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 2 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
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 2 Assignment Answer
Week 2 : Assignment 2
Due date: 2025-02-05, 23:59 IST.
Q1. Are the Vectors are linearly Independent ?
Options:
a. Yes
b. No
Answer: [ B ] No
Solution:
Q2. Does the set, S = (1,1), (1,2) spans R^2 ?
Options:
a. Yes
b. No
Answer: [ A ] Yes
Solution:
Q3. Consider the following system of linear equations of the form Ax=b:
2x -3y+6z = 14
x+y-2z = -3
which among the following are correct ?
Answer: [ A ] [ D ]
Solution:
Consider the following system of linear equation
x+y+z = -2
x+2y-z = 1
2x + ay + bz = 2
Q4. Find the Conditions for a and b for which the above system has no solution.
Options:
Answer: [ B ]
Solution:
Q5. Find Conditions on a and b for which the above system has a unique solution.
Options:
Answer: [ D ]
Solution:
Q6. Find Conditions on a and b for which the above system has a infinite number of Solutions.
Options:
Answer: [ C ]
Solution:
In solving the system Ax=b in the variables x1, x2, x3 and Gaussian Elimination on the Augmented matrix [ A ] [ B ] led to the following row echelon form.
Q7. Identify the number of free variable from above row echelon matrix.
Options:
A. 0
B. 1
C. 2
D. 3
Answer: [ B ] 1
Solution:
Q8. Which among the following is correct for the above system Ax = b ?
Options:
A. It has infinite number of solutions
B. It has a unique solutions
C. It has no solution
Answer: [ A ]
Q9. For what values of a are matrix A = [ a 1 ] not invertible
[ -2 a+3 ]
Options:
A. a = 1
B. a = -2
C. a = -1
D. a = 2
D. a = 2
Answer: [ B ] [ C ]
Solution:
Q10. Which among the following is true for the determinant of a matrix?
Options:
A. The determinant of a diagonal matrix is the product of its diagonal entries.
B. If one row of a matrix is a scalar multiple of another, the determinant is 1.
C. If one row of a matrix is a scalar multiple of another, the determinant is 0.
D. The determinant of a permutation matrix can only be 1.
Answer: [ A ] [ C ]
Q11. Which among the Eigen Values of matrix A ?
Options:
A. 1, 3, -3
B. 1, 3, 3
C. -1, 3, 3
D. 1, -3, -3
Answer: [ D ]
Q12. Find Nullity of A ?
Answer: 2
Q13. Let A = Suppose the eigen values corresponding to AAT are a,b and c, then find the value of ab+bc+ca.
Options:
A. 9
B. 0
C. 81
D. 18
Answer: [ B ] 0