NPTEL Introduction to Machine Learning Week 2 Assignment Answers 2025
1. In a linear regression model y=θ0+θ1x1+θ2x2+…+θpxp, what is the purpose of adding an intercept term (θ0)?
- To increase the model’s complexity
- To account for the effect of independent variables.
- To adjust for the baseline level of the dependent variable when all predictors are zero.
- To ensure the coefficients of the model are unbiased.
Answer :- c
2. Which of the following is true about the cost function (objective function) used in linear regression?
- It is non-convex.
- It is always minimized at θ = 0.
- It measures the sum of squared differences between predicted and actual values.
- It assumes the dependent variable is categorical.
Answer :- c
3. Which of these would most likely indicate that Lasso regression is a better choice than Ridge regression?
- All features are equally important
- Features are highly correlated
- Most features have small but non-zero impact
- Only a few features are truly relevant
Answer :- d
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4. Which of the following conditions must hold for the least squares estimator in linear regression to be unbiased?
- The independent variables must be normally distributed.
- The relationship between predictors and the response must be non-linear.
- The errors must have a mean of zero.
- The sample size must be larger than the number of predictors.
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5. When performing linear regression, which of the following is most likely to cause overfitting?
- Adding too many regularization terms.
- Including irrelevant predictors in the model.
- Increasing the sample size.
- Using a smaller design matrix.
Answer :-
6. You have trained a complex regression model on a dataset. To reduce its complexity, you decide to apply Ridge regression, using a regularization parameterλ. How does the relationship between bias and variance change asλ becomes very large? Select the correct option
- bias is low, variance is low.
- bias is low, variance is high.
- bias is high, variance is low.
- bias is high, variance is high.
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7. Given a training data set of 10,000 instances, with each input instance having 12 dimensions and each output instance having 3 dimensions, the dimensions of the design matrix used in applying linear regression to this data is
- 10000 × 12
- 10003 × 12
- 10000 × 13
- 10000 × 15
Answer :-
8. The linear regression model y=a0+a1x1+a2x2+…+apxp is to be fitted to a set of N training data points having P attributes each. Let X be N x (p+1) vectors of input values (augmented by 1‘s), Y be N x 1 vector of target values, and θ be (p+1)×1 vector of parameter values (a0,a1,a2,…,ap). If the sum squared error is minimized for obtaining the optimal regression model, which of the following equation holds?
- XTX = XY
- Xθ = XTY
- XTXθ = Y
- XTXθ = XTY
Answer :-
9. Which of the following scenarios is most appropriate for using Partial Least Squares (PLS) regression instead of ordinary least squares (OLS)?
- When the predictors are uncorrelated and the number of samples is much larger than the number of predictors.
- When there is significant multicollinearity among predictors or the number of predictors exceeds the number of samples.
- When the response variable is categorical and the predictors are highly non-linear.
- When the primary goal is to interpret the relationship between predictors and response, rather than prediction accuracy.
Answer :-
10. Consider forward selection, backward selection and best subset selection with respect to the same data set. Which of the following is true?
- Best subset selection can be computationally more expensive than forward selection
- Forward selection and backward selection always lead to the same result
- Best subset selection can be computationally less expensive than backward selection
- Best subset selection and forward selection are computationally equally expensive
- Both (b) and (d)
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NPTEL Introduction to Machine Learning Week 1 Assignment Answers 2025
1. Which of the following is/are unsupervised learning problem(s)?
- Sorting a set of news articles into four categories based on their titles
- Forecasting the stock price of a given company based on historical data
- Predicting the type of interaction (positive/negative) between a new drug and a set of human proteins
- Identifying close-knit communities of people in a social network
- Learning to generate artificial human faces using the faces from a facial recognition dataset
Answer :- d, e
2. Which of the following statement(s) about Reinforcement Learning (RL) is/are true?
- While learning a policy, the goal is to maximize the reward for the current time step
- During training, the agent is explicitly provided the most optimal action to be taken in each state.
- The actions taken by an agent do no affect the environment in any way.
- RL agents used for playing turn based games like chess can be trained by playing the agent against itself (self play).
- RL can be used in a autonomous driving system.
Answer :- d, e
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3. Which of the following is/are regression tasks(s)?
- Predicting whether an email is spam or not spam
- Predicting the number of new CoVID cases in a given time period
- Predicting the total number of goals a given football team scores in an year
- Identifying the language used in a given text document
Answer :- c, d
4. Which of the following is/are classification task(s)?
- Predicting whether or not a customer will repay a loan based on their credit history
- Forecasting the weather (temperature, humidity, rainfall etc.) at a given place for the following 24 hours
- Predict the price of a house 10 years after it is constructed.
- Predict if a house will be standing 50 years after it is constructed.
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5. Consider the following dataset. Fit a linear regression model of the form y=β0+β1x1+β2x2
using the mean-squared error loss. Using this model, the predicted value of y at the point (x1,x2) = (0.5, −1.0) is
- 4.05
- 2.05
- −1.95
- −3.95
Answer :-
6. Consider the following dataset. Using a k-nearest neighbour (k-NN) regression model with k = 3, predict the value of y at (x1,x2) = (1.0, 0.5). Use the Euclidean distance to find the nearest neighbours.
- −1.766
- −1.166
- 1.133
- 1.733
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7. Consider the following dataset with three classes: 0, 1 and 2. x1 and x2 are the independent variables whereas y is the class label. Using a k-NN classifier with k = 5, predict the class label at the point (x1,x2) = (1.0, 1.0). Use the Euclidean distance to find the nearest neighbours.
- 0
- 1
- 2
- Cannot be predicted
Answer :-
8. Consider the following statements regarding linear regression and k-NN regression models. Select the true statements.
- A linear regressor requires the training data points during inference.
- A k-NN regressor requires the training data points during inference.
- A k-NN regressor with a higher value of k is less prone to overfitting.
- A linear regressor partitions the input space into multiple regions such that the prediction over a given region is constant.
Answer :-
9.
Answer :-
10.
- On a given training dataset, the mean-squared error of (i) is always less than or equal to that of (ii).
- (i) is likely to have a higher variance than (ii).
- (ii) is likely to have a higher variance than (i).
- If (i) overfits the data, then (ii) will definitely overfit.
- If (ii) underfits the data, then (i) will definitely underfit.
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