Numerical Methods20795 marksNumerical: Least squares polynomial fittingLeast squares method for function fitting
What is least squares method of fitting a function? Fit the second order polynomial for the following data values. | x | 1 | 2 | 3 | 4 | 5 | 6 | 7 | |---|---|---|---|---|---|---|---| | y | 2 | 6 | 7 | 8 | 10 | 12 | 15 |
What is least squares method of fitting a function? Fit the second order polynomial for the following data values.
| x | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| y | 2 | 6 | 7 | 8 | 10 | 12 | 15 |
[5]
The least squares method finds the best-fit curve for a set of data points by minimizing the sum of squares of residuals (differences between observed values $yi$ and fitted values $f(xi)$): $$S = \sum{i=1}^{n} [yi - f(xi)]^2 \to \text{minimum}$$ $$x: 1, 2, 3, 4, 5, 6, 7$$ $$y: 2, 6, 7, 8, 10, 12...