3. (23 pts) Ossian intends to apply for a job at the mine. Note that all of applicants need to participate in interviews, from which they receive a score from the interviewer. Suppose that Ossian wants to evaluate the probability that he receives a job offer. He is given the following dataset about the past 3 candidates: Candidate # Scores 1 4 Offer (Y/N) 1 2 1 0 3 5 0 (a) To make a prediction, suppose that the Ossian decides to apply the linear regression model Ya+b*x+e where x is the scores. Given the dataset, what is the optimization problem formulation for the least square estimators. Specify the decision variables and the objective function. (b) Following part (a), what are the first order conditions for the optimization problem and what are the least square estimators?