Problem 2. (Least Squares and model fitting). Assume the following experimental data has been obtained: At: t1 = 1, R(t) = 4; t2 = 2, R(t2) = 6; t3 = 3, R(ts) = 7; t4 = 4, R(a) = 11 . The following linear model for the dependence of the "output" R on the "input" variable t is assumed that depends on unknown parameters i and a2: (a) Write a system of linear equations that reflects the model and the experimental data obtained (b) Write the system of equations in the form and determine if it has an exact solution. (c) Find the least square fit parameters given by (d) Plot the fitted line and the experimental data in the same plot (rough hand drawing is fine, a computer generated figure is preferred) Problem 2. (Least Squares and model fitting). Assume the following experimental data has been obtained: At: t1 = 1, R(t) = 4; t2 = 2, R(t2) = 6; t3 = 3, R(ts) = 7; t4 = 4, R(a) = 11 . The following linear model for the dependence of the "output" R on the "input" variable t is assumed that depends on unknown parameters i and a2: (a) Write a system of linear equations that reflects the model and the experimental data obtained (b) Write the system of equations in the form and determine if it has an exact solution. (c) Find the least square fit parameters given by (d) Plot the fitted line and the experimental data in the same plot (rough hand drawing is fine, a computer generated figure is preferred)