Part II. Short-Answer Questions.

Problem I. Questions 16-20 are based on the below.

Please check the following chatGPT answer and see whether you agree or disagree. Please provide your answer if you disagree.

ChatGPT

Q for ChatGPT: what is in-sample model mean squared error with degrees of freedom?

ChatGPT Part1: In-sample model mean squared error (MSE) is a metric used to evaluate the performance of a machine learning model. It measures the average squared difference between the predicted values and the actual values in the training set.

Degrees of freedom (df) refer to the number of independent variables in the model that are allowed to vary. It is typically calculated as the difference between the total number of observations in the dataset and the number of parameters estimated in the model.

The formula for in-sample model MSE with degrees of freedom is:

MSE = (1/n) * (yi - i)^2

where n is the number of observations in the dataset, yi is the actual value of the target variable for the ith observation, i is the predicted value of the target variable for the ith observation, and df is the degrees of freedom.

Question 16: Do you agree or disagree with the above? If you disagree, please provide your answer and emphasize the part you disagree. ChatGPT Part1: In the case of linear regression with p independent variables, the degrees of freedom would be n - p - 1.

Question 17:Why are the degrees of freedom "n-p-1" rather than "n-p" in classical linear regression? Question 18: For a categorical predictor with 5 levels, how many dummy variables are they equivalent to? Question 19: For generalized additive models, what is the common name for the degrees of freedom? Are they always integers? Question 20: For neural networks/deep learning regression models, the number of parameters can be huge. One common phenomenon with a such complex model is "overfitting". Please explain in sentences in terms of the languages of "in-sample MSE" and "out-of-sample MSPE".