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The explained sum of squares (ESS) is the sum of the squares of the deviations of the predicted values from the mean value of a response variable, in a standard regression model — for example, y i = a + b 1 x 1i + b 2 x 2i + ... + ε i, where y i is the i th observation of the response variable, x ji is the i th observation of the j th ...
Scope (computer science) In computer programming, the scope of a name binding (an association of a name to an entity, such as a variable) is the part of a program where the name binding is valid; that is, where the name can be used to refer to the entity. In other parts of the program, the name may refer to a different entity (it may have a ...
The sum of squares of residuals, also called the residual sum of squares: The total sum of squares (proportional to the variance of the data): The most general definition of the coefficient of determination is. In the best case, the modeled values exactly match the observed values, which results in and R2 = 1.
A fitted model having been produced, each observation in turn is removed and the model is refitted using the remaining observations (similar to leave-one-out cross-validation). The out-of-sample predicted value is calculated for the omitted observation in each case, and the PRESS statistic is calculated as the sum of the squares of all the ...
Smoothing splines are function estimates, , obtained from a set of noisy observations of the target , in order to balance a measure of goodness of fit of to with a derivative based measure of the smoothness of . They provide a means for smoothing noisy data. The most familiar example is the cubic smoothing spline, but there are many other ...
Sum ← Sum + x. SumSq ← SumSq + x × x. Var = (SumSq − (Sum × Sum) / n) / (n − 1) This algorithm can easily be adapted to compute the variance of a finite population: simply divide by n instead of n − 1 on the last line. Because SumSq and (Sum×Sum)/n can be very similar numbers, cancellation can lead to the precision of the result to ...
The squared Euclidean distance between two points, equal to the sum of squares of the differences between their coordinates. Heron's formula for the area of a triangle can be re-written as using the sums of squares of a triangle's sides (and the sums of the squares of squares) The British flag theorem for rectangles equates two sums of two squares.
The Gauss–Newton algorithm is used to solve non-linear least squares problems, which is equivalent to minimizing a sum of squared function values. It is an extension of Newton's method for finding a minimum of a non-linear function. Since a sum of squares must be nonnegative, the algorithm can be viewed as using Newton's method to iteratively ...