Calculating a Confusion Matrix

Question

Can someone help me understand how to find the values of a confusion matrix?

I know that essentially a confusion matrix looks like this:

True Positive |False Positive
False Negative|True Negative

I've encountered a problem where I have around 1000 cases in my test data.

In the approximate middle of its ROC chart there is a point where the false positive rate is 0.5, the true positive rate is 0.7, and the accuracy is 0.7.

This is my approach to this problem and I just want to verify if I am doing it correctly:

To calculate the count of True Positives:

$$0.7 * 1000\,Cases = 700\,Cases$$

To calculate the count of False Positives:

$$0.5 * 1000\,Cases = 500\,Cases$$

I would assume calculating the True Negatives would be $1000 - 700 = 300$.

Then solving for False Negatives =

$$.7 (Accuracy) = 700 + 300 / 700 + 300 + 500 + FN$$

Can someone confirm if this is the right approach?

Answer 1

Your approach is not correct.

Some hints that should help you to understand your mistakes

1. the sum over all elements of the confusion matrix should be 1000 in your case.
2. TPR=TP / Num_positives

Good guide to confusion matrix terminology