Answered

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As the flexibility of a statistical learning method increases, determine whether each of the following statements is true or false.

1. The method becomes more sensitive to the changes in the training set.
[Choose: True / False]

2. The average responses estimated by the method get closer to the true average responses.
[Choose: True / False]

3. The amount of errors between the predicted responses estimated by the method and the true responses in the training data becomes larger.
[Choose: True / False]

4. The amount of errors between the predicted responses estimated by the method and the true responses in unseen data (not used in training) becomes smaller.
[Choose: True / False]

Sagot :

GinnyAnswer
Sure, let's tackle each statement one by one and determine whether they are true or false, providing detailed reasoning.

1. "As the flexibility of a statistical learning method increases, the method becomes more sensitive to the changes in the training set."
- Increasing the flexibility of a statistical learning method means that it can capture more complex patterns in the training data. However, this also means it will more closely follow the training data points, making it more sensitive to any variations or noise in the data.
- Answer: True

2. "As the flexibility of a statistical learning method increases, the average responses estimated by the method get closer to the true average responses."
- While increased flexibility allows the model to fit the training data better, it does not necessarily lead to estimates that are closer to the true average responses. In fact, it could lead to overfitting, where the model fits the noise in the training data instead of the underlying true pattern.
- Answer: False

3. "As the flexibility of a statistical learning method increases, the amount of errors between the predicted responses estimated by the method and the true responses in the training data becomes larger."
- With increased flexibility, a model tends to fit the training data very closely, often capturing even the noise. This usually results in lower errors on the training data itself because the model is tailored to fit the training points very precisely.
- Answer: False

4. "As the flexibility of a statistical learning method increases, the amount of errors between the predicted responses estimated by the method and the true responses in unseen data (not used in training) becomes smaller."
- Increased flexibility usually leads to a better fit on the training data but poorer generalization to unseen data. This means that the prediction errors on unseen data are likely to increase due to overfitting.
- Answer: False

Summarizing the results:
1. True
2. False
3. False
4. False
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