Questions about LogisticRegregation(1)

14) Suppose you have been given a fair coin and you want to find out the odds of getting heads. Which of the following option is true for such a case?

A) odds will be 0
B) odds will be 0.5
C) odds will be 1
D) None of these

Solution: C

Odds are defined as the ratio of the probability of success and the probability of failure. So in case of fair coin probability of success is 1/2 and the probability of failure is 1/2 so odd would be 1

15) The logit function(given as ℓ(x)) is the log of odds function. What could be the range of logit function in the domain x=[0,1]?

A) (– ∞ , ∞)
B) (0,1)
C) (0, ∞)
D) (- ∞, 0)

Solution: A

For our purposes, the odds function has the advantage of transforming the probability function, which has values from 0 to 1, into an equivalent function with values between 0 and ∞. When we take the natural log of the odds function, we get a range of values from -∞ to ∞.

16) Which of the following option is true?

A) Linear Regression errors values has to be normally distributed but in case of Logistic Regression it is not the case
B) Logistic Regression errors values has to be normally distributed but in case of Linear Regression it is not the case
C) Both Linear Regression and Logistic Regression error values have to be normally distributed
D) Both Linear Regression and Logistic Regression error values have not to be normally distributed

Solution:A

Only A is true. Refer this tutorial https://czep.net/stat/mlelr.pdf

17) Which of the following is true regarding the logistic function for any value “x”?

Note:
Logistic(x): is a logistic function of any number “x”

Logit(x): is a logit function of any number “x”

Logit_inv(x): is a inverse logit function of any number “x”

A) Logistic(x) = Logit(x)
B) Logistic(x) = Logit_inv(x)
C) Logit_inv(x) = Logit(x)
D) None of these

Solution: B

Refer this link for the solution: https://en.wikipedia.org/wiki/Logit