Lecture 17 The Gravity Model And Nodal Characteristics17-2 Chicago Traffic Flow Map Based on Truck Traffic17-3 Chicago Traffic Flow Map Based on Air Traffic17-4 Regression Analysis and the Gravity Model17-5 Salt Lake City Example17-5 Salt Lake City Example (Cont.)Slide 7PowerPoint PresentationSlide 9Slide 10Slide 11Slide 1219/1/1419/1/14Jun Liang, Geography @ UNCJun Liang, Geography @ UNC11Lecture 17 The Gravity Model And Nodal Characteristics17-1Chicago traffic flow map based on phone calls19/1/1419/1/14Jun Liang, Geography @ UNCJun Liang, Geography @ UNC2217-2 Chicago Traffic Flow Map 17-2 Chicago Traffic Flow Map Based on Truck TrafficBased on Truck Traffic19/1/1419/1/14Jun Liang, Geography @ UNCJun Liang, Geography @ UNC3317-3 Chicago Traffic Flow Map 17-3 Chicago Traffic Flow Map Based on Air TrafficBased on Air Traffic19/1/1419/1/14Jun Liang, Geography @ UNCJun Liang, Geography @ UNC4417-4 Regression Analysis and the 17-4 Regression Analysis and the Gravity ModelGravity ModelHere 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.19/1/1419/1/14Jun Liang, Geography @ UNCJun Liang, Geography @ UNC5517-5 Salt Lake City Example17-5 Salt Lake City ExampleScatter diagram of actual Salt City air traffic plotted against gravity model expectation.19/1/1419/1/14Jun Liang, Geography @ UNCJun Liang, Geography @ UNC6617-5 Salt Lake City Example (Cont.)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=-4.04+126.8x*108R2 indicates two-thirds of the variation in air traffic was associated with the population and proximity of other cities.r2=0.67719/1/1419/1/14Jun Liang, Geography @ UNCJun Liang, Geography @ UNC7717-5 Salt Lake City Example (Cont.)17-5 Salt Lake City Example (Cont.)y=-4.04+126.8(Pi Pj/ Dij)*10-8The 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)=1.87+1.02(log(Pi Pj/ Dij)))y = alog(1.87) * (Pi Pj/ Dij))1.02R2=0.43 (is a more reliable measure of the relationship.)19/1/1419/1/14Jun Liang, Geography @ UNCJun Liang, Geography @ UNC8819/1/1419/1/14Jun Liang, Geography @ UNCJun Liang, Geography @ UNC9917-5 Salt Lake City Example (Cont.)17-5 Salt Lake City Example (Cont.)y = alog(1.87) * (Pi Pj/ Dij))1.02With 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)ß19/1/1419/1/14Jun Liang, Geography @ UNCJun Liang, Geography @ UNC1010Regression 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.19/1/1419/1/14Jun Liang, Geography @ UNCJun Liang, Geography @ UNC111119/1/1419/1/14Jun Liang, Geography @ UNCJun Liang, Geography @
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