Which one of the following is true for Ridge Regression (RR)

The correct option is: The regularizer of RR may increase the bias of the model, but it helps in reducing the variance in prediction.

Here is the step-by-step explanation of why this statement is correct and why the other options are incorrect:

1. Understanding Ridge Regression and Regularization:
Ridge Regression is a variant of linear regression that introduces a regularization term (penalty) to the ordinary least squares (OLS) loss function. The objective function of Ridge Regression is given by:

$$L(\beta) = \sum_{i=1}^{n} (y_i - x_i^T\beta)^2 + \lambda \sum_{j=1}^{p} \beta_j^2$$

where $\lambda$ (lambda) is the regularization parameter that controls the penalty strength, and $\beta$ represents the model coefficients.

2. Analysis of the Correct Statement (Bias-Variance Trade-off):
The penalty term $\lambda \sum \beta_j^2$ shrinks the estimated coefficients towards zero. By constraining the size of the coefficients, Ridge Regression prevents the model from fitting noise in the training data too closely.
This constraint introduces a restriction (bias) on the model's capacity, meaning the model's predictions might deviate slightly from the true average relationship (increased bias). However, because the coefficients are smaller and more stable, the model becomes much less sensitive to fluctuations in the training dataset, significantly reducing the variance of its predictions. This is a classic example of the bias-variance trade-off, where we accept a small increase in bias in exchange for a substantial decrease in variance.

3. Why the other options are incorrect:
- "The reg. of RR uses L1 norm": Incorrect. Ridge Regression uses the L2 norm (squared sum of coefficients). Lasso Regression is the technique that uses the L1 norm (absolute sum of coefficients).
- "RR aims to reduce the num. of parameters that have -ve value.": Incorrect. Ridge Regression shrinks all parameters toward zero regardless of whether they are positive or negative.
- "The reg. in the objective fn. of RR is used to guard against scenarios where the model works well for the test data but poorly for the training data.": Incorrect. Regularization is used to prevent overfitting, which is a scenario where the model performs exceptionally well on the training data but poorly on unseen test data, not the other way around.