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

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


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  • Introduction
  • Data
  • Statistics
  • Results presentation
  • Samples
  • Popular statistics and data analysis
  • Taylor polynomials.

    Function that has derivatives at point a can be presented by polynom with coefficients that are calculated by Taylor formula. For details visit this page for example.

    With the help of LeoStatistic we can investigate how good is approximation with Taylor polynomials for sin(x) near the x=0.

    Open LeoStatistic.

    In tab "Data" click in "Insert" button. Insert parameter as argument with arithmetic progression from 0 to 9.99 with step 0.01.

    Add others as arguments by formulas:

    • sin(x)
    • x-(x^3)/6+(x^5)/120
    • x-(x^3)/6+(x^5)/120-(x^7)/5040
    • x-(x^3)/6+(x^5)/120-(x^7)/5040+(x^9)/362880
    • x-(x^3)/6+(x^5)/120-(x^7)/5040+(x^9)/362880-(x^11)/39916800

    Result presentation has to be like this:

    Obviously the large grade of Taylor polynom the longer from initial point x=0 they can approximate the sin(x). What is really amazing is that if to use approximation scheme of LeoStatistic and one can find that formula:

    s = +0.806542*x +0.504436*x^2 -0.591369*x^3 +0.15451*x^4 -0.0156156*x^5 +0.000548931*x^6

    will practically exact fit all displayed domain:

    Taylor polynom
     

    This circumstance has not to surprised us too much. At first approximation polynom in above has one more extra coefficient that is had happened more important then a highest grade of its term. Other important distinction from Taylor polynomial presentation is  that just approximation of the data in interval 0 - 10 not guarantee a fit data outside the interval. If you look at behavior of the fitting curve outside of interval special in negative region of argument.

    As for Taylor polynomial approximation it is symmetrically good matcher from basic point. In our example area of fit with Taylor polynom 11th grade is about from -4.5 till 4.5. Just about the same by all range as our approximating formula that covers dominion from 0 to 10.

    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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