Least Square Regression. (50%) A set of data from an experiment on motion of accelerating bodies, such as airplanes or rockets, is obtained as shown on the right. The following equations are used to fit the data. (1). y=a.x+b (2). y ax+b-x+c (3). y=b.ex (a) Find the coefficients (manually, not in a spreadsheet) for the equation (1) using a least squares approximation discussed in class (i.e., the tabular form). Show your steps, and the data table, of approaching the solution. Time Velocity (s) (m/s) 0.1 10.00 0.2 10.57 0.3 11.24 0.5 12.97 0.7 15.38 0.8 16.93 1.0 20.90 1.1 23.41 1.3 29.74 1.5 38.17 1.7 49.21 2.0 79.10 (b) Find coefficients (Using a spreadsheet, e.g., Microsoft Excel) for the equations (1), (2) and (3) using trend-line capabilities. Plot the above data and show the three regression curves with equations and the R value on the same graph. Attach a print-out of such a graph with your returned homework.