Suppose we fit “Lasso Regression” to a data set, which has 100 features (X1,X2…X100). Now, we rescale one of these feature by multiplying with 10 (say that feature is X1), and then refit Lasso regression with the same regularization parameter. Now, which of the following option will be correct?

The correct answer is: A. It is more likely for X1 to be excluded from the model.

Lasso regression is a regularization method that penalizes models for having too many parameters. This can be useful in situations where there is a lot of noise in the data or where there are many correlated features. When a feature is rescaled, its variance is also rescaled. This means that a feature with a large variance is more likely to be penalized by Lasso regression and excluded from the model.

In this case, X1 is rescaled by multiplying it with 10. This means that the variance of X1 is increased by a factor of 10. As a result, X1 is more likely to be penalized by Lasso regression and excluded from the model.

Here is a more detailed explanation of each option:

• Option A: It is more likely for X1 to be excluded from the model. This is the correct answer, as explained above.
• Option B: It is more likely for X1 to be included in the model. This is incorrect, as X1 is more likely to be penalized and excluded from the model.
• Option C: Can’t say. This is incorrect, as we can make a clear prediction about whether X1 is more likely to be included or excluded from the model.
• Option D: None of these. This is incorrect, as one of the options is correct.