We have been given a dataset with n records in which we have input attribute as x and output attribute as y. Suppose we use a linear regression method to model this data. To test our linear regressor, we split the data in training set and test set randomly. What do you expect will happen with bias and variance as you increase the size of training data?

The correct answer is C. Bias decreases and Variance decreases.

Bias is the difference between the expected value of the model’s output and the true value. Variance is a measure of how spread out the model’s predictions are.

When the size of the training data set increases, the model will be able to learn the underlying relationship between the input and output variables more accurately. This will reduce the bias of the model.

In addition, as the size of the training data set increases, the model will be less likely to overfit the data. This will reduce the variance of the model.

Therefore, as the size of the training data set increases, we expect the bias and variance of the model to decrease.

Here is a diagram that illustrates the relationship between bias and variance:

The diagram shows that as the size of the training data set increases, the bias and variance of the model decrease. This is because the model is able to learn the underlying relationship between the input and output variables more accurately.

Here is a brief explanation of each option:

• Option A: Bias increases and Variance increases. This is not the correct answer because as the size of the training data set increases, the bias of the model should decrease.
• Option B: Bias decreases and Variance increases. This is not the correct answer because as the size of the training data set increases, the variance of the model should decrease.
• Option C: Bias decreases and Variance decreases. This is the correct answer because as the size of the training data set increases, the bias and variance of the model should decrease.
• Option D: Bias increases and Variance decreases. This is not the correct answer because as the size of the training data set increases, the bias of the model should decrease.