28. The selling prices of a number of houses in a particular section of the city overlooking the bay are given in the following table, along with the size of the lot and its elevation: Selling price Lot size (sq. ft.) Pi Li Elevation (feet) Ei $155,000 $12,000 350 120,000 10,000 300 100,000 9,000 100 70,000 8,000 200 60,000 6,000 100 100,000 9,000 200 A real-estate agent wishes to construct a model to forecast the selling prices of other houses in this section of the city from their lot sizes and elevations. The agent feels that a linear model of the form P =bo+b1+b2E would be reasonably accurate and easy to use. Here b₁ and by would indicate how the price varies with lot size and elevation, respectively, while bo would reflect a base price for this section of the city. The agent would like to select the "best" linear model in some sense, but he is unsure how to proceed. It he knew the three parameters bo, b₁ and b₂, the six observations in the table would each provide a forecast of the selling price as follows: P₁ = bo+biLi + b₂Ei i = 1, 2, ..., 6. However, since bo, b1, and b2 cannot, in general, be chosen so that the actual prices P; are exactly equal to the forecast prices P; for all observations, the agent would like to minimize the absolute value of the residuals R₁ = Pi - Ĥi. Formulate mathematical programs to find the "best" values of bo, b₁, and by by minimizing each of the following criteria: 6 a) (PP)², i=1 - Least squares