Geographically Weighted Regression (GWR) is a regression model that takes into account the spatial
heterogeneity effect. In the application of the GWR, inference on regression coefficients is often of interest, as is
estimation and prediction of the response variable. Empirical research and studies have demonstrated that local
correlation between explanatory variables can lead to estimated regression coefficients in GWR that are strongly
correlated, a condition named multicollinearity. It later results on a large standard error on estimated regression
coefficients, and, hence, problematic for inference on relationships between variables. Geographically Weighted Lasso
(GWL) is a method which capable to deal with spatial heterogeneity and local multicollinearity in spatial data sets. GWL
is a further development of GWR method, which adds a LASSO (Least Absolute Shrinkage and Selection Operator)
constraint in parameter estimation. In this study, GWL will be applied by using fixed exponential kernel weights matrix
to establish a poverty modeling of Java Island, Indonesia. The results of applying the GWL to poverty datasets show that
this method stabilizes regression coefficients in the presence of multicollinearity and produces lower prediction and
estimation error of the response variable than GWR does.