1. Here is an example test set of 18 entities (7 actives, 11 decoys) that are shown in Table 1 in the ascending order of their scores. Their scores (probabilities to be decoy) are obtained by using Logistic Regression model M.

id	score	active/decoy
O	0.03	a
L	0.48	a
J	0.08	a
K	0.56	d
D	0.10	d
P	0.65	d
A	0.11	a
Q	0.71	d
I	0.22	d
C	0.72	d
G	0.32	a
N	0.73	a
B	0.35	a
H	0.80	d
M	0.42	d
R	0.82	d
F	0.44	d
E	0.99	d

1. We can manually setup the thresholdt=0.48.Please calculate the four outcomes in the confusion matrix in this case. Calculate the precision, recall, sensitivity and specificity.

2. For this small test set,the ROC curve can be drawn as a stepping function. Please calculate the TPRs and FPRs according to the threshold values. To achieve the highest resolution of the ROC curve, we can use {0.03, 0.08, 0.10, 0.11, 0.22, ..., 0.82, 0.99} (i.e., all scores appear in the table) to be the set of all the possible threshold values. Therefore, you are required to calculate TPR and FPR in terms of the different thresholds. Then draw the ROC curve.
3. Can you draw the ROC curve with a higher resolution by picking up more threshold values? Why or why not?
4. Please calculate AUC

2. Download Fisher Iris data. This is a dataset made famous by Fisher, who used it to illustrate principles of discriminant analysis. It contains 6 variables with 150 observations.

Link: http://math.tntech.edu/ISR/Statistical_Methods_I/Data_and_Story_Library/iris.txt Variables. Species_No: Flower species as a code Species_Name: Species name

Petal_Width: Petal Width Petal_Length: Petal Length Sepal_Width: Sepal Width Sepal_Length: Sepal Length

Please implement the KNN (K=5) method on classifying the data. Please apply the 5-fold cross-validation method for evaluating the testing accuracy.