Question5 If you decide to use a polynomial regression, which of the following options affects the bias-variance trade-off most? (select one) Including or excluding the constant term in the input Whether we learn the weights by matrix inversion or gradient descent The variance of the Gaussian noise The degree of the polynomial ResetMaximum marks: 2 Flag question undefinedSingle choice
A
Including or excluding the constant term in the input
B
Whether we learn the weights by matrix inversion or gradient descent
C
The variance of the Gaussian noise
D
The degree of the polynomial

Question

Question5 If you decide to use a polynomial regression, which of the following options affects the bias-variance trade-off most? (select one) Including or excluding the constant term in the input Whether we learn the weights by matrix inversion or gradient descent The variance of the Gaussian noise The degree of the polynomial ResetMaximum marks: 2 Flag question undefinedSingle choice

A

Including or excluding the constant term in the input

B

Whether we learn the weights by matrix inversion or gradient descent

C

The variance of the Gaussian noise

D

The degree of the polynomial

BlackTom AI · Accepted Answer

In evaluating how a polynomial regression model trades off bias and variance, we should examine what aspect of the model actually changes its capacity and flexibility.
Option 1: Including or excluding the constant term in the input. This changes the overall intercept of the model but does not meaningfully alter the model’s capacity to fit nonlinear patterns. Its effect on bias and variance is typically minor compared to changing the polynomial degree.
Option 2: Whether we learn the weights by matrix inversion or gradient descent. This concerns the optimization algorithm, not the model’s representational capacity. If both methods converge to the same model, the bias-variance trade-off remains governed by the hypothesis class, not the solver.
Option 3: The variance of the Gaussian noise. While noise level in the data affects the observed variance of the estimator and the overall performance, it does not change the inherent bias-variance properties of the chosen model class. It shifts the error but not the trade-off curve defined by model complexity.
Option 4: The degree of the polynomial. This directly controls the model’s flexibility: low degrees may introduce high bias by underfitting, while high degrees can fit noise and increase variance. This is the core lever that moves along the bias-variance frontier and hence has the largest impact on the trade-off.
In summary, among the options, the degree of the polynomial is the primary dial that shifts the balance between bias and variance in polynomial regression, whereas the others influence factors that do not fundamentally alter the capacity of the hypothesis class or its fundamental bias-variance characteristics.