Reduced major axis regression

Figure 2.2 Three types of regression line discussed in the text, (a) Ordinary least squares regression ofy on x in this case the vertical distance between the point and the line is mininiized. (b) Ordinary least squares regression of x onjq the horizontal distance between the point and the line is minimized, (c) Both ordinary least squares lines pass through the means (f, y), the centroid of the data, (d) Reduced major axis regression the line is hcted to minimize the area of the shaded triangles.

Reduced major axis regression is a more appropriate form of regression analysis for geochemistry than the more popular ordinary least squares regression. The method. (Kermack and Haldane, 1950) is based upon minimizing the areas of the triangles f/ I between points a ... 

In Figure 2.3 a comparison of regression lines is shown. Using the variables Fc203 and CaO from Table 2.2 the ordinary least squares (regressing both x ony andy on x), and the reduced major axis methods are used to fit straight lines to the data. The equation for each line is given. 

Three dUTerent regression lines drawn for the same data with their regression equations (data taken from Table 2.2). The regression lines are ordinary least squares regression of a- on jr (x on — slope and intercept calculated from Eqns [2,5] and [2.6] reduced major axis (RMA) — slope and intercept calculated from Eqns [2.7] and [2,5] ordinary least squares regression of y on X. (y on x) slope and intercept calculated from Eqns [2.5] and [2.6]. 

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