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Urban Start-up Agglomeration and Venture Capital Investment (view source)
Revision as of 17:05, 3 September 2019
, 17:05, 3 September 2019→Approach
#Maximum R-Squared
We might also dolooked at:
*Elbow on fraction of maximum hull area in hulls
====Discarding Outliers====
====Elbow on fraction of locations in hulls====
[[File:ElbowdataresultAgglomerationFLHGraph.png|right]] The '''elbowcalc''' and '''elbowdata''' queries provide the data. '''elbowdata''' takes layer/finallayer (i.e., fraction unclustered, as the layer 1 is the all encompassing hull and final layer is the raw locations), rounds it to two digits, and then calculates the average fraction of locations in hulls and the average hull area fraction of all encompassing hull area. The former gives a nice curve with an elbow (found by taking the second derivative and setting it equal to zero) at x=0.40237.
We then identify the layer that is closest to having a fraction of locations in hulls of 0.40237, taking the lower level (i.e., the more clustered level) whenever there is a tie. The resulting indicator variable is called '''elbowflhlayer''' and is made in table '''Elbowflh'''. This is analyzed in a sheet in "Images Review.xlsx" in E:\projects\agglomeration.
====Fraction of Maximum Hull Area in Hulls====
[[File:AgglomerationFHAGraph.png|right]] We also tried computing the fraction of the maximum hull area (MHA) in covered by hulls for each layer. The maximum hull area is on layer one, when every location is in an all-encompassing hull. A cubic was a mediocre fit to this data, giving an R2 of 83% but with lots of deviation concentrated right around the local minimum ({-0.0224722, {x -> 0.446655}} [https://www.wolframalpha.com/input/?i=minimum+-2.3595x%5E3+%2B+4.3803x%5E2+-+2.5008x+%2B+0.4309], point of inflection and local maximum. A quartic had an R2 of 90% at around x=0.44 (6.408 x^4 - 15.176 x^3 + 12.592 x^2 - 4.3046 x + 0.517≈0.00825284 at x≈0.440275). I tried a quintic but it didn't really add any information. I expect that this approach is flawed.
===Image Analysis===
