NPTEL Data Science for Engineers Week 4 Assignment Answer

ABOUT THE COURSE :

Learning Objectives :

Introduce R as a programming language
Introduce the mathematical foundations required for data science
Introduce the first level data science algorithms
Introduce a data analytics problem solving framework
Introduce a practical capstone case study

Learning Outcomes:

Describe a flow process for data science problems (Remembering)
Classify data science problems into standard typology (Comprehension)
Develop R codes for data science solutions (Application)
Correlate results to the solution approach followed (Analysis)
Assess the solution approach (Evaluation)
Construct use cases to validate approach and identify modifications required (Creating)

INTENDED AUDIENCE: Any interested learner

PREREQUISITES: 10 hrs of pre-course material will be provided, learners need to practise this to be ready to take the course.

INDUSTRY SUPPORT: HONEYWELL, ABB, FORD, GYAN DATA PVT. LTD.

NPTEL Data Science for Engineers Week 4 Assignment Answer

Course layout

Week 1: Course philosophy and introduction to R

Week 2: Linear algebra for data science

1. Algebraic view – vectors, matrices, product of matrix & vector, rank, null space, solution of over-determined set of equations and pseudo-inverse)
2. Geometric view – vectors, distance, projections, eigenvalue decomposition

Week 3: Statistics (descriptive statistics, notion of probability, distributions, mean, variance, covariance, covariance matrix, understanding univariate and multivariate normal distributions, introduction to hypothesis testing, confidence interval for estimates)

Week 4: Optimization

Week 5: 1. Optimization

2. Typology of data science problems and a solution framework

Week 6: 1. Simple linear regression and verifying assumptions used in linear regression

2. Multivariate linear regression, model assessment, assessing importance of different variables, subset selection

Week 7: Classification using logistic regression

Week 8: Classification using kNN and k-means clustering

NPTEL Data Science for Engineers Week 4 Assignment Answer

Week 4 : Assignment 4

Due date: 2025-02-19, 23:59 IST.

Assignment not submitted

3 points

Let $f (x) = x^{3} + 3 x^{2} - 24 + 7.$ Select the correct options from the following:

$x = 2$ will give the maximum for $f (x) .$

$x = 2$ will give the minimum for $f (x) .$

Maximum value of $f (x)$ is 87.

The stationary points for $f (x)$ are 2 and 4.

2 points

Find the gradient of $f (x) = x^{2} y$ at $(x, y) = (1, 3) .$

$\nabla f = [\begin{matrix} 1 \\ 6 \end{matrix}]$

$\nabla f = [\begin{matrix} 6 \\ 1 \end{matrix}]$

$\nabla f = [\begin{matrix} 6 \\ 9 \end{matrix}]$

$\nabla f = [\begin{matrix} 3 \\ 3 \end{matrix}]$

2 points

Find the Hessian matrix for $f (x, y) = x^{2} y$ at $(x, y) = (1, 3)$

$\nabla^{2} f = [\begin{matrix} 3 & 2 \\ 2 & 0 \end{matrix}]$

$\nabla^{2} f = [\begin{matrix} 3 & 3 \\ 3 & 0 \end{matrix}]$

$\nabla^{2} f = [\begin{matrix} 6 & 2 \\ 2 & 0 \end{matrix}]$

$\nabla^{2} f = [\begin{matrix} 6 & 3 \\ 3 & 0 \end{matrix}]$

1 point

Let $f (x, y) = - 3 x^{2} - 6 x y - 6 y^{2} .$ The point (0, 0) is a

saddle point

maxima

minima

1 point

For which numbers $b$ is the matrix $A = [\begin{matrix} 1 & b \\ b & 9 \end{matrix}]$ positive definite?

$- 3 < b < 3$

$b = 3$

$b = - 3$

$- 3 \leq b \leq 3$

1 point

Consider $f (x) = x^{3} - 12 x - 5$ Which among the following statements are true?

$f (x)$ is increasing in the interval $(- 2, 2) .$

$f (x)$ is increasing in the interval $(2, \infty)$

$f (x)$ is decreasing in the interval $(- \infty, - 2)$

$f (x)$ is decreasing in the interval $(- 2, 2)$

1 point

Consider the following optimization problem:
$max_{x ϵ R} f (x)$
, where
$f (x) = x^{2} + 7 x^{3} + 5 x^{2} - 17 x + 3$

Let $x^{*}$ be the maximizer of $f (x) .$ What is the second order sufficient condition for $x^{*}$ to be the maximizer of the function $f (x) ?$

$4 x^{2} + 21 x^{2} + 10 x - 17 = 0$

$12 x^{2} + 42 x + 10 = 0$

$12 x^{2} + 42 x + 10 > 0$

$12 x^{2} + 42 x + 10 < 0$

1 point

In optimization problem, the function that we want to optimize is called

Decision function

Constraints function

Optimal function

Objective function

1 point

The optimization problem ${min}_{x} f (x)$ can also be written as ${max}_{x} f (x)$

True

False

1 point

Gradient descent algorithm converges to the local minimum

True

False

NPTEL Data Science for Engineers Week 4 Assignment Answer

NPTEL Data Science for Engineers Week 4 Assignment Answer

Course layout

NPTEL Data Science for Engineers Week 4 Assignment Answer

Week 4 : Assignment 4

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