Multivariate Data
Initial Publication Date: December 21, 2006
There are many examples of multivariate data in the geosciences. For example, a plausible hypothesis might be that the hydrocarbon content of a formation depends of the formation's mean porosity, mean bulk density, and mean resistivity. In this case the dependent variable Y would be an assumed function of the independent variables X1, X2, and X3 (porosity, density, and resistivity). Each variable may be measured at 100 different depths giving a total of 400 different measurements.
Y=(y1, y2, . . . , y100)
X1=(x1,1, x1,1, . . . ,x1,100)
X2=(x2,1, x2,2, . . . ,x2,100)
X3=(x3,1, x3,2, . . . ,x3,100)
In a linear multivariate regression analysis we would assume that the dependent variable Y can be expressed in terms of the independent variables X1, X2, and X3 according to:
Y=a0 + a1X1 + a2X2 + a3X3
Y=(y1, y2, . . . , y100)
X1=(x1,1, x1,1, . . . ,x1,100)
X2=(x2,1, x2,2, . . . ,x2,100)
X3=(x3,1, x3,2, . . . ,x3,100)
In a linear multivariate regression analysis we would assume that the dependent variable Y can be expressed in terms of the independent variables X1, X2, and X3 according to:
Y=a0 + a1X1 + a2X2 + a3X3
