## NPTEL Introduction to Machine Learning Week 2 Assignment Answers 2024

1. The parameters obtained in linear regression

- can take any value in the real space
- are strictly integers
- always lie in the range [0,1]
- can take only non-zero values

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2. Suppose that we have N independent variables (X1,X2,…Xn) and the dependent variable is Y. Now imagine that you are applying linear regression by fitting the best fit line using the least square error on this data. You found that the correlation of X1 with Y is -0.005.

- Regressing Y on X1 mostly does not explain away Y
- Regressing Y on X1 explains away Y
- The given data is insufficient to determine if regressing Y on X1 explains away Y or not
- None of the above

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3. The relation between studying time (in hours) and grade on the final examination (0-100) in a random sample of students in the Introduction to Machine Learning Class was found to be:

**Grade** = 30.5+15.2(h)

How will a student’s grade be affected if she studies for four hours, compared to not studying?

- It will go down by 30.4 points
- It will go up by 60.8 points
- The grade will remain unchanged
- It cannot be determined from the information given

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4. Consider the following 4 training examples:

We want to learn a function f(x)=ax+b which is parametrized by (a,b). Using squared error as the loss function, which of the following parameters would you use to model this function.

- (1,1)
- (1,2)
- (2,1)
- (2,2)

Answer :-

5. Consider a modified k−NN method in which once the k nearest neighbours to the query point are identified, you do a linear regression fit on them and output the fitted value for the query point. Which of the following is/are true regarding this method.

- This method makes an assumption that the data is locally linear
- In order to perform well, this method would need dense distributed training data
- This method has higher bias compared to k−NN
- This method has higher variance compared to k−NN

Answer :-

6. Which of the statements is/are True?

- Ridge has sparsity constraint, and it will drive coefficients with low values to 0
- Lasso has a closed form solution for the optimization problem, but this is not the case for Ridge
- Ridge regression may reduce the number of variables
- If there are two or more highly collinear variables, Lasso will select one of them randomly

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7. Choose the correct option(s) from the following:

- When working with a small dataset, one should prefer low bias/high variance classifiers over high bias/low variance classifiers
- When working with a small dataset, one should prefer high bias/low variance classifiers over low bias/high variance classifiers
- When working with a large dataset, one should prefer high bias/low variance classifiers over low bias/high variance classifiers
- When working with a large dataset, one should prefer low bias/high variance classifiers over high bias/low variance classifiers

Answer :-

8. Consider the following statements:

Statement A: In Forward stepwise selection, in each step, that variable is chosen which has the maximum correlation with the residual, then the residual is regressed on that variable, and it is added to the predictor.

Statement B: In Forward stagewise selection, the variables are added one by one to the previously selected variables to produce the best fit till then

- Both the statements are True
- Statement A is True, and Statement B is False
- Statement A if False and Statement B is True
- Both the statements are False

Answer :-

9. 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×(p+1) vectors of input values (augmented by 1’s), Y be N×1 vector of target values, and θ be (p+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

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