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Love's Lines, Angles and Rhymes is the sixth album by the American pop group the 5th Dimension, released in 1971. The title song had been recorded originally by Diana Ross the previous year. It reached #17 on Billboard 's Top 200 Album Chart and became the band's third consecutive album to be certified Gold.
The dimension of the statistical model is 3: the intercept of the line, the slope of the line, and the variance of the distribution of the residuals. (Note the set of all possible lines has dimension 2, even though geometrically, a line has dimension 1.)
Model-based assumptions. These include the following three types: Distributional assumptions. Where a statistical model involves terms relating to random errors, assumptions may be made about the probability distribution of these errors. [5] In some cases, the distributional assumption relates to the observations themselves. Structural assumptions.
An illustration of the five-point stencil in one and two dimensions (top, and bottom, respectively). In numerical analysis, given a square grid in one or two dimensions, the five-point stencil of a point in the grid is a stencil made up of the point itself together with its four "neighbors".
In one dimension, computing the analysis could be as simple as forming a weighted average of a forecasted and observed value. In multiple dimensions the problem becomes more difficult. Much of the work in data assimilation is focused on adequately estimating the appropriate weighting factor based on intricate knowledge of the errors in the system.
The rate of convergence must be chosen carefully, though, usually h ∝ n −1/5. In many cases, highly accurate results for finite samples can be obtained via numerical methods (i.e. computers); even in such cases, though, asymptotic analysis can be useful. This point was made by Small (2010, §1.4), as follows.
An important uniform 5-polytope is the 5-demicube, h{4,3,3,3} has half the vertices of the 5-cube (16), bounded by alternating 5-cell and 16-cell hypercells. The expanded or stericated 5-simplex is the vertex figure of the A 5 lattice , .
The thing is that the value in the 5th dimension points to every possible version of the 4th dimension. The 5th dimensions give the 4th dimension all possible properties of the physical universe, probably also the abstract universe. In the 4th dimension we observe time when the value of the 5th dimension is 1. When the 5th dimension value is 2 ...