3. A certain experiment produces the data \[ (1,1.8),(2,2.7),(3,3.4),(4,3.8),(5,3.9) \] Suppose we wish to find a least-squares fit of these points by a function of the form \[ y=\beta_{1} x+\beta_{2} x^{2} \] (a) What property would we expect the data to have in order to select such a function? (b) Give the design matrix, the observation vector, and the unknown parameter vector for this model and data. (c) Use Mathematica to find the associated least-squares curve for the data.