Affine is a type of transformation used to map one set of points onto another.
It preserves collinearity (points which are on a straight line stay on a straight line) and ratios of distances (the ratio of the distances between two points in the original set is the same as the ratio of the distances between the same two points in the transformed set).
It is used in many areas of mathematics and statistics, such as in linear algebra, linear regression, and research methods.
How to calculate
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Choose two sets of points, A and B. These points should include at least three non-collinear points (i.e. not all on a straight line).
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Compute the affine transformation matrix, T, which maps points in A to points in B.
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Apply the transformation to any point in A to get the corresponding point in B.
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Check that the transformation has been successful by verifying that collinearity and ratios of distances have been preserved.
Examples
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Affine transformations are used in linear regression models to transform variables such that the linear relationship between them is more easily visible.
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Affine transformations can also be used to simplify and reduce the complexity of a multivariate statistical model.
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Affine transformations can be used to normalize data prior to conducting a regression analysis.
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Affine transformations are often used in time series analysis to account for seasonality in the data.