Hello Learners, In this Post, you will find **NPTEL Data Science for Engineers Assignment 5 Week 5 Answers 2023**. All the Answers are provided below to help the students as a reference don’t straight away look for the solutions.

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## NPTEL Data Science for Engineers Assignment 5 Answers 2023:

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#### Q.1. Which of the following statements is/are **not TRUE** with respect to the multi variate optimization?

I – The gradient of a function at a point is parallel to the contours II – Gradient points in the direction of greatest increase of the function III – Negative gradient points in the direction of the greatest decrease of the function IV – Hessian is a non-symmetric matrix

#### Q.2. The solution to an unconstrained optimization problem is always the same as the solution to the constrained one.

- True
**False**

#### Q.3. Gradient based algorithm methods compute

- only step length at each iteration
**both direction and step length at each iteration**- only direction at each iteration
- none of the above

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#### Q.4. For an unconstrained multivariate optimization given f(x¯¯¯), the necessary second order condition for x¯¯¯∗ to be the minimizer of f(x) is

Use the following information to answer Q5, 6, 7 and 8

minx1,x2∈R f(x1,x2)=x21+4×22−2×1+8×2.

#### Q.5.** **Which among the following is the stationary point for f(x1,x2)?

#### Q.6. Find the eigen values corresponding to Hessian matrix of f.

- 1,−1
- 1,1
**2,8**- 0,2

#### Q.7. Find the minimum value of f.

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#### Q.8. What is the minimum value of f(x1,x2) subject to the constraint x1+2×2=7?

- -5
- -1
**27**- 0

#### Q.9. Find the maximum value of f(x,y)=49−x2−y2 subject to the constraint x+3y=10.

#### Q.10. Consider an optimization problem minx1,x2 x2−xy+y2 subject to the constraints

2x+y≤1x+2y≥2x≥−1

**Answer:****C**

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#### About NPTEL Data Science for Engineers 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)

##### 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

**CRITERIA TO GET A CERTIFICATE**:

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.

Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

**YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.**

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