4 (MATH 4300-01) Due date: Friday, Oct. 9, 2015 1. Name (Print): Consider the least-squares error E2 for a linear function yM = a x + b, ~ ~~ ~ 2 E 2 Y 2 2a XY a 2 X 2 b Y a X . a) Determine directly the optimal b value that minimizes E2. Do not apply the Second Derivatives Test. b) Determine in the same way the optimal a value that minimizes E2. 2. Assume that this data set can be modeled by a power function yM = a xb. X Y 1 0.4 2 0.65 3 0.86 4 1.06 5 1.23 a) Introduce new variables that are linearly related. Find the optimal model parameter values for this linear model by using the least-squares error. b) Graph the resulting optimal power function yM = a xb and the data. 3. Assume that this data set can be modeled by a power function P = P0 + b ta. t P 0 100 1 101 2 108 3 140 4 230 a) Introduce new variables that are linearly related. Find the optimal model parameter values for this linear model by using the least-squares error. b) Graph the resulting optimal power function P = P0 + b ta and the data