This is a result of a class project for Math 170B (Spring 2018) in UCLA. The goal of the project was to get hands-on experience with fititng heteroskedastic data and analyzing the peroformance of various regresson models on it.
In the course of the project we were able to conclude that theoretically the best tool for fitting data with heteroskedasticity is Generalized Least Square (GLSE) regression. However, in practice, for the datasets we had, ordinary Least Square Regression (LSE) had a better performance (see metrics below)
- Full Report with the explanations of out work and conclusions is avaliable here
- Final estimates of the a and b parameters of y = a + bx + e model are here
- Below you can find the most visually attractive results of our work, namely two tables with the metrics of model performance and 5 graphs with visualized data and model predictions (only more relevant models are included, feel free to generate more plots by slightly modifying the code
| file/ reg type | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| LSE | 0.1639863122 | 0.3980894410 | 0.10319995 | 0.0275947359 | 0.280575792 |
| GLSEI | 0.1166125126 | 0.09153352884 | -0.01553730364 | -0.1297663105 | -0.1286472674 |
| GLSEII | 0.04640626767 | 0.06940218455 | -0.04114628643 | -0.1472103778 | 0.280575792 |
| WLSE | 0.1403769574 | 0.1834023549 | 0.01624763418 | -0.01781630477 | -0.04060542850 |
| LASSO | 0.1639739902 | 0.3980894371 | 0.1031952438 | 0.02759473565 | 0.2805757898 |
| RIDGE | 0.1638634355 | 0.3980877000 | 0.1031988620 | 0.02670308780 | 0.2805165134 |
| HUBER | 0.1573759139 | 0.3937864654 | 0.08307870806 | 0.006033289644 | 0.2581856714 |
| file/ reg type | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| lSE | 5.2949701007221 | 15.4237819098164 | 17.5180183493125 | 5.07326984135883 | 11.1023251073797 |
| GLSEI | 5.4429261248202 | 18.9486967923493 | 18.6416825140806 | 5.468379190303 | 13.9059458626989 |
| GLSEII | 5.6550768614652 | 19.178114585660 | 18.875264406678 | 5.5104345123976 | 11.1023251073797 |
| WLSE | 5.3692155871704 | 17.9650717619072 | 18.347633724117 | 5.1903783156856 | 13.3525576166922 |
| LASSO | 5.2950091220463 | 15.423781960821 | 17.5180643853534 | 5.0732698420786 | 11.1023251290293 |
| HUBER | 5.2953592119916 | 15.4238042169278 | 17.518029046899 | 5.0755952787186 | 11.1027825033413 |
| RIDGE | 5.3158626672572 | 15.4788149751225 | 17.71345162456 | 5.1292070631290 | 11.2737662497784 |
