## Practical Least Squares |

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### Common terms and phrases

accidental errors adjusted values Adjustment of Observations angle equations approximate values arithmetic mean assumed best value central-point figure closure coefficients column condition equations constant term convenient corrections correlates corresponding curve derived equations determined diagonal differences of elevation discrepancies elimination empirical formula equa equal Error Curve errors of observation example function horizontal angles indicated indirect observations Law of Error Least Squares left-hand length logarithms logsin mean square error measured Method of Least multiplied normal equations number of conditions number of errors number of observations observation equations observation of weight observed quantity observed values obtain plotted precision probable error problem propagation of error quadrilateral readings reduced residuals satisfy set of observations side equation single observation slide-rule solution spherical excess station Substituting sum-term tion total number triangle true error unity unknown quantities V₁ vations w+b+r weighted mean write written zero

### Popular passages

Page 24 - Weighted average is used in this report to indicate discharge-weighted average. It is computed by multiplying the discharge for a sampling period by the concentrations of individual constituents for the corresponding period and dividing the sum of the products by the sum of the discharges.

Page ii - COal Age v Electric Railway JOurnal Electrical World v Engineering News-Record American Machinist v Ingenieria Internacional Engineering 8 Mining Journal "• POwer Chemical 6 Metallurgical Engineering Electrical Merchandising THE CONSTRUCTION OF GRAPHICAL CHARTS BY JOHN B.

Page 23 - Multiply each payment by its term of credit, and divide the sum of the products by the sum of the payments ; the quotient will be the average term of credit.

Page 200 - Thus in the opening chapter, there is a definition of the probability of an event as the ratio of the number of favorable outcomes to the total number of possible outcomes if the latter are equally likely and mutually exclusive.

Page 149 - The standard deviation may be defined as the square root of the mean of the squares of the deviations from the mean of the distribution.

Page 22 - ... the reports from the different corps of correspondents are very nearly identical and how often the final figures arrived at by the individual members of the board agree with each other. These State estimates, which are in percentages, are then multiplied into the acreages for their respective States. The sum of these products is divided by the sum of the acreages giving the percentage for the entire crop for the United States. METHOD OF ISSUING REPORTS. Reports in relation to cotton thus prepared...

Page 19 - The method of least squares gives the line for which the sum of the squares of the residuals is a minimum.

Page 14 - ... for which the sum of the weighted squares of the residuals is a minimum: where w.

Page 200 - Symbolized by p + g = 1. probability: n. 1. (math.) the likelihood of the occurrence of an event, estimated as a ratio between the number of ways in which the event may occur and the number of ways in which alternative events may occur. ->-Eg, a die may fall equally well with any of the six faces up.

Page 19 - F=F(u) is required, such that according to the principle of least squares, the sum of the squares of the deviations F(u)—y shall be a minimum; the values of the variable и being equidistant ui+l — u{ = h.