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	Values only (just a sequence of numbers)Serie of (x,y) points
x-values
y-values
Maximum polynomial degree (polynomial with higher order will not be calculated)

Results - approximation of your dataset#

Regression type	Approximation formula	Coefficient of determination R²
Logarithmic regression	Show source $y=-12.2406886256+17.1079184613 \cdot ln\left(x\right)$	0.945714039
Linear regression	Show source $y=\frac{153461}{2000000000}~x+\frac{31771810983}{500000000}$	0.285736587
Polynomial regression of 1-th degree	Show source $y=\frac{153461}{2000000000}~x+\frac{635436079243}{10000000000}$	0.285736587
Polynomial regression of 2-th degree	Show source $y=\frac{-1}{2000000000}~x^{2}+\frac{5056641}{5000000000}~x+\frac{345579190561}{10000000000}$	0.268579423
Polynomial regression of 0-th degree	Show source $y=88$	0
Power regression	Show source $y=\frac{3084209917}{2500000000}~x^{\frac{1008711331}{2500000000}}$	-0.019128704
Exponential regression	Show source $y=\frac{1849979645099}{10000000000}~e^{\frac{531}{10000000000}~x}$	-0.942310326

Summary - function best fitting to your data#

Measurement points
Number of points	7
Points you entered	(10, 1), (2, 2), (20100, 202), (2, 2), (201000, 203), (2, 2), (2010000, 204)
Approximation
Regression type	Logarithmic regression
Function formula	Show source $y=-12.2406886256+17.1079184613 \cdot ln\left(x\right)$
Coefficient of determination R²	0.945714039

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:

$\sum_{i=1}^{n} \left[y_i - f(x_i)\right]^2 = min.$
where:
- $(x_i, y_i)$ - coordinations of the i-th measurement point, these are points that we know,
- $f(x)$ - the function we are searching for, we want this function to best match to the measurement points,
- $n$ - number of measurement points.
Depending on used function we say about:
- linear regression:
  
  $y = ax + b$
- logarithmic regression:
  
  $y=a + ln(bx)$
- exponential regression:
  
  $y=a \times e^{bx}$
- power regression:
  
  $y=a \times b^x$
- polynomial regression:
  
  $y=W_n(x) = a_{n} x^n + a_{n-1} x^{n-1} + \dots + a_1 x + a_0$
- etc.
The least squares method allow us to find coefficients for above functions (a, b, etc.) to fits best to measurement data.

Tags and links to this website#

Tags:

regression_calculator · function_estimation · function_approximation · data_fits_calculator · nonlinear_regression · regression_finder

Tags to Polish version:

kalkulator_regresji · estymacja_funkcji · aproksymacja_funkcji · dopasowanie_do_danych_pomiarowych · szukanie_regresji

What tags this calculator has#

CALCULATOR · MATH · A -> Z (all)

Permalink#

This is permalink. Permalink is the link containing your input data. Just copy it and share your work with friends:

https://calculla.com/regression_calculator?inDataFormat=xy&inValuesX=10%252C%2520100%252C%25201000%252C%252010000&inValuesY=1%252C%25202%252C%25203%252C%25204&inMaxPolynomialOrder=2

Links to external sites (leaving Calculla?)#