Can coefficients of an AR(p) be estimated by OLS? Explain how  estimated regression function can be used for forecasting?

In a multivariate model (ROC analysis), the area under the curve is 0.705 ,  explain how this is statistically significant.  Images of the predictive power graph is attached. Please help explain the results.

given the observed data (obsX,obsY), learning rate (alpha), error change threshold, and delta from the huber loss model,write a  function returns theta0 and theta1 that minimizes the error. Use pseudo huber loss function

You trained the regression model with 100 regressors and 1000 observations in the training and another 1000 in the test sample. You found that in-sample R2 over the training sample is 70% and the out-of-sample R2 over the test sample only - 30%. (select all that apply) a) Do you think there is any problem and how would you characterize it? Can adding more regressors (if you have them) help the model? b) Which approaches you may use to solve the problem? c) What would you expect the in-sample R2 to increase or decrease after that? What about the out-of-sample (test) R2?