Linear and nonlinear regression calculator
Calculator applies various types of regression (linear, exponential, logarithmic, etc.) to your meassurement data and finds out function, which fits them best.

Beta version#

BETA TEST VERSION OF THIS ITEM
This online calculator is currently under heavy development. It may or it may NOT work correctly.
You CAN try to use it. You CAN even get the proper results.
However, please VERIFY all results on your own, as the level of completion of this item is NOT CONFIRMED.
Feel free to send any ideas and comments !

Calculation data - measurement points#

Format of input data
x-values
y-values
Maximum polynomial degree
(polynomial with higher order will not be calculated)

Results - approximation of your dataset#

Regression typeApproximation formulaCoefficient of determination R2
Logarithmic regressionShow sourcey=0+0.4342944819ln(x)y=0+0.4342944819\cdot\mathrm{ln}\left( x\right)1
Power regressionShow sourcey=0.7071067812 x0.1982271233y=0.7071067812~{ x}^{0.1982271233}0.946028784
Polynomial regression of 2-th degreeShow sourcey=1.559107 x2+0.001821188 x+1.3787878788y=-1.559\cdot10^{-7}~{ x}^{2}+0.001821188~ x+1.37878787880.929257195
Linear regressionShow sourcey=2.20022104 x+1.888888895y=2.20022\cdot10^{-4}~ x+1.8888888950.679207921
Polynomial regression of 1-th degreeShow sourcey=2.20022104 x+1.8888888889y=2.20022\cdot10^{-4}~ x+1.88888888890.679207921
Exponential regressionShow sourcey=2.0734271897 e6.79306105 xy=2.0734271897~{ e}^{6.79306\cdot10^{-5}~ x}0.643858466
Polynomial regression of 0-th degreeShow sourcey=2.5y=2.50

Summary - function best fitting to your data#

Measurement points
Number of points4
Points you entered(10, 1), (100, 2), (1000, 3), (10000, 4)
Approximation
Regression typeLogarithmic regression
Function formulaShow sourcey=0+0.4342944819ln(x)y=0+0.4342944819\cdot\mathrm{ln}\left( x\right)
Coefficient of determination R21

Some facts#

  • Approximation of a function consists in finding a function formula that best matches to a set of points e.g. obtained as measurement data.
  • The least squares method is one of the methods for finding such a function.
  • The least squares method is the optimization method. As a result we get function that the sum of squares of deviations from the measured data is the smallest. Mathematically, we can write it as follows:
    i=1n[yif(xi)]2=min.\sum_{i=1}^{n} \left[y_i - f(x_i)\right]^2 = min.
    where:
    • (xi,yi)(x_i, y_i) - coordinations of the i-th measurement point, these are points that we know,
    • f(x)f(x) - the function we are searching for, we want this function to best match to the measurement points,
    • nn - number of measurement points.
  • Depending on used function we say about:
  • The least squares method allow us to find coefficients for above functions (a, b, etc.) to fits best to measurement data.

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