1. Lecture 17 The Gravity Model And Nodal Characteristics
17-1Chicago traffic flow map based on phone calls
2018/11/23
Jun Liang, UNC

2. 17-2 Chicago Traffic Flow Map Based on Truck Traffic
2018/11/23
Jun Liang, UNC

3. 17-3 Chicago Traffic Flow Map Based on Air Traffic
2018/11/23
Jun Liang, UNC

4. 17-4 Regression Analysis and the Gravity Model
Here ordinary least squares regression (OLS) are designed to measure the closeness of fit between the actual flow of traffic from a single node and a gravity model estimate of that flow.
The r2measue indicates the percentage of variation in the dependent variable (actual traffic) that can be associated with variation in the independent variable (gravity model estimates).
The regression constants will provide estimates of the distance effect.
2018/11/23
Jun Liang, UNC

5. 17-5 Salt Lake City Example
Scatter diagram of actual Salt City air traffic plotted
against gravity model expectation.
2018/11/23
Jun Liang, UNC

6. 17-5 Salt Lake City Example (Cont.)
Regression line fitted to the relation between actual Salt Lake City traffic and gravity model expectations. The placing of the regression line is overly influenced by a few high values.y= x*108
R2 indicates two-thirds of the variation in air traffic was associated with the population and proximity of other cities.
r2=0.677
2018/11/23
Jun Liang, UNC

7. 17-5 Salt Lake City Example (Cont.)
y= (Pi Pj/ Dij)*10-8
The scatter of points suggests that a simple arithmetic relationship between air traffic and gravity model does not provide a very good description. The relationship may be more geometric than arithmetic.
log(y)= (log(Pi Pj/ Dij)))
y = alog(1.87) * (Pi Pj/ Dij))1.02
R2=0.43 (is a more reliable measure of the relationship.)
2018/11/23
Jun Liang, UNC

8. Jun Liang, Geography @ UNC
2018/11/23
Jun Liang, UNC

9. 17-5 Salt Lake City Example (Cont.)
y = alog(1.87) * (Pi Pj/ Dij))1.02
With above formula, we still did not isolate the distant factor. A simple to isolate distance factor is to check the relation between the log of Salt Lake City passengers per capita and the log of distance:
y/ Pi Pj VS A(Dij)ß
2018/11/23
Jun Liang, UNC

10. Jun Liang, Geography @ UNC
Regression line fitted to the relation between the log of Salt Lake City passengers per capita and the log of distance. This permits us to isolate the effects of distance without using a multiple regression.
2018/11/23
Jun Liang, UNC

11. Jun Liang, Geography @ UNC
2018/11/23
Jun Liang, UNC

12. Jun Liang, Geography @ UNC
2018/11/23
Jun Liang, UNC