Regression chance effects

Multiple regression—robustness, chance effects, and the comparison of models... 

This chapter has described some of the more commonly used supervised learning methods for the analysis of data discriminant analysis and its relatives for classified dependent data, variants of regression analysis for continuous dependent data. Supervised methods have the advantage that they produce predictions, but they have the disadvantage that they can suffer from chance effects. Careful selection of variables and test/training sets, the use of more than one technique where possible, and the application of common sense will all help to ensure that the results obtained from supervised learning are useful. 

The Michaelis-Menten model was fitted to the experimental data using standard nonlinear regression techniques to obtain estimates of and K (Fig. 4.1). Best-fit values of and K of corresponding standard errors of the estimates plus the number of values used in the calculation of the standard error, and of the goodness-of-fit statistic are reported in Table 4.3. These results suggest that succinate is a competitive inhibitor of fumarase. This prediction is based on the observed apparent increase in Ks in the absence of changes in Vmax (see Table 4.1). At this point, however, the experimenter cannot state with any certainty whether the observed apparent increase in Ks is a tme effect of the inhibitor or merely an act of chance. A proper statistical analysis has to be carried out. For the comparison of two values, a two-tailed t-test is appropriate. When more than two values are compared, a one-way analysis of variance (ANOVA),... 

The regression-to-the mean effect means that high or low accident levels tend to approach the mean value in the subsequent period by pure chance, and without any measures being taken. We run the risk of making erroneous conclusions about the positive effects of safety measures if we do not take this effect into account. 

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