1. Spatial Data Analysis Iowa County Land Values (1926)

2. Data Description  County Level Data (Circa 1926, n=99)  Latitude/Longitude Co-Ordinates of County Seat  Land Values per Acre (Federal/State)  Corn Yield per Acre  Percent Corn  Percent Other Grains  Percent Un-plowable Land

3. Map of Federal Land Values

4. Summary Statistics StatisticCorn Yield/AcrePercent CornPercent GrainPercent Un-plowFederal ValueState Value q136.527.517129788.5 min30131086649 median39332217118108 max46483344173161 q342382623.5140124 Mean39.1132.4721.5618.85118.68106.25 Std Dev3.407.095.987.8326.7324.38

7. Weight Matrices  We consider 2 weight matrices:  Inverse distance:  Queen’s Case:  Each is scaled to have rows sum to 1 with W ii =0

9. Test for Autocorrelation  Moran’s I statistic under Randomization:

10. Moran’s I – Federal Land (Queen’s W)  N = 99 Counties  S 0 = 99 (Rows sum to 1)  S 1 = 34.82809  S 2 = 400.6013  k = 2.6268  e’We = 45395.6967  e’e = 70033.6566  I = 0.6482  E(I) = -0.0102  V(I) = 0.003373  Z obs = 11.34

11. Moran’s I – Federal Land (Inverse Distance)  N = 99 Counties  S 0 = 99 (Rows sum to 1)  S 1 = 3.2919  S 2 = 397.1385  k = 2.0925  e’We = 9772.80233  e’e = 70033.6566  I = 0.1395  E(I) = -0.0102  V(I) = 0.00012972  Z obs = 13.15

12. SemiVariogram Estimates  Counties assigned to 34 distance classes: <0.35,0.40 to 2.00 by 0.05

15. Several Semivariogram Models

16. Fitted Semivariograms – (R gstat)

17. Regression Model  Response: FEDVAL = Federal land value  Predictors:  CORNYLD = Corn yield/acre  PCTCORN = Percent of land planted corn  PCTGRAIN = Percent of land for other grains  PCTUNPLOW = Percent land un-plowable

18. Regression Output Federal land values are: Positively associated with corn yield per acre Positively associated with percent of land planted corn Positively associated with percent of land planted other grains Negatively associated with percent of land un-plowable No evidence of autocorrelated residuals (see following slides)

19. Moran’s I – Residuals (Queen’s W)  N = 99 Counties  S 0 = 99 (Rows sum to 1)  S 1 = 34.82809  S 2 = 400.6013  k = 4.1487  e’We = 998.2657  e’e = 12677.997  I = 0.07874  E(I) = -0.0102  V(I) = 0.00330  Z obs = 1.548

20. Moran’s I – Residuals (Inverse Distance)  N = 99 Counties  S 0 = 99 (Rows sum to 1)  S 1 = 3.2919  S 2 = 397.1385  k = 4.1487  e’We = 91.9083  e’e = 12677.997  I = 0.00725  E(I) = -0.0102  V(I) = 0.00012693  Z obs = 1.549

22. Map of OLS Residuals