Reduced major axis

In this situation the error behavior of the two variables is reflected in the slope. The model is called the reduced major axis (RMA) model... 

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]. 

A considerable reduction in stress concentration could be achieved by using a cross-bore which is eUiptical in cross-section, provided the major axis of the eUipse is normal to the axis of the main cylinder. A more practical method of achieving the same effect is to have an offset radial hole whose axis is parallel to a radius but not coincident with it (97,98). Whenever possible the sharp edges at the intersection of the main bore with the cross bore are removed and smooth rounded corners produced so as to reduce the stress raising effects. 

Lissajous figure. Set the selector switch on the scope to horizontal input. Now both the horizontal and the vertical inputs come from the oscillator. Generally an ellipsoidal pattern will be seen on the scope. The width (minor axis) of the ellipse can be reduced by balancing the reactance. The null point occurs when the major axis of the ellipse is as nearly horizontal as possible. 

If we now generalize the definition of director to be the unit vector parallel to the major axis of the order parameter tensor, we find that at vanishingly low shear rates, where the order parameter tensor is nearly uniaxial, this definition reduces to the usual meaning of the term director. ... 

Gersten suggested that the strong electric fields produced near sharp metallic tips may cause some of the Raman enhancement. For an ellipsoid perfect conductor, the field at its tip can be even 10 times larger than the external electric field producing it. This was calculated for a point located 0.1 nm from the tip of an ellipsoid with a major axis of 50 nm and a minor axis of 2.5 nm. Lio and Wokaun " obtain 10" Raman enhancement due to these effects at the tip of an ellipsoid of 3 1 axial ratio. At other points, on or near the ellipsoid, they find the electric field greatly reduced. 

There is some evidence [Santos et a/ 1991] that bacteria in contact with flowing water become orientated so that each cell offers the least resistance to flow thereby reducing the tendency to slough, i.e. for rod shape bacteria the major axis was in line with the flow velocity. It is not clear whether this is a "deliberate" attempt by the bacteria to remain on the surface, or whether it is due to the natural elimination of cells that are susceptible to shear forces due to their position in relation to flow. 

Hence the high-frequency impedance of a reduced nonconducting polymer and the low-frequency capacitance of an oxidized polymer both depend linearly on layer thickness (via the N factor). The linear dependence of capacitance on thickness is of considerable diagnostic importance in model verification, since we usually expect the total capacitance of a thin film to be inversely proportional to film thickness. We can explain the prediction in Eqn. 438 by noting that low-frequency capacitance is confined to pore walls, which has its major axis orientated at right angles to the electrode surface. Thus the deeper the pore, the more capacitors there are in parallel in the pore wall and consequently the greater the total capacitance. 

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