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Mathematics, 26.02.2020 00:33 kovachb11

Consider a classification problem where we are building a logistic regression classifier. The task is to predict if a given city has a risk of a disease epidemic or not. The data is defined using two input features or variables -
(1) logarithm of size of the city
(2) distance to the nearest city with epidemic
The target is a binary (0 - no risk and 1 - risk). Consider the following training data set

City # Log Size of City Distance Risk?
1 2.18 0.01 1
2 1.09 18.30 1
3 -0.37 3.00 0
4 0.00 4.10 1
5 -0.42 9.00 0
6 0.09 7.20 0
7 -0.48 10.00 0
8 0.62 2.70 0
9 0.57 2.80 1
10 0.44 0.01 1

Assume that a bias term is added in the beginning. Consider the following weight vector for logistic regression: w0 = 1.05, w1 = -.52, w2 = 0.85. Answer the following:
(a) The classifier labels 5 cities at risk
(b) The classifier is over 90% confident for 3 cities only
(c) The classifier's most confident correct prediction is for city #2
(d) The classifier makes 4 mistakes

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