Sum of Square of Differences Between Experimental Data and Predicted Results (SSE) for Flowthrough and Batch Reactors Without Acid Addition at 180°C [Pg.969]

The sum of squares of differences between points on the regression line yi at Xi and the arithmetic mean y is called SSR [Pg.70]

Coaxial parallel squares of different edge length [Pg.605]

Temp. = 0. Volume of gas = r., Difference between Calculated and Observed. Square of Difference between Calculated and Observed. [Pg.328]

Figure 5.6 Mean square of differences between consecutive Raman spectra as a function of mixing time of a binary system. Reprinted from Vergote etal. (2004)62 with permission from Elsevier. |

Figure 1. An oxide mask of square type a), b) and c) - rows of oxide squares of different area with side orientation like [110], [100] and [100] + 30", respectively. |

Figure 2.3 Hydrogen storage capacity at RT (diamonds) and 77 K (squares) of different carbon materials versus their BET specific surface area [52]. The dotted line represents the theoretical curve according to [50], |

SOLUTION. This is an example of linear least-squares analysis (LLSA), where the objective function is continuous. Typically, LLSA is performed on a discrete set of data points and one seeks to minimize the sum of squares of differences between the data and a continuous model function. In this case, we seek to minimize the square of the difference between two continuous functions over the complete range of reactant conversions that are possible (i.e., 0 < x < 1 for irreversible reactions). Hence, the sum of squares in the objective function to be [Pg.453]

Eor the overdetermined system. Ax does not equal b. This is because the solution minimizes the sum of squares of differences between Ax and b. The least squares solution is useful in several applications, such as regression, which is covered in Chapter 7. [Pg.75]

This technique fits a straight line to data as dependent vtJues related to a single set of values of an independent parameter. The set of equations that are used minimizes the sum of the squares of differences between the dependent vtdues and the line. [Pg.86]

If all force constants are being refined simultaneously with different, carefully selected weights, W,, attached to them, then the differences between the observed and calculated values, = Xi(obs) — A./(calc), and Jij are calculated for each datum Xi. The corresponding contributions are added to the scalar sum of weighted squares of differences e We, to the vector J We, and to the matrix J WJ. The normal equations are formed as [Pg.24]

Fig. 12.6 (A) Calculated (solid curves) and measured (points) mean bromide concentrations, normalized by the mass of appUed solute per unit soil surface, at times r = 18 and 32 days (B) Mean bromacd concentrations, normalized by the mass of apphed solute per unit soU surface, at times r = 18 and 32 days (solid curves best-fit based on least squares of differences between computed and measured mean concentrations, = 0.14 mL/g, X = 0.022dashed curves based on sum of squares of differences, = 0.16 mL/g, day X = 0.012 daysdotted-dashed curves |

See also in sourсe #XX -- [ Pg.261 ]

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