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Written homework problem 11 Assigned 10/2 and due 10/7 (This problem was from the second take-home exam when I taught Math 113 in Fall 2014.) A statistician is trying to determine precisely the optimal amount of ice cream to eat. They have gathered data from a number of people about how much ice cream they ate and how they felt afterwards. The data is given below. i Ice cream eaten (in fluid ounces) xi Goodness of feeling yi 1 16 18 2 5 8 3 8 20 4 10 17 5 25 13 6 40 -42 7 30 5 8 17 23 9 2 10 12 18 10 The statistician believes that this data can be accurately modeled by a parabola y = β0 + β1 x + β2 x2 , where x is the quantity of ice cream eaten, and y is the goodness of feeling. Find the choice of β0 , β1 and β2 that best fits the data given, that is, the one that minimizes the function 10 X 2 SSE(β0 , β1 , β2 ) = yi − (β0 + β1 xi + β2 x2i ) . i=1 You may assume that a minimum exists. Based on the values of β0 , β1 and β2 obtained, what is the optimal quantity of ice cream to eat (on one occasion)? [In order to do this, you will need to solve a system of three linear equations in three unknowns. Also, the numbers on this problem don’t work out particularly nicely.] 1