Logistic Regression is likely the most commonly used algorithm for solving all classification problems. It is also one of the first methods people get their hands dirty on.

We saw the same spirit on the test we designed to assess people on Logistic Regression. More than 800 people took this logistic regression interview questions. This skill test is specially designed for you to test your knowledge on logistic regression and its nuances.

If you are one of those who missed out on this skill test, here are the questions and solutions. You missed on the real time test, but can read this article to find out how many could have answered correctly. In this article you will get to know about logistic regression interview questions.Also, you will get insights about the linear regression interview questions , with that how we are explaining logistic regression interview questions that will help you for preparation of the logistic regression interview questions.

In this article, you will learn about logistic regression for multiclass classification. We will cover common interview questions on logistic regression and explain how multiclass logistic regression works.

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Below is the distribution of the scores of the participants:

You can access the scores **here**. More than 800 people participated in the skill test and the highest score obtained was 27.

Here are some resources to get in depth knowledge in the subject.

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A) TRUE

B) FALSE

**Solution:** ATrue, Logistic regression is a supervised learning algorithm because it uses true labels for training. Supervised learning algorithm should have input variables (x) and an target variable (Y) when you train the model

A) TRUE

B) FALSE

**Solution: B**

Logistic regression is a classification algorithm, don’t confuse with the name regression.

A) TRUE

B) FALSE

**Solution: A**

True, Neural network is a is a *universal* approximator so it can implement linear regression algorithm.

A) TRUE

B) FALSE

**Solution: A**

Yes, we can apply logistic regression on 3 classification problem, We can use One Vs all method for 3 class classification in logistic regression.

A) Least Square Error

B) Maximum Likelihood

C) Jaccard distance

D) Both A and B

**Solution: B**

Logistic regression uses maximum likely hood estimate for training a logistic regression.

A) AUC-ROC

B) Accuracy

C) Logloss

D) Mean-Squared-Error

**Solution: D**

Since, Logistic Regression is a classification algorithm so it’s output can not be real time value so mean squared error can not use for evaluating it

A) We prefer a model with minimum AIC value

B) We prefer a model with maximum AIC value

C) Both but depend on the situation

D) None of these

**Solution: A**

We select the best model in logistic regression which can least AIC. For more information refer this source: Click here

A) TRUE

B) FALSE

**Solution: B**

Standardization isn’t required for logistic regression. The main goal of standardizing features is to help convergence of the technique used for optimization.

A) LASSO

B) Ridge

C) Both

D) None of these

**Solution: A**

In case of lasso we apply a absolute penality, after increasing the penality in lasso some of the coefficient of variables may become zero.

**Context: 10-11**

Consider a following model for logistic regression: P (y =1|x, w)= g(w0 + w1x)

where g(z) is the logistic function.

In the above equation the P (y =1|x; w) , viewed as a function of x, that we can get by changing the parameters w.

A) (0, inf)

B) (-inf, 0 )

C) (0, 1)

D) (-inf, inf)

**Solution: C**

For values of *x* in the range of real number from −∞ to +∞ Logistic function will give the output between (0,1)

A) logistic function

B) Log likelihood function

C) Mixture of both

D) None of them

**Solution: A**

Explanation is same as question number 10

**Context: 12-13**

Suppose you train a logistic regression classifier and your hypothesis function H is

A)

B)

C)

D)

**Solution: B**

Option B would be the right answer. Since our line will be represented by y = g(-6+x2) which is shown in the option A and option B. But option B is the right answer because when you put the value x2 = 6 in the equation then y = g(0) you will get that means y= 0.5 will be on the line, if you increase the value of x2 greater then 6 you will get negative values so output will be the region y =0.

A)

B)

c)

D)

**Solution: D**

Same explanation as in previous question.

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

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 ∞*.*

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**

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**

Suppose you have given the two scatter plot “a” and “b” for two classes( blue for positive and red for negative class). In scatter plot “a”, you correctly classified all data points using logistic regression ( black line is a decision boundary).

A) Bias will be high

B) Bias will be low

C) Can’t say

D) None of these

**Solution: A**

Model will become very simple so bias will be very high.

**Note: Consider remaining parameters are same.**

A) Training accuracy increases

B) Training accuracy increases or remains the same

C) Testing accuracy decreases

D) Testing accuracy increases or remains the same

**Solution: A and D**

Adding more features to model will increase the training accuracy because model has to consider more data to fit the logistic regression. But testing accuracy increases if feature is found to be significant

A) We need to fit n models in n-class classification problem

B) We need to fit n-1 models to classify into n classes

C) We need to fit only 1 model to classify into n classes

D) None of these

**Solution: A**

If there are n classes, then n separate logistic regression has to fit, where the probability of each category is predicted over the rest of the categories combined.

**Which of the following statement(s) is true about β0 and β1 values of two logistics models (Green, Black)?****Note: consider Y = β0 + β1*X. Here, β0 is intercept and β1 is coefficient.**

A) β1 for Green is greater than Black

B) β1 for Green is lower than Black

C) β1 for both models is same

D) Can’t Say

**Solution: B**

β0 and β1: β0 = 0, β1 = 1 is in X1 color(black) and β0 = 0, β1 = −1 is in X4 color (green)

**Context 22-24**

Below are the three scatter plot(A,B,C left to right) and hand drawn decision boundaries for logistic regression.

