Unweighted regression equations

It should also be noted that, in contrast to the situation described in the previous paragraph, results can be transformed to produce data that can be treated by unweighted methods. Data of the form y = bx with y-direction errors strongly dependent on X are sometimes subjected to a log-log transformation the errors in log y then vary less seriously with log x, so the transformed data can reasonably be studied by unweighted regression equations. 

In the least squares analyses, the individual ST energies were weighted inversely as the squares of the experimental enthalpy-of-formation uncertainty intervals only. (The uncertainty intervals for the combined EE are identical for each data point.) The standard errors in the regression equations were generated from the unweighted enthalpies of formation. 

Apply simple (unweighted) linear regression (Equations [8.19] and [8.23]) calculate and plot residuals (Yj-Yj jxed) vs Xj to search for evidence of heteroscedacity and/or nonlinearity of the data (Figure 8.9). At this point determine whether or not the cahbration obtained is fit for purpose the statistical test for goodness of fit (Equations [8.33-8.38]) wiU be helpful here, as will the calculated confidence limits for x (Equation [8.32]). 

Because there is only one independent variable, the subscript has been omitted. We now note that Zx/n = x and Zy/n = y, so we find Eqs. (2-75) as the normal equations for unweighted univariate least-squares regression. 

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. 

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