Which of the following expression is true?

In sample error > out sample error
In sample error = out sample error
All of the mentioned

The correct answer is: C. In sample error = out sample error.

In-sample error is the error that is calculated using the same data that was used to build the model. Out-of-sample error is the error that is calculated using data that was not used to build the model.

In general, in-sample error is lower than out-of-sample error. This is because the model is trained on the in-sample data, so it is able to fit the data very well. However, when the model is used to make predictions on out-of-sample data, it is not able to fit the data as well, and so the error is higher.

However, there are some cases where in-sample error can be higher than out-of-sample error. This can happen if the model is overfitted to the in-sample data. Overfitting occurs when the model learns the noise in the data instead of the underlying patterns. As a result, the model does not generalize well to out-of-sample data.

In summary, in-sample error is typically lower than out-of-sample error. However, there are some cases where in-sample error can be higher than out-of-sample error. This can happen if the model is overfitted to the in-sample data.