The correct answer is D. None of these.
A linear regression model that perfectly fits the training data (train error is zero) does not necessarily mean that the test error will also be zero. This is because the training data and the test data are two different sets of data. The training data is used to fit the model, while the test data is used to evaluate the model’s performance. The test error is a measure of how well the model generalizes to new data.
There are a number of reasons why a linear regression model that perfectly fits the training data may not have a zero test error. One reason is that the training data may not be representative of the test data. This can happen if the training data is too small or if it is not randomly selected. Another reason is that the model may be overfitting the training data. This means that the model is too closely tied to the specific data that it was trained on, and it does not generalize well to new data.
In order to avoid overfitting, it is important to use a regularization technique. Regularization helps to prevent the model from becoming too complex, and it can improve the model’s performance on the test data.
Here are some additional details about each option:
- Option A: You will always have test error zero. This is not necessarily true. As explained above, a linear regression model that perfectly fits the training data does not necessarily mean that the test error will also be zero.
- Option B: You can not have test error zero. This is also not necessarily true. As explained above, it is possible for a linear regression model to have a zero test error. However, this is not always the case.
- Option C: Both A and B. This is not correct. As explained above, both options A and B are not necessarily true.
- Option D: None of these. This is the correct answer.