Does anyone have a useful link to learn more about the least squares best fit. I'm looking forward to do manual calculations for a line profile data set.
The deviations can be calculated by different ways :
- least square (alone) just uses distances between measured values and theo values :
ASSIGN/V1=SQRT(DOT(SCN1.HIT[1..SCN1.NUMHITS].XYZ-SCN1.HIT[1..SCN1.NUMHITS].TXYZ,SCN1.HIT[1..SCN1.NUMHITS].XYZ-SCN1.HIT[1..SCN1.NUMHITS].TXYZ))
and then minimizes the sum of the square of deviations.
- least square vector uses the definition of the deviation, which is the projection of the deviation along the theo vector :
ASSIGN/V2=DOT(SCN1.HIT[1..SCN1.NUMHITS].XYZ-SCN1.HIT[1..SCN1.NUMHITS].TXYZ,SCN1.HIT[1..SCN1.NUMHITS].TIJK)
and then minimizes the sum of the square of deviations.
- minmax vector uses also the definition of deviations, but the algorithm search to minimize the difference between the max deviation and the min deviation.
You can try using the excel sheet in the #6 here, I'm not sure it works fine in english...
The deviations can be calculated by different ways :
- least square (alone) just uses distances between measured values and theo values :
ASSIGN/V1=SQRT(DOT(SCN1.HIT[1..SCN1.NUMHITS].XYZ-SCN1.HIT[1..SCN1.NUMHITS].TXYZ,SCN1.HIT[1..SCN1.NUMHITS].XYZ-SCN1.HIT[1..SCN1.NUMHITS].TXYZ))
and then minimizes the sum of the square of deviations.
- least square vector uses the definition of the deviation, which is the projection of the deviation along the theo vector :
ASSIGN/V2=DOT(SCN1.HIT[1..SCN1.NUMHITS].XYZ-SCN1.HIT[1..SCN1.NUMHITS].TXYZ,SCN1.HIT[1..SCN1.NUMHITS].TIJK)
and then minimizes the sum of the square of deviations.
- minmax vector uses also the definition of deviations, but the algorithm search to minimize the difference between the max deviation and the min deviation.
You can try using the excel sheet in the #6 here, I'm not sure it works fine in english...
