 | Education - 1919 - 924 pages
...quantity that can be deduced from a series of observations made with equal care and skill, is that for which the sum of the squares of the residuals is a minimum." . . . "This is the so-called most probable value, and it is the office of the principle of Least Squares,... | |
 | Education - 1919 - 960 pages
...quantity that can be deduced from a series of observations made with equal care and skill, is that for which the sum of the squares of the residuals is a minimum." . . . "This is the so-called most probable value, and it is the office of the principle of Least Squares,... | |
 | Le Roy Dougherty Weld - Error analysis (Mathematics). - 1916 - 216 pages
...quantity that can be deduced from a series of direct observations, made with equal care and skill, is that for which the sum of the squares of the residuals is a minimum.. The law governing the distribution of errors has already been deduced theoretically, and the experience... | |
 | Joseph Lipka - Engineering - 1918 - 288 pages
...becomes r = 70.59 + 0.293 C. III. Method of Least Squares. — The best values of the constants are those for which the sum of the squares of the residuals is a minimum, ie, H (r — a — bC)2 = minimum; hence the partial derivatives of this expression with respect to... | |
 | Ora Miner Leland - Mathematics - 1921 - 266 pages
...nxo— (Mi+Af2+ . . ,., _[«! and n (7) That is, the best value of the observed quantity — the one for which the sum of the squares of the residuals is a minimum, is the mean. 28. Computation of the Mean. Owing to the close agreement of the observations of which... | |
 | Frederick Cecil Mills - Business - 1924 - 632 pages
...constants, the true values being unknown. As in the simpler case the most probable values are those for which the sum of the squares of the residuals is a minimum. In this case, however, the residuals are deviations, not from a single magnitude, as in the case of... | |
 | Mineral industries - 1970 - 742 pages
...squares (4) : The best value obtainable from a set of measurements of the same accuracy is that value for which the sum of the squares of the residuals is a minimum. If we let then - y± » V - y 2» n = f(xn> •••V (1) and the principle of least squares tells... | |
 | Engineering - 1918 - 1070 pages
...relation between x and y. According to the theory of least squares, the best values for a and b are those for which the sum of the squares of the residuals is a minimum. The values to be substituted for a and b can be found from the equations 5i/ = na+62x and 2)yx = a2a;... | |
 | United States. Congress. House. Post Office and Civil Service - 1971 - 288 pages
...of fit. The method of leant ftquarcs given the line for which ih* sum of the tquare* of the renduals is a minimum. There is only one such line for a given get of points, so the mult does not depend upon any choice of group*. In thin section we shall show... | |
 | Vladimir B. Ginzburg - Technology & Engineering - 1993 - 880 pages
...fitted to the calibration data. For example, "least-squares linearity" is referenced to that straight line for which the sum of the squares of the residuals is minimized. The term "residual" refers to the deviations of output readings from their corresponding... | |
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The most probable value of a measured quantity that can be deduced from a series of observations made with equal care and skill, is that for which the sum of the squares of the residuals is a minimum. 
