Data Science for Engineers Week 6 NPTEL Assignment Answers 2025

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✅ Subject: Data Science for Engineers
📅 Week: 6
🎯 Session: NPTEL 2025 July-October
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NPTEL Data Science for Engineers Week 6 Assignment Answers 2025

1. What is the relationship between the variables, Coupon rate and Bid price?

• Coupon rate = 99.95 + 0.24 * Bid price
• Bid price = 99.95 + 0.24 * Coupon rate
• Bid price = 74.7865 + 3.066 * Coupon rate
• Coupon rate = 74.7865 + 3.066 * Bid price

Answer : See Answers

2. Choose the correct option that best describes the relation between the variables Coupon rate and Bid price in the given data.

• Strong positive correlation
• Weak positive correlation
• Strong negative correlation
• Weak negative correlation

Answer :

3. What is the R-Squared value of the model obtained in Q1?

• 0.2413
• 0.12
• 0.7516
• 0.5

Answer :

4. What is the adjusted R-Squared value of the model obtained in Q1?

• 0.22
• 0.7441
• 0.088
• 0.5

Answer :

5. Based on the model relationship obtained from Q1, what is the residual error obtained while calculating the bid price of a bond with coupon rate of 3?

• 10.5155
• -10.5155
• 6.17
• 0

Answer :

6. State whether the following statement is True or False.
Covariance is a better metric to analyze the association between two numerical variables than correlation.

• True
• False

Answer : See Answers

7. If R² is 0.4, SSR=200 and SST=500, then SSE is

• 500
• 200
• 300
• None of the above

Answer :

8. Linear Regression is an optimization problem where we attempt to minimize

• SSR (residual sum-of-squares)
• SST (total sum-of-squares)
• SSE (sum-squared error)
• Slope

Answer :

9. The model built from the data given below is Y=0.2x+60. Find the values for R² and Adjusted R²

• R2 is 0.22 and Adjusted R2 is −0.303
• R2 is 0.022 and Adjusted R2 is −0.303
• R2 is 0.022 and Adjusted R2 is 0.303
• None of the above

Answer :

10. Identify the parameters β₀ and β₁ that fits the linear model β₀+β₁x using the following information: total sum of squares of X,SSXX=52.53,SSXY=52.01, mean of X,X¯¯¯¯=4.46, and mean of Y,Y^=6.32.

• 1.9 and 0.99
• 10.74 and 1.01
• 4.42 and 1.01
• None of the above

Answer : See Answers

NPTEL Data Science for Engineers Week 6 Assignment Answers 2024

1. What is the relationship between the variables, Coupon rate and Bid price?

• a. Coupon rate = 99.95 + 0.24 * Bid price
• b. Bid price = 99.95 + 0.24 * Coupon rate
• c. Bid price = 74.7865 + 3.066 * Coupon rate
• d. Coupon rate = 74.7865 + 3.066 * Bid price

✅ Answer :- c
✏️ Explanation: This is a standard linear regression output format, where Bid price is the dependent variable and Coupon rate is the independent variable.

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2. Choose the correct option that best describes the relation between the variables Coupon rate and Bid price in the given data.

• a. Strong positive correlation
• b. Weak positive correlation
• c. Strong negative correlation
• d. Weak negative correlation

✅ Answer :- a
✏️ Explanation: Since the slope (3.066) is large and positive, and the R-squared value is high (from Q3), the correlation is strong and positive.

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3. What is the R-Squared value of the model obtained in Q1?

• a. 0.2413
• b. 0.12
• c. 0.7516
• d. 0.5

✅ Answer :- c
✏️ Explanation: An R² value of 0.7516 means that ~75% of the variance in Bid price is explained by the Coupon rate.

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4. What is the adjusted R-Squared value of the model obtained in Q1?

• a. 0.22
• b. 0.7441
• c. 0.088
• d. 0.5

✅ Answer :- b
✏️ Explanation: Adjusted R² is slightly lower than R² and accounts for the number of predictors. 0.7441 is close to R² = 0.7516.

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5. Based on the model relationship obtained from Q1, what is the residual error obtained while calculating the bid price of a bond with coupon rate of 3?

• a. 10.5155
• b. -10.5155
• c. 6.17
• d. 0

✅ Answer :- a
✏️ Explanation:
Predicted Bid price = 74.7865 + 3.066 × 3 = 84.9845
If actual value is 95.5, then Residual = 95.5 – 84.9845 = 10.5155

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6. Covariance is a better metric to analyze the association between two numerical variables than correlation.

• a. True
• b. False

✅ Answer :- b
✏️ Explanation: Covariance is not standardized and depends on the units of measurement. Correlation is better for comparing strength of relationships.

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7. If R² is 0.6, SSR = 200 and SST = 500, then SSE is

• a. 500
• b. 200
• c. 300
• d. None of the above

✅ Answer :- c
✏️ Explanation: SST = SSR + SSE → 500 = 200 + SSE → SSE = 300

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8. Linear Regression is an optimization problem where we attempt to minimize

• a. SSR (residual sum-of-squares)
• b. SST (total sum-of-squares)
• c. SSE (sum-squared error)
• d. Slope

✅ Answer :- c
✏️ Explanation: Linear regression minimizes SSE to best fit the line to the data points.

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9. The model built from the data given below is Y = 0.2x + 60. Find the values for R² and Adjusted R²

• a. R² is 0.022 and Adjusted R² is −0.303
• b. R² is 0.022 and Adjusted R² is −0.0303
• c. R² is 0.022 and Adjusted R² is 0.303
• d. None of the above

✅ Answer :- a
✏️ Explanation: A low R² (0.022) and a negative Adjusted R² implies the model performs worse than a horizontal line (no predictor).