Introduction to Machine Learning Week 2 NPTEL Assignment Answers 2025

NPTEL Introduction to Machine Learning Week 2 Assignment Answers 2025

1. In a linear regression model y=θ₀+θ₁x₁+θ₂x₂+…+θ_px_p, 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,…,a_p). If the sum squared error is minimized for obtaining the optimal regression model, which of the following equation holds?

X^TX = XY
Xθ = X^TY
X^TXθ = Y
X^TXθ = X^TY

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)