A) A

B) B

C) C

D)None of these

**Solution: C**

Since in figure 3, Decision boundary is not smooth that means it will over-fitting the data.

- The training error in first plot is maximum as compare to second and third plot.
- The best model for this regression problem is the last (third) plot because it has minimum training error (zero).
- The second model is more robust than first and third because it will perform best on unseen data.
- The third model is overfitting more as compare to first and second.
- All will perform same because we have not seen the testing data.

A) 1 and 3

B) 1 and 3

C) 1, 3 and 4

D) 5

**Solution: C**

The trend in the graphs looks like a quadratic trend over independent variable X. A higher degree(Right graph) polynomial might have a very high accuracy on the train population but is expected to fail badly on test dataset. But if you see in left graph we will have training error maximum because it underfits the training data

A) A

B) B

C) C

D) All have equal regularization

**Solution: A**

Since, more regularization means more penality means less complex decision boundry that shows in first figure A.

**Solution: A**

The best classification is the largest area under the curve so yellow line has largest area under the curve.

Suppose you are using a Logistic Regression model on a huge dataset. One of the problem you may face on such huge data is that Logistic regression will take very long time to train.

A) Decrease the learning rate and decrease the number of iteration

B) Decrease the learning rate and increase the number of iteration

C) Increase the learning rate and increase the number of iteration

D) Increase the learning rate and decrease the number of iteration

**Solution: D**

If you decrease the number of iteration while training it will take less time for surly but will not give the same accuracy for getting the similar accuracy but not exact you need to increase the learning rate.

**Following is the loss function in logistic regression(Y-axis loss function and x axis log probability) for two class classification problem.**

**Note: Y is the target class**

A) A

B) B

C) Both

D) None of these

**Solution: A**

A is the true answer as loss function decreases as the log probability increases

A) 1

B) 2

C) 3

D) 4

**Solution: C**

There are three local minima present in the graph

Suppose, you save the graph for future reference but you forgot to save the value of different learning rates for this graph. Now, you want to find out the relation between the leaning rate values of these curve. Which of the following will be the true relation?

**Note:**

- The learning rate for blue is l1
- The learning rate for red is l2
- The learning rate for green is l3

A) l1>l2>l3

B) l1 = l2 = l3

C) l1 < l2 < l3

D) None of these

**Solution: C**

If you have low learning rate means your cost function will decrease slowly but in case of large learning rate cost function will decrease very fast.

Note: You can use only X1 and X2 variables where X1 and X2 can take only two binary values(0,1).

A) TRUE

B) FALSE

C) Can’t say

D) None of these

**Solution: B**

No, logistic regression only forms linear decision surface, but the examples in the figure are not linearly separable.

The Logistic Regression skill test offered a robust evaluation platform for participants, with over 800 individuals engaging in assessing their comprehension. Scores varied, indicating diverse levels of proficiency. The test, comprising true-false and multiple-choice questions, covered fundamental concepts and practical applications. Detailed solutions provided clarity and reinforcement. Additionally, suggested resources facilitated further learning. Overall, the test served as an invaluable self-assessment tool, highlighting the significance of continuous learning in mastering logistic regression and machine learning principles. Hope you like the article for logistic regression interview questions that we are explaining logistic regression and also linear regression interview questions . These logistic regression interview questions will help you for you interview preparation.

Hope you find this information on logistic regression for multiclass classification helpful, especially when preparing for interview questions on multiclass logistic regression!

q.19. Option A should be training accuracy increases

Updated. Thanks for pointing it out

30 contradicts 22, funny

Hi, You may have misunderstood the term linear separability. If the training data are linearly separable, we can select two hyperplanes in such a way that they separate the data and there are no points between them, and then try to maximize their distance. But in q30 image, it is not so.

linear seperable in the sense

q.22 shows a non-linear decision surface and q.30 states, that logistic regression has a linear decision surface. I guess, author should indicate, when exactly the decision surface is linear

Thank you so much sharing a good knowledge

i am glad you find them useful

In question no. 21 you yourself proved B1 for black is greater than B1 for green. So that makes the answer to be B.

Q. 28: I can count four local minima.

you are considering global minima as local minima.

You could edit the post and put the answers in the end of the post, lol

question 20 I guess should be n-1 classifiers. the posterior probability should sum up to one. so if p(c_1/x)+p(c_2/x)+....p(c_k/x)=1 therfore p(c_k/x)= 1- sum(p(c_1/x)+.....p(c_(k-1)/x) and we need the density estimate of only k-1 classes and the classes are assigned by arg max p(c_i/x) Is there something i dont know about OVA?

For question no. 29 blue line (learning rate = l1) converges faster than black or any other lines. So probable answer should be l1>l2>l3 Am i missing something here ?

By definition a local minima can be a global minima. for a point x to be a local minima, it only requires a number epsilon such that f(x) is the smallest in the neighborhood x+- epsilon. If x happens to be the global minima, it does not contradict with the definition of local minima.

The answer for no.15 is C,the range of logit function can not be less than zero .

Answer for question no.15 is C.the range of logit function is canot be less than zero.

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