Strictly speaking, calculating accuracy doesn't require the details of a confusion matrix: it's simply the proportion of correct predictions.
Since there are 4 possible classes in this exercise and we are interested only in the accuracy of the class 'fail', this means that the 3 other classes are considered like a single class 'not fail'.
So to obtain the accuracy of fail, sum:
- the number of students predicted as 'fail' who truly fail (True Positive cases)
- the numbers of students predicted as 'not fail' who truly don't fail (True Negative cases)
And then divide by the total number of students.
edit to answer comment:
the DT shows for every node the proportion of instances by class, for the subset of data that it receives based on the previous conditions (see a short explanation about DTs here).
The instances are predicted at the level of leaf nodes, i.e. nodes with no children. The leaf node simply assigns the majority class. For example if we take the leaf node "studied_credits>=82.500" (just below the root), the majority class is 'withdrawn'. This means that the 5565 instances in this leaf are predicted 'withdrawn', which means 'not fail' for our purpose. This includes 1120 instances which actually should be 'fail', so this leaf node results in 4445 TNs and 0 TPs (and also 1120 FNs but we are not interested in those for accuracy).
By doing this for every leaf node you should obtain the total number of TPs and TNs. The total number of instances is given in the root node, it's 15370.
