Industrial Engineering Question

Problem 2. [25 points] Consider the following data fitting problem. We are given m data points of the form (a1,...,0,0) i = 1,...,m. The data (a),...,4.) for i = 1, ..., m represent n explanatory factors, and the data b' for i = 1,...,m represent the response. For example, the data might come from m different people, where (a,...,) represents various types of demographic and educational attainment information for person i, and Bi represents person i's salary. 2 We wish to use these data points to estimate a linear predictive model between the explanatory factors and the response: we want to estimate parameters (21,..., In) such that n b ba;d j=1 for explanatory factors (al, ..., An) and response b. Given a particular parameter vector (11, ... , In), the residual, or prediction error, at the ith data point is defined as Given a choice between alternative predictive models, one typically chooses a model that "explains the available data as best as possible, i.e., a model that results in small residuals. (a). One possibility is to minimize the total prediction error m n min i=1 j=1 with respect to (21,...,n), subject to no constraints. Formulate this problem as a linear program. (b). In an alternative formulation, one could minimize the largest residual min max i=1,...,m 1o 4:03 j=1 with respect to (11,...,n, subject to no constraints. Formulate this problem as a linear program