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Regression analysis builds on mathematical statistics. Regression analysis was one of the first major advances in the application of statistics to economics and business. It is a mathematical means of relating independent variables (the factors that influence a dependent variable) and the dependent variable, by constructing a mathematical model.

A topic in statistical inference is hypothesis testing. For example, we might want to test whether a particular single factor, like smoking, or a combination of more than one factor, like smoking and diet, can be used to predict lung cancer. In the single factor analysis, we do a regression of lung cancer incidence on smoking. In the multiple factor analysis, we do a regression of lung cancer incidence on smoking and diet. We can also examine how well a linear combination of smoking, diet, and other factors (e.g., age, sex, race, poverty) explains lung cancer incidence, and we can test whether that linear combination has a better R-squared than any of the single factors. In hypothesis testing, we test whether a null hypothesis is true or false and the design of the test determines the power of the test. In practice, we often perform statistical hypothesis testing in the context of a research study and report the probability of rejecting the null hypothesis. [See: How to design a good research study ]

Figure 4. A volume mesh is composed of triangular tetrahedra, each tetrahedron subdivided into two triangles. A single mappable volume is constructed by joining the four corners of the mesh using four edges and the edges are joined by four planar vertices. The edges, in turn, are joined by four planar vertices.

Figure 6. The same volume, now subdivided into two tetrahedra. The subdivision of a tetrahedron into two tetrahedra reduces the number of faces to eight, the number of edges to six, and the number of vertices to four.

Figure 6 shows the same volume, now subdivided into two tetrahedra. The subdivision of a tetrahedron into two tetrahedra reduces the number of faces to eight, the number of edges to six, and the number of vertices to four.

Some applications, such as Java, require that the application directories and libraries are updated to a newer version before the user can update. However, there are some applications that are not explicitly API-specific, such as the X Window System, the X server source code, are automatically updated as required.

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