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Correlation and regression of simulated data
for different types of aggregation
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Aggregation method |
Correlation coefficient (r) |
Regression coefficient (b) |
Standard error (s.e.) |
| Raw data | 0.479 |
0.991 |
0.015 |
| Random | 0.471 |
0.944 |
0.148 |
| Systematic | 0.982 |
0.990 |
0.016 |
| Spatial | 0.776 |
1.078 |
0.074 |
| Spatial autocorrelation in Y but not in X | |||
| Raw data | 0.711 |
1.007 |
0.008 |
| spatial | 0.346 |
0.957 |
0.218 |
The data were generated using this formula: Y = 10 + X + €
The X values were generated by, first, generating random numbers for each cell in a 120 X 120 square grid. The value of X was then computed using a moving window (i.e., X was the average of the cell itself and its four neighbours), so that a known pattern of spatial autocorrelation existed in the X's.
The aggregration strategy varied between the three methods: 100 cells were selected randomly, systematically on the basis of their X values (i.e., the first 100 cells along the x-axis were grouped, etc.), and in contiguous blocks of 10 x 10 cells.