What is an advantage of using polynomial regression over linear regression.

Why is it possible to model non-linear functions with polynomial regression?

What are the shortcomings of using polynomial regression? Select all that apply.

For a multivariate linear regression problem with multivariate output , the loss function is minimised with respect to the weight matrix by setting the partial derivative . Which of the following terms is used to denote the partial derivative matrix, in such a scenario?

For a multivariate linear regression problem, the loss function is minimized with respect to the weight vector by setting the partial derivative . Which of the following correctly shows the expansion of the partial derivative, ?

In the closed form solution to multivariate linear regression, why do we use the pseudo-inverse of instead of the simple inverse?

An engineer has IID Gaussian observations where both and are unknown. The engineer makes the following argument:

"The standardised sample mean is standard normal. Therefore, I can replace the unknown by the sample standard deviation and obtain the exact confidence interval Afterall, since the chi-squared confidence interval for is exact for a Gaussian population, this substitution must also be exact."

Which assessment is correct?