1. (Curve Fitting:) A quantity y is known to depend upon another quantity x. A set of corresponding values has been collected for x and y and is presented in the Table below
|
X
|
0.0
|
0.5
|
1.0
|
1.9
|
2.5
|
3.0
|
3.5
|
|
Y
|
1.0
|
0.9
|
0.7
|
2.0
|
2.4
|
3.2
|
2.0
|
a) Fit the best straight line y = bx + a to this set of data points. The objective is to minimize the sum of absolute deviation of each observed value of y from the value predicted by the linear relationship. Write this as a linear programming model
b) Fit the best quadratic line y =cx2 + bx + a to this set of data points. The objective is to minimize the sum of absolute deviation of each observed value of y from the value predicted by the linear relationship. Write this as a linear programming model