Question

Sample ID	Predicted Value	Sample Label
1	.9	0
2	.7	1
3	.5	1
4	.8	1
5	.4	0
6	.3	1

(a) Using 0.5 as a cutoff, namely >=0.5 then predict the sample as 1, and 0 otherwise. Please compute true positive rate and the false positive rate.

(b) please compute its AUC manually https://www.coursehero.com/file/27125786/Fall-16-Quiz-5pdf/ This study re

Answer 1

Sample ID	Predicted Value	Predicted Label(threshold >=0.5)	Sample Label
1	.9	1	0
2	.7	1	1
3	.5	1	1
4	.8	1	1
5	.4	0	0
6	.3	0	1

(a)

True positive Rate: ration of correct positive label predicted and total positive label

here correct positive label predicted are of sample ID: 2,3 ,4

thus TP = 3

and positive label are of sample: 2, 3 ,4 6

and P = 4

Then

False positive Rate: ration of incorrect negative label predicted as positive and total negative label

here incorrect negative label predicted as positive are of sample ID: 1

thus FP = 1

and negative label are of sample: 1,5

and N = 2

Then