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The algorithm performs summation with two accumulators: sum holds the sum, and c accumulates the parts not assimilated into sum, to nudge the low-order part of sum the next time around. Thus the summation proceeds with "guard digits" in c , which is better than not having any, but is not as good as performing the calculations with double the ...
One takes as estimates of α and β the values that minimize the sum of squares of residuals, i.e., the sum of squares of the differences between the observed y-value and the fitted y-value. To have a lack-of-fit sum of squares that differs from the residual sum of squares, one must observe more than one y -value for each of one or more of the ...
The general regression model with n observations and k explanators, the first of which is a constant unit vector whose coefficient is the regression intercept, is = + where y is an n × 1 vector of dependent variable observations, each column of the n × k matrix X is a vector of observations on one of the k explanators, is a k × 1 vector of true coefficients, and e is an n× 1 vector of the ...
This is the modular sum of the values taken by the simple checksum as each block of the data word is added to it. The modulus used is the same. So, for each block of the data word, taken in sequence, the block's value is added to the first sum and the new value of the first sum is then added to the second sum.
Any non-linear differentiable function, (,), of two variables, and , can be expanded as + +. If we take the variance on both sides and use the formula [11] for the variance of a linear combination of variables (+) = + + (,), then we obtain | | + | | +, where is the standard deviation of the function , is the standard deviation of , is the standard deviation of and = is the ...
The vertical blue lines represent the absolute errors from the pink line to each data point. The pink line is one of infinitely many solutions within the green area. To understand why there are multiple solutions in the case shown in Figure A, consider the pink line in the green region. Its sum of absolute errors is some value S.
When each measured value can be assumed to have the same weighting, or significance, the biased and unbiased (or "sample" and "population" respectively) estimators of the variance are computed as follows: = = (¯) = = = (¯).
The Spreadsheet Value Rule. Computer scientist Alan Kay used the term value rule to summarize a spreadsheet's operation: a cell's value relies solely on the formula the user has typed into the cell. [48] The formula may rely on the value of other cells, but those cells are likewise restricted to user-entered data or formulas.