe three regression criteria relevant to Section 3.5. These criteria can be used to assess how well a model is performing. The three criteria are - the residual sum of squares (RSS), the R-squared (R ) measure and the predictive residual sum of squares (PRESS). The residual sum of squares and R-squared criteria both measure how well the model fits the data. These criteria are respectively defined 

The RSS measures the sum of squared deviations between the actual and predicted values of the response. A lower measure of the RSS is preferred. The R criterion ranges from zero to one, with values closer to one being preferred, provided that a high R is not a consequence of overfitting. 

We will test the performance of the adaptive wavelet algorithm for regression purposes using an independent test set. For this reason we have decided to formulate an R- measure for the test set which is denoted by R,  

The residual and total sum of squares for the testing data are defined, respectively to be 

Define the PRESS statistic to be PRESS = 51 , (y - y i) . Here, y is the predicted value for y but object Xj was left out when estimating the parameters in the regression model. Another way of calculating the PRESS statistic is simply by using 

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The third criterion is that the model should target an endpoint relevant for REACH. Only models that address the endpoints of interest for REACH are appropriate within this purpose. We notice that REACH mentions different purposes for the QSAR models classification and labeling, is one possible target of the model, and risk assessment in another. In the first case models are classifiers in the second case a regression more is more suitable. Indeed, in the first case the... 

The parameters associated with the degradation and error models are estimated using linear regression. Finally, the fitted degradation model can be used to estimate the mean lifetime of the ceU at a specified temperature for a given end-of-life criterion. The details of this battery life estimation methodology along with Monte Carlo simulation to assess lack-of-fit statistic are provided in Ref. [82]. 

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