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researchers discovered what is known as an inverse square relation between the number of people in a given urban location and the distance they traveled to get thereThe found that the frequency of visiting a place, multiplied by the distance traveled (rf) forms a stable parameter which can be used as a single dependent variable. There is then an (approximate, statistically fitted) inverse square law involving this combined variable. Or two square laws.
If we hold frequency constant (say "once a month" or whatever), then the number of people visiting some place drops off inverse square with distance. If 400 people are willing to visit some place once a month that is 10 km away, about 100 once-a-month visitors will come from 20 km away.
Or if we hold distance constant: if 400 people are visiting some place that is 10 km away once a month, about 100 will be visiting twice a month.
> It accurately predicts, for instance, that the number of people coming from two kilometers away five times per week will be the same as the number coming from five kilometers twice a week.
It doesn't predict this; rather this frequency-distance product being a stable parameter is a discovery from the data, on which the formula is then based. I.e this frequency-distance product becomes a model assumption baked into the formula, not a prediction.
The found that the frequency of visiting a place, multiplied by the distance traveled (rf) forms a stable parameter which can be used as a single dependent variable. There is then an (approximate, statistically fitted) inverse square law involving this combined variable. Or two square laws.
If we hold frequency constant (say "once a month" or whatever), then the number of people visiting some place drops off inverse square with distance. If 400 people are willing to visit some place once a month that is 10 km away, about 100 once-a-month visitors will come from 20 km away.
Or if we hold distance constant: if 400 people are visiting some place that is 10 km away once a month, about 100 will be visiting twice a month.
> It accurately predicts, for instance, that the number of people coming from two kilometers away five times per week will be the same as the number coming from five kilometers twice a week.
It doesn't predict this; rather this frequency-distance product being a stable parameter is a discovery from the data, on which the formula is then based. I.e this frequency-distance product becomes a model assumption baked into the formula, not a prediction.