Autocorrelation: variable correlated on itself.

Observations that are “proximate” will have similar values (positive autocorrelation). “Proximate” can be defined in many ways:

• Closer together in time (1 dimension). Temporal autocorrelation.

• Closer together in space (2 dimensions). Spatial autocorrelation.

Degree of autocorrelation can be calculated:

• For dependent or independent variables.

• For regression residuals.

Autocorrelation of regression residuals creates problem.

• Usual view: estimated coefficients are unbiased, but standard errors are biased.

• Alternative view: autocorrelated residuals signal presence of omitted variables. estimated coefficients are biased.

Residuals: Hedonic House Price Model (Blue paid too little; Red paid too much)

Red: Brick; Blue: No Brick

Soccer Scores

Protein per Capita 1997

TB rate 1997

HIV rate 1997

% children in LF 1995-2000

Fertility Rate 1995-2000

Per Capita GDP 1995-2000

12 Proximity Matrices

1. Physical Distance2. Language Phylogeny3. Religion4. Huntington Civlization5. Colonial/Imperial6. Level of Development7. Ecology8. Trade9. Formal Treaty10.Allies11.Enemies12.Event Frequency

The 12 selected languages are on the periphery of the digraph. Links point toward higher taxonomic levels, with all nodes ultimately connected to the node labeled Indo-European. The numbers indicate for selected nodes the maximum path length leading to that node. The taxonomy is from Grimes 2000

Danish

Norwegian BokmaalSwedish English

Standard German

Armenian

Hindi

Dari

Spanish

Portuguese

French

Cajun French

Indo-European

Indo-Iranian

Germanic

Italic

10

5

23

5

61

2

5

West Germanic

Danish

Norwegian BokmaalSwedish English

Standard German

Armenian

Hindi

Dari

Spanish

Portuguese

French

Cajun French

Indo-European

Indo-Iranian

Germanic

Italic

10

5

23

5

61

2

5

West Germanic

Language Macro-Families

GIS: Ecological Regions