Weighted linear regression

Model parameters estimated by linear regression, weighted linear regression, and unweighted non-linear regression are shown in Table B-1. 

Parameter Unweighted linear regression Weighted linear regression Non-linear regression... 

Determination of model least squares multi-linear regression weighted multi-linear regression robust regression ridge regression partial least squares generalised inverse... 

Determine the relationship between S eas and Ca using a weighted linear regression model. ... 

CA Weighted Linear Regression with Errors in Both x andy... 

Determine the standardization relationship using a weighted linear regression. 

Nimura, Y. Carr, M. R. Reduction of the Relative Error in the Standard Additions Method, Analyst 1990, 115, 1589-1595. The following paper discusses the importance of weighting experimental data when using linear regression Karolczak, M. To Weight or Not to Weight An Analyst s Dilemma, Curr. Separations 1995, 13, 98-104. 

Figure 10. Graph of Number of Compounds against Error % Obtained from the Linear Regression of the Graph of the Corrected Peak Dispersion (Z) against the Reciprocal of the Diffusivity Molecular Weight to the Power of 0.833...

In the following the standard unweighted linear regression model is introduced. All necessary equations are found in Table 2.1 and are used in program LINREG. In a later section (2.2.10) nonuniform weighting will be dealt with. 

LINEAR REGRESSION Table 2.13. Equations for Weighted Linear Regression 125... 

LINREG (Standard unweighted and weighted linear regression) Section 2.2... 

The soil residue level is determined from the relative responses of the analytes to the internal standards. A five-point calibration curve is analyzed in triplicate, and the data are analyzed by a weighted 1 /x linear regression model. The calculated slope and intercept from the linear regression are used to calculate the residue levels in the soil samples. A 20% aliquot of the sample extract receives 10 ng of each internal standard... 

Perform a 1/x weighted linear regression analysis of relative response versus standard concentration in ng per 5 ng of internal standard. Calculate the slope and intercept values from the regression analysis. Use the following equation to determine the residue levels in the sample ... 

As a result of the linear regression, the values of fo (r) are now known for a sequence of discrete r. From Eq. (8.27) it is clear that fo (r) itself represents a weighted relative variance of the lattice distortions. If it is found to be almost constant, its square root directly describes the total amount of relative lattice distortion ( in percent ). 

---