# Model used in ListStreamPlot and statistics of result? [closed]

I have a number of water flow measurements that I use as an input for ListStreamPlot to show how water flows through a transect of the river. It looks really nice, but I would like to get some statistics from this. I'm sure Mathematica uses some sort of model that my measurements are fitted to. I would like to extract this model and get something like R^2 or similar.

Here are some example measurement values {x,y,xvel,yvel}:

xy1 = {{0.75, 0.6, 0.2432214285714285714, -0.0032285714285714286}, {2.25,
1.2, -0.0130909090909090909, 0.1693969696969696970}, {2.25, 0.2,
0.0051228571428571429, 0.16554571428571428571}, {1.5, 1.8,
0.2067933333333333333, -0.1746966666666666667}, {2.25, 0.6,
0.0738333333333333333, 0.0093393939393939394}, {1.5, 1.2,
0.2102258064516129032, -0.0555451612903225807}, {1.5, 0.2,
0.1615791666666666667, -0.02004583333333333333}, {0.75, 1.2,
0.2198725000000000000, -0.0172975000000000000}, {0.75, 0.2,
0.1580366666666666667, 0.0221100000000000000}, {2.25,
1.8, -0.0058160000000000000, -0.08341200000000000000}, {1.5, 0.6,
0.20290344827586206897, -0.04414827586206896552}, {0.75, 1.8,
0.0030500000000000000, -0.01323846153846153846}, {0, 0, 0, 0}, {0,
0.6, 0, 0}, {0, 1.2, 0, 0}, {0, 1.8, 0, 0}, {0, 2, 0, 0}, {3, 0, 0,
0}, {3, 0.6, 0, 0}, {3, 1.2, 0, 0}, {3, 1.8, 0, 0}, {3, 2, 0,
0}, {1.5, 0, 0, 0}, {1.5, 2, 0, 0}}


I use those values like this:

ListStreamPlot[xy1, StreamScale -> 0.11, StreamStyle -> Black,
PlotRange -> {{0, 3}, {0, 2}},
PlotLabel -> "0.75 m from upstream wall"]


What I would like to get out is something similar to when you run a linear model fit and you can do mylm["ANOVAtable"] or mylm["Rsquared"]... And also display the actual model being used like z = ax * by or whatever.

Oh, and another question about the model behind the stream plots... The example values I provided above are the mean values for each measurement point. But I can also submit all the measured values to ListStreamPlot so that each point has many values to it. However, doing so will yield a different result than if I just provide the means of each point. Why is this? Shouldn't it be roughly the same if I give the means?

I have created ListStreamPlots according to the above, but instead I want to used the measured values to create a model and input that to StreamPlot. How do I do that?

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What is your question, again? –  Yves Klett Oct 17 at 12:54
Instead of just getting the plot, how do a get a plot and also things like R^2 and ANOVA and some definition of the model that is used? Or in other words; how do I get some measure of the quality of the plot output? –  GaRyu Oct 17 at 12:58
The plot hasn't an underlying model beneath it, so there is no way you can have any statistic about it. It's just a best effort interpolation. Voting to close –  belisarius Nov 8 at 1:22
OK, but even if ListStreamPlot uses interpolation, I should be able to create a model (vector calculus?) and then input that model to StreamPlot to create the same result as the interpolation in ListStreamPlot. Right? –  GaRyu Nov 9 at 9:36
@belisarius It seems the question is really "how do I reproduce a StreamPlot". Would that be a valid question? (or has it been answered?) –  tkott Nov 12 at 15:42