# Machine Learning Questions and Answers – Logistic Regression – Decision Boundary

This set of Machine Learning Multiple Choice Questions & Answers (MCQs) focuses on “Logistic Regression – Decision Boundary”.

1. h(x) > 0.6 -> y = 1. What does the value 0.6 represent?
a) Cost function
b) Threshold value
d) Sigmoid function

Explanation: In logistic regression, a particular value is taken. If the value of the hypothesis is greater than this value, the output y is considered to b true or 1. This value is the threshold value. Here, 0.6 is the threshold value.

2. The value of a sigmoid function is the threshold value.
a) True
b) False

Explanation: Sigmoid function is used in machine learning models to predict the probability of an event happening. The value of the function varies for different instances in the training set. The threshold value is fixed for a particular dataset.

3. Threshold value is 0.5. h(x) = 0.7 for a particular instance. What is the value of y?
a) 0
b) 0.3
c) 0.7
d) 1

Explanation: The decision boundary depends on the value of threshold. If output of function h(x) is greater than the threshold value, the output y is equal to 1. Here, h(x) = 0.7 and threshold value = 0.5. Since 0.7 > 0.5, y = 1.

4. Let g be the sigmoid function. Let a >= 0. What is the value of g(a)?
a) g(a) >= 1/2
b) g(a) <= 0
c) g(a) <= 1/2
d) g(a) >= 0

Explanation: The sigmoid function is given by g(x) = 1/1+e-x. a >= 0
Hence, g(a) >= 1/1+e-0
g(a) >= 1/1+1
g(a) >= 1/2.

5. Probability of an event occurring is 0.2. What is odds ratio?
a) -4:1
b) 4:1
c) 1:4
d) 1:0.4

Explanation: p = 0.2 i.e. 2/10 i.e. 1/5, hence (1-p) = 1 – 1/5 = 4/5
Odds ratio = p/(1-p)
= (1/5)/(4/5) = 1:4.

6. Probability of an event occurring is 0.8. What is odds ratio?
a) 0.8:1
b) 4:1
c) 1:4
d) 2:0.8

Explanation: p = 0.8 i.e. 8/10, hence (1-p) = 1 – 8/10 = 2/10
Odds ratio = p/(1-p)
= (8/10)/(2/10) = 4:1.

7. Let g be the sigmoid function. Let a = infinite. What is the value of g(a)?
a) 1/2
b) -1
c) 1
d) 0

Explanation: The sigmoid function is given by g(x) = 1/1+e-x. a = infinite
Hence, g(a) = 1/1+e-infinite
= 1/1+0
= 1.

8. The decision boundary is an important parameter in logistic regression.
a) True
b) False

Explanation: In logistic regression, the decision boundary is based on the threshold value. It separates the area where output y = 0 and y = 1. Without the decision boundary, the output cannot be calculated. Thus, it is very important.

9. Let g be the sigmoid function. Let a = -(infinite). What is the value of g(a)?
a) -1/2
b) 1
c) 1/2
d) 0

Explanation: The sigmoid function is given by g(x) = 1/1+e-x. a = -(infinite)
Hence, g(a) = 1/1+einfinite
= 1/1+infinite
= 1/infinite
= 0.

10. Threshold value is 0.6. h(x) = 0.3 for a particular instance. What is the value of y?
a) 0
b) 0.3
c) 0.7
d) 1

Explanation: The threshold value separates the positive instances from the negative instances. If output of function h(x) is lesser than the threshold value, the output y is equal to 0. Here, h(x) = 0.3 and threshold value = 0.6. Since 0.3 < 0.6, y = 0.

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