This set of Machine Learning Multiple Choice Questions & Answers (MCQs) focuses on “Hypothesis Representation”.

1. What function is used for hypothesis representation in logistic regression?

a) Cos function

b) Laplace transformation

c) Lagrange’s function

d) Sigmoid function

View Answer

Explanation: In logistic regression, the output is based on a probability and thus must be within the range of 0 and 1. The sigmoid function is used for models whose output is given as a probability i.e. the range lies between 0 and 1. So, the sigmoid function is used in hypothesis representation.

2. The value of a sigmoid function is 1.5.

a) True

b) False

View Answer

Explanation: Sigmoid function can be used for machine learning models where output is based on the prediction of a probability. The function only exists between 0 and 1. Thus its value can never be 1.5.

3. How is the hypothesis represented? Transpose of t is t^{T}.

a) h(X) = t_{0} + t_{1}x_{1}

b) h(X) = 1/(1 + e^{(tTx)})

c) h(X) = e^{(-tTx)}/(1 + e^{(-tTx)})

d) h(X) = 1/(1 + e^{(-tTx)})

View Answer

Explanation: The hypothesis is a function of the term t

^{T}x. Since its value should be between 0 and 1, sigmoid function is used. Sigmoid function is given by g(a) = 1/(1 + e

^{-a}).

h(x) = g (t

^{T}x)

⇨h(X) = 1/(1 + e

^{(-tTx)}).

4. Let g be the sigmoid function. Let a = 0. What is the value of g(a)?

a) 1/2

b) 1/4

c) 1

d) 0

View Answer

Explanation: The sigmoid function is given by g(x) = 1/1+e

^{-x}. a=0

Hence, g(a) = 1/1+e

^{-0}

= 1/1+1

= 1/2.

5. Probability of an event occurring is 1.2. What is odds ratio?

a) 6:1

b) -6:1

c) Undefined

d) 1:2

View Answer

Explanation: Probability p has to be within the range of 0 to 1. p can never be 1.2. Odds ratio is calculated as the ratio of p and (1-p). Since p can never be 1.2, odds ratio calculation is also possible.

6. Probability of an event occurring is 0.9. What is odds ratio?

a) 0.9:1

b) 9:1

c) 1:9

d) 1:0.9

View Answer

Explanation: p = 0.9 i.e. 9/10, hence (1-p) = 1 – 9/10 = 1/10

Odds ratio = p/(1-p)

= (9/10)/(1/10) = 9:1.

7. What is the odds ratio?

a) p/(1-p)

b) p

c) 1-p

d) p*(1-p)

View Answer

Explanation: p is the probability that event y occurs. Then the probability of event y not occurring can be given as (1-p). Odds ratio is given by the ratio of the probability of an event occurring and the probability that an event is not occurring. Thus, odds ratio is p/(1-p).

8. The output of logistic regression is always 0 or 1.

a) True

b) False

View Answer

Explanation: The output of logistic regression is not always 0 or 1. It can be yes or no. It can be even true or false. The output of binary logistic regression is always 0 or 1.

**Sanfoundry Global Education & Learning Series – Machine Learning**.

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