weighted least square regression

A technique for correcting the problem of heteroskedasticity by log-likelihood estimation of a weight that adjusts the errors of prediction

if some assumptions of ordinarly least square OLS regression do not hold.
.... in case of heteroscedasticity
.....unequal precision/reliability of datapoints

1. san Houston Uni - Weighted least squares regression XXX
http://www.shsu.edu/~icc_cmf/cj_789/weightedLeastSquares2.doc
- very good and detailed review of the technique, from the description of situations when to use WLS /ie if violation of homoscedasticity/ to detailed and very clear examples how to perform it /mainly applies to SPSS, the output is provided/.
- discusses both approaches on calculating weights 1/residualising the response variable 2/log-likelihood estimation of weights
- includes some basic mathematics, mostly well comprehensible college-level, formulas perfectly support the statements in text
/dr Charles M. Friel - author of this text provides lecture notes to a wide selection of statistical topics, comparable to Garson's Statnotes, in some topic I found dr Friel's explanations more poignant.
http://www.shsu.edu/~icc_cmf/directory.htm

2. statnotes - garson -including exemplification on SPSS ooutput - insightful, but not much regarding the mechanics of weight estimation / but maybe not so important/.

3. NIST Handbook - nice figures, comparison of WLS with alternative of nonlinear transformation of response and predictor variables.

relationship between

median, mean, mode

in skewed distributions

violations in discrete distributions and multimodal continuous ADVANCED, but accessible

by Hippel 2005 , journal of statistical education

transformations

Transformations

Statnotes - transformations - as part of testing assumptions, by Garson
- very nice, some pictures


Dallal's example of transformation in linear REGRESSION
RULE of THUMB: first transform the response variable y to correct heteroscedasticity (heterogeneity of variance) than apply transformation to predictiors to achieve linear relationship (bivariate scatterplot)


similar recommendations by NIST
Transformations:
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

NIST handbook of statistics
http://www.itl.nist.gov/div898/handbook/index.htm

from STATNOTES: To correct left (negative) skew, first subtract all values from the highest value plus 1, then apply square root, inverse, or logarithmic transforms.

Journal

chass

journal of statistical teaching and education ???