A certain experiment produces the data (1, 1.8), (2, 2.6), (3, 3.3), (4, 3.8), and (5, 4.1). Describe the model that produces a least-squares fit of these points by a function of the form y = ??x + ??x². Such a function might arise, for example, as the revenue from the sale of x units of a product, when the amount offered for sale affects the price set for the product. a. Give the design matrix and observation vector for the unknown parameter vector ? = [?? / ??]. b. Find the associated least-squares curve for the data. a. The design matrix is X = ?.
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