LeoStatistic
software for data presentation, statistical analysis, marketing and prediction.

Free download:
LeoStatistic.zip or
LeoStatistic.exe
(selfextracting winzip file)


Registration

  • Introduction
  • Data
  • Statistics
  • Results presentation
  • Samples
  • Popular statistics and data analysis
  • Fit curve in space.

    This is very tricky topic in data analysis. Not to say that it's special difficult but demand very clear understanding...

    The formula:
    a*x+ b*y + c*z = d (1)
    described a plane in space. Other one :
    z= a2*x2+a1*x+ b2*y2 + b1*y + c (2)
    can be used for representing a parabolic like surface.

    What is the formula of the curve in the space? For specificity sake, what is the formula of the line in space? The answer is surprising in the way. There is not one. There are at least two equations needed. The line in space is the result of interception of two planes. So two equations of a planes is enough. There are several styles of presentations of a line in space. Most obvious approach is based on the notion that a live is defined by coordinates of two points in space. So you need six numbers of coordinates of two points:
    P0(x0,y0,z0) and P1(x1,y1,z1)
    to define a line in space.

    The example of visual presentation of of two lines in three dimensional space are shown on the picture:

    Lines in space 

    If we set only one parameter as an argument we can at once get fitting formulas for projections of these two lines in space on the planes y-x and z-x:

    Fit

    Instantly by going in "Result" tab and clicking on the "Copy formulas on screen" we get them in clipboard memory and then past here:

    y1 = +7.4 +3.5*x
    y2 = +56 -5.4*x
    z1 = -10.8 +4.3*x
    z2 = +2.71 -3.14*x

    There are four coefficients defined for line. Looks like not enough... Where could we get two more? Let's calculate coordinates of two points with x=0 and x=1.

    For line #1 P0(0, 7.4, -10.8) and P1(1, 10.9, -6.5); for line #2 P0(0, 56, 2.71) and P1(1, 51.6, -0.43). That is it. Had happened that projections of the line in space on two coordinates planes are quite enough. We just have to remember that x domain of lines has no limits and we select any values for x coordinates of base points.

    The approximation of the nonlinear curves in space is much more difficult of course. The ultimately helpful feature of LeoStatistic is a visual presentation of correlation between parameters. This pictures can be considered as a projections of the data on the all possible combination of two parameters. If all projections of data are curves the figure in multidimensional space can be considered as a curve too.

    As a example of the such task is presented on the next picture of vortex like curve:

    Vortex line in space

    If to set statistical scheme to "Correlation" it's very clear how this vortex like picture is built:

    Projection of vortex on coordinates planes

    The actual reconstruction of the parametric equations x(t), y(t), z(t) not  difficult too much if to know that parametric equations for spiral are like these:
    x=a*t*sin(b*t)
    y=a*t*cos(b*t))

    Screenshots of the LeoStatistic software:
    click on picture to enlarge

    Building histograms
    Building histogram

    Distribution of two variables.
    Distribution of two variables.

    Approximation (constructor style interface).
    Approximation
    (constructor style interface).

    3D view.
    3D view.

    DOW trend.
    DOW trend.

    Signals revealing
    Signals revealing.

    Near neighbors method
    Near neighbors method.

    Harmonic analysis.
    Harmonic analysis.

    Fit with free format formula.
    Fit with free format formula.

    Curve fit of crystal growth rate.
    Curve fit of crystal growth rate.

    Get data from image file.
    Get data from image file.

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