1. Chapter 4 The Gravity Model
Newton=s First Law of Migration:
The Gravity Model
Activity 1: Predicting Migration with the Gravity Model
Activity 2: Scatter Diagram
Activity 3: Residual Map
Activity 4: Evaluation

2. Learning Outcomes After completing the chapter, you will be able to:
Apply principles of spatial interaction to patterns of movement
Identify the major source areas for migration to your state
Use functions of a spreadsheet
Produce and interpret a scatter diagram
Discriminate between positive and negative residuals
Identify outliers on a scatter diagram
Think critically about models in human geography

3. Figure 4.1

4. Figure 4.2

5. Figure 4.3

6. Figure 4.4

7. Figure 4.5

8. Figure 4.6

9. Gravity Model:
Iij = predicted interaction between origin i and destination j.
k = a scaling constant
Pi = a measure of size, usually population, for origin I
Pj = a measure of size, usually population, for destination j
dij = distance between origin i and destination j
b = an exponent which adjusts for the rate of distance decay unique to the type of interaction
being measured

10. Figure 4.7

11. Figure 4.8

12. Figure 4.9

13. Figure 4.10

14. Figure 4.11

15. Figure 4.12

16. Figure 4.13

17. Definitions of Key Terms
Distance Decay: The declining intensity of an activity with increasing distance from its point of origin.
Extreme Value: A point on a scatter diagram that is roughly in line with the main trend but is separated from the main group of points because of its extremely high or low value. Contrast with outlier.
Gravity Model: A model to predict spatial interaction, where size (population) is directly related to interaction and distance is inversely related to interaction.
Migration: A permanent change in residence to outside one’s community of origin.

18. Migration Selectivity:
Migration Selectivity: The tendency for certain types of people to migrate. Age, education, and other sociodemographic characteristics are migration selectivity factors.
Migration Stream: A well-defined migration channel from a specific origin to a particular destination.
Migration Counterstream: Migration that runs opposite to a migration stream.
Outlier: Point on a scatter diagram that lies far off the trend line. Outliers on the graph correspond to cases that are poorly predicted by the model. Outliers are not to be confused with extreme values, which may lie far from any other point but which are still close to the best-fitting line (see Figure 4.13).

19. Pull Factors: Reasons to move to a particular place.
Push Factors: Reasons to move from a particular place.
Residuals: The difference between an actual observed value of some variable and its predicted value using the gravity model.
Scatter Diagram: A scatter of dots showing the relationship between two variables. Each dot on the graph represents the x and y coordinates of a different observation or case.
Spatial Interaction: Movements of ideas, information, money, products, and people between places.