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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