Selective Problem 2: General Least-Squares Regression for Data Fitting

We discussed about general linear least-squares regression (LLSR) for data fitting, as well as conversion of other nonlinear forms into linear formula for LLSR, and other nonlinear regression techniques. In this final project problem, you will be working with some selected experimental data from my research laboratory, as depicted below:

Objective:

(1) Use polynomial functions for fitting the stress-strain data as provided in the text file prob2_data.txt, with polynomial degree from 2 (with x0, x1, x2 terms) to 6 (with x0, x1, x2, x3, x4, x5, x6 terms). Derive the corresponding linear system of equations for solving each polynomial degrees function, and implement a generic MATLAB program for handling these system equations with a for loop structure. Make an individual plot of your fitting results in solid line superimposed onto the data for each polynomial degree.

Data:

strain stress

0 0

0.0167377799999999 0.685700000000000

0.0239808450000001 1.02860000000000

0.0295234049999999 3.39880000000000

0.0354055200000000 2.62360000000000

0.0421528449999999 1.92300000000000

0.0474764800000000 2.04220000000000

0.0554580000000000 2.95160000000000

0.0612701250000001 2.83230000000000

0.0682846050000000 2.84720000000000

0.0739489799999999 3.98010000000000

0.0800722049999999 4.32300000000000

0.0872028450000001 5.21740000000000

0.0926338450000001 5.44100000000000

0.100388820000000 5.33670000000000

0.106320720000000 7.15530000000000

0.111949845000000 7.60250000000000

0.118049620000000 8.40750000000000

0.124403125000000 9.31680000000000

0.130339920000000 9.31680000000000

0.135853645000000 8.97400000000000

0.141957805000000 11.3591000000000

0.148091125000000 12.3877000000000

0.154711245000000 13.6398000000000

0.160675125000000 15.1156000000000

0.166781520000000 16.1293000000000

0.173496180000000 18.4101000000000

0.179078580000000 20.2287000000000

0.185737605000000 22.7331000000000

0.191605605000000 25.2374000000000

0.198207445000000 28.8598000000000

0.203891125000000 32.3778000000000

0.209836125000000 37.2673000000000

0.216165120000000 42.6040000000000

0.222522205000000 49.7742000000000

0.228545205000000 57.6153000000000

0.233866125000000 68.3035000000000

0.241031380000000 80.7955000000000

0.246642000000000 94.9869000000000

0.252764500000000 114.440400000000

0.258665620000000 134.549900000000

0.265084500000000 159.325200000000

0.270909445000000 189.884400000000

0.276881125000000 225.213800000000

0.284127645000000 267.370600000000

0.291156205000000 316.921200000000

350 300 250 2 150 100 Oooooooo coc0 0.1 0.3 0.15 strain 0 0.05 0.2 0.25