# Introduction to Machine Learning NPTEL Week 3 Solutions NPTEL 2023

This set of MCQ(multiple choice questions) focuses on the Introduction to Machine Learning NPTEL Week 3 Solutions NPTEL 2023.

With the increased availability of data from varied sources there has been increasing attention paid to the various data driven disciplines such as analytics and machine learning. In this course we intend to introduce some of the basic concepts of machine learning from a mathematically well motivated perspective. We will cover the different learning paradigms and some of the more popular algorithms and architectures used in each of these paradigms.

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### Introduction to Machine learning NPTEL 2023 Week 3 Solutions

Q1. Which of the following is false about a logistic regression based classifier?

a)  The logistic function is non-linear in the weights
b) The logistic function is linear in the weights
c) he decision boundary is non-linear in the weights
d) The decision boundary is linear in the weights

Q2. Consider the case where two classes follow Gaussian distribution which are centered at (3, 9) and (−3, 3) and have identity covariance matrix. Which of the following is the separating decision boundary using LDA assuming the priors to be equal?

a) y−x=3
b) x+y=3
c) x+y=6
d) both (b) and (c)
e) None of the above
f) Can not be found from the given information

Q3. Consider the following relation between a dependent variable and an independent variable identified by doing simple linear regression. Which among the following relations between the two variables does the graph indicate?

a)  as the independent variable increases, so does the dependent variable
b) as the independent variable increases, the dependent variable decreases
c) if an increase in the value of the dependent variable is observed, then the independent variable will show a corresponding increase
d) if an increase in the value of the dependent variable is observed, then the independent variable will show a corresponding decrease
e)  the dependent variable in this graph does not actually depend on the independent variable
f) none of the above

Introduction to Machine Learning NPTEL Week 3 Solutions

Q4. Given the following distribution of data points:

What method would you choose to perform Dimensionality Reduction?

a) Linear Discriminant Analysis
b) Principal Component Analysis

Q5. In general, which of the following classification methods is the most resistant to gross outliers?

b) Linear Regression
c) Logistic regression
d) Linear Discriminant Analysis (LDA)

Introduction to Machine Learning NPTEL Week 3 Solutions

Q6. Suppose that we have two variables, X and Y (the dependent variable). We wish to find the relation between them. An expert tells us that
relation between the two has the form Y=m+X2+c=+2+. Available to us are samples of the variables X and Y. Is it possible to apply linear regression to this data to estimate the values of m and c?

a) no
b) yes
c) insufficient information

Introduction to Machine Learning NPTEL Week 3 Solutions

Q7. In a binary classification scenario where x is the independent variable and y is the dependent variable, logistic regression assumes that the conditional distribution y|x| follows a

a) Bernoulli distribution
b) binomial distribution
c) normal distribution
d) exponential distribution

Q8. Consider the following data:

Assuming that you apply LDA to this data, what is the estimated covariance matrix?

a) [1.8750.31250.31250.9375][1.8750.31250.31250.9375]
b) [2.50.41670.41671.25]
c) [1.8750.31250.31251.2188]
d) [2.50.41670.41671.625]
e) [3.251.16671.16672.375]
f) [2.43750.8750.8751.7812]
g) None of these

Introduction to Machine Learning NPTEL Week 3 Solutions

Q9. Given the following 3D input data, identify the principal component.

(Steps: center the data, calculate the sample covariance matrix, calculate the eigenvectors and eigenvalues, identify the principal component)

a) ⎢−0.10220.00180.9948⎤⎦⎥
b) ⎡⎣⎢0.5742−0.81640.0605⎤⎦⎥
c) ⎢0.57420.81640.0605⎤⎦⎥
d) ⎡⎣⎢−0.57420.81640.0605⎤⎦
e) ⎡⎣⎢0.81230.57740.0824⎤⎦⎥
f) None of the above

Q10. For the data given in the previous question, find the transformed input along the first two principal components.

a) ⎡⎣⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢0.6100−0.4487−1.26511.33450.5474−1.0250−1.26721.5142−0.0196−0.1181−0.11630.5702−0.72570.27270.1724−0.0355⎤⎦⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥
b) ⎡⎣⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢−0.1817−1.2404−2.05680.5428−0.2443−1.8167−2.05890.72250.89440.79590.79771.48420.18841.18681.08640.8785⎤⎦⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥
c) ⎡⎣⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢−6.2814−4.3143−3.7368−1.79502.29173.52894.91865.38830.6100−0.4487−1.26511.33450.5474−1.0250−1.26721.5142⎤⎦⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥
d) ⎡⎣⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢1.47213.43924.01665.958410.045111.282312.672013.1418−0.1817−1.2404−2.05680.5428−0.2443−1.8167−2.05890.7225⎤⎦⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥
e) None of the above

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