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Treatment of experiment results  Example
Example
By means of a method of the least squares to pick up the 2nd degree polynomial for the results of measurements of values of function y presented by the table at equidistant values of argument х:
х

у 
0.1 
1.316 
0.2 
1.633 
0.3 
1.976 
0.4 
2.378 
0.5 
2.723 
0.6 
3.201 
0.7 
3.572 
0.8 
4.051 
0.9 
4.500 
S o l u t i o n . As is known, a general view of the 2nd degree polynomial: Let's make system of Gauss’ normal equations:
Coefficients of system of these equations according to data of the table are equal to:
After substitution of numerical values of coefficients the system of Gauss’normal equations becomes:
Its solution: Thus, the 2nd degree required polynomial:
