# Machine Learning Questions and Answers – Hypothesis Representation

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

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

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 tT.
a) h(X) = t0 + t1x1
b) h(X) = 1/(1 + e(tTx))
c) h(X) = e(-tTx)/(1 + e(-tTx))
d) h(X) = 1/(1 + e(-tTx))

Explanation: The hypothesis is a function of the term tTx. 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 (tTx)
⇨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

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

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

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)

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

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.