Function approximation with regression analysis
This online calculator uses several simple regression models for approximation of unknown function given by set of data points.
Articles that describe this calculator
Function approximation with regression analysis
Digits after the decimal point: 4
Linear regression
y=0.6233x+129.5721
Linear correlation coefficient
0.7883
Coefficient of determination
0.6214
Average relative error, %
2.4459 %
Quadratic regression
y=−0.0168x2+3.0867x+41.3745
Correlation coefficient
0.8164
Coefficient of determination
0.6665
Average relative error, %
2.0026 %
Cubic regression
y=0.0001x3−0.0392x2+4.6976x+3.1981
Correlation coefficient
0.8165
Coefficient of determination
0.6666
Average relative error, %
2.0166 %
Power regression
y=56.4834x0.2642
Correlation coefficient
0.7981
Coefficient of determination
0.6369
Average relative error, %
2.3409 %
ab-Exponential regression
y=134.4458⋅1.0036x
Correlation coefficient
0.7842
Coefficient of determination
0.6150
Average relative error, %
2.4781 %
Logarithmic regression
y=−20.1773+45.6282⋅lnx
Correlation coefficient
0.8013
Coefficient of determination
0.6421
Average relative error, %
2.3080 %
Hyperbolic regression
y=220.7742−3264.2257x
Correlation coefficient
0.8106
Coefficient of determination
0.6570
Average relative error, %
2.1698 %
Exponential regression
y=e4.9012+0.0036x
Correlation coefficient
0.7842
Coefficient of determination
0.6150
Average relative error, %
2.4781 %
Results
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y
Linear regression
Quadratic regression
Cubic regression
Power regression
ab-Exponential regression
Logarithmic regression
Hyperbolic regression
Exponential regression
Results
| i | x | y | Linear regression | Quadratic regression | Cubic regression | Power regression | ab-Exponential regression | Logarithmic regression | Hyperbolic regression | Exponential regression |
|---|---|---|---|---|---|---|---|---|---|---|
| 53.6 | 162.9809 | 158.4548 | 158.0846 | 161.6911 | 163.0991 | 161.4938 | 159.8745 | 163.0991 | ||
| 1 | 57 | 163 | 165.1002 | 162.6187 | 162.5014 | 164.3394 | 165.1101 | 164.3000 | 163.5071 | 165.1101 |
| 2 | 58 | 164 | 165.7235 | 163.7694 | 163.7038 | 165.0961 | 165.7063 | 165.0936 | 164.4944 | 165.7063 |
| 3 | 59 | 158 | 166.3468 | 164.8863 | 164.8633 | 165.8433 | 166.3047 | 165.8735 | 165.4483 | 166.3047 |
| 4 | 62 | 175 | 168.2167 | 168.0351 | 168.0907 | 168.0303 | 168.1127 | 168.1366 | 168.1254 | 168.1127 |
| 5 | 64 | 171 | 169.4633 | 169.9660 | 170.0394 | 169.4454 | 169.3290 | 169.5852 | 169.7707 | 169.3290 |
| 6 | 64 | 172 | 169.4633 | 169.9660 | 170.0394 | 169.4454 | 169.3290 | 169.5852 | 169.7707 | 169.3290 |
| 7 | 65 | 175 | 170.0866 | 170.8809 | 170.9546 | 170.1408 | 169.9404 | 170.2926 | 170.5553 | 169.9404 |
| 8 | 68 | 165 | 171.9565 | 173.4237 | 173.4714 | 172.1808 | 171.7880 | 172.3514 | 172.7709 | 171.7880 |
| 9 | 69 | 178 | 172.5797 | 174.2039 | 174.2360 | 172.8461 | 172.4083 | 173.0175 | 173.4666 | 172.4083 |
Calculators used by this calculator
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PLANETCALC, Function approximation with regression analysis
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