A certain experiment produces the data (1, 1.7), (2, 2.9), (3, 3.2), (4, 3.7), and (5, 3.9). Describe the model that produces a least-squares fit of these points by a function of the form y = ̡₁x + ̡₂x². 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 ̡ = [̡₁, ̡₂].
b. Find the associated least-squares curve for the data.
a. The design matrix is X = ________.
The observation vector is y = ________.
b. The least-squares curve for the data is given by the function y = ________ x + (________)x².
(Round to two decimal places as needed.)