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@@ -134,3 +134,85 @@ alt="4D contour plot for the linear model in section [[]]" />
4D contour plot for the linear model in
section [[]]
+
+## Leave one out methodology
+
+R2 is : . Relation to ML training set. what corerlation coeffi is and
+isnt
+
+Chemistry data hard to come by so need to make the most of the data we
+have. LOOM!
+
+We make a training set of 1 point, and build N models of N-1 points.
+Should get similar R2 for each model and the errors should be evenly
+distributed around zero.
+
+The final model is averaged. Q2 calculated from each model separaetly.
+
+Over-fitting. undertraining. R2 always more than Q2. etc. what r2 of 0
+means (or less than 0).
+
+Is your model valid? is Q2 above 0.5? if not - could be not enough data
+etc.
+
+What makes a good model *Q*2 \> 0.5, *R*2 \> 0.5,
+*R*2 − *Q*2 \< 0.2.
+
+### Example of analysing the averaged model
+
+\[\[To-do read DoNUT to find out what all this is! is averaged error the
+error for all points on that model?\]\]
+
+Means should be similar for train and test set. Q2 calcualted etc.
+
+Table 1 and figure
+ [fig:error_plot] show data from a
+first order lienar model.
+Figure [fig:error_plot] shows that the
+first 16 experiments are well distributed, but the last one is an
+outlier.
+
+hhiger r2 (see table). Higher error (see figure) We do not remove this
+outlier!
+
+why? Is the highest yield point, ie what we are searching for. But this
+high error suggests that the model is not very predictive at this point.
+See figure [fig:linear_model_pre], which
+shows a yield above 100% in this area.
+
+models are only predictive in the range they have been trianed over Do
+not know chemical or phsycial facts, such that a yield above 100% is
+impossible. We know that 91% is the true yeild here.
+
+relate back to OVAT which would get the correct answer.
+
+But our answers is close enough to proceed and test that area for better
+yeilds.
+
+Figure [fig:observed_vs_predicted]A
+shows the model response for this data.
+
+| Missing data point | model *R*2 | Average error |
+|:-------------------|:----------------------|:--------------|
+| 0 | 0.801 | -16.5 |
+| 1 | 0.857 | -3.63 |
+| 2 | 0.873 | 10.5 |
+| 3 | 0.862 | -13.2 |
+| 4 | 0.852 | -0.916 |
+| 5 | 0.86 | 5.03 |
+| 6 | 0.854 | 2.59 |
+| 7 | 0.881 | 12.9 |
+| 10 | 0.85 | 3.17 |
+| 11 | 0.856 | 5.89 |
+| 12 | 0.854 | -8.72 |
+| 13 | 0.855 | -4.17 |
+| 14 | 0.861 | 9.52 |
+| 15 | 0.858 | 5.21 |
+| 16 | 0.92 | -25.3 |
+
+ Output from 17 models trained for LOOM