Variables pure error

Danckwerts age distribution function also Laplace transform variable pure error variance... 

If there are n replications at q different settings of the independent variables, then the pure-error sum of squares is said to possess (n — 1) degrees of freedom (1 degree of freedom being used to estimate y) while the lack-of-fit sum of squares is said to possess N — p — q(n — 1) degrees of freedom, i.e., the difference between the degrees of freedom of the residual sum of squares and the pure-error sum of squares. 

Because (28.74) > F-p (2.73), we reject FIq at the a = 0.10 level. The rejection, i.e., the model is portrayed to lack fit, is primarily because there is too little variability within each of the j replicates used to obtain pure error. Therefore, even though the actual data are reasonably well represented by the regression model, the model could be better. 

The Y-block variance (t 2) is the percentage of the output variance explained by the model over all output variables. This is analogous to the R -values calculated for the individual output variables. The values indicated by maxima were those where the pure error component had been subtracted. Only the linear PLS model was able to perform better than the NNPLS model on the R2-scores calculated for the overall model. The reason for this is the fact that except for C5, the C-class rocket motor irradiance spectra were most accurately predicted using the linear PLS model. 

If critical pressure and critical temperature are given in Pa and K, respectively, viscosities in centipoise result. The variable Io is either the low pressure pure component or mixture viscosity according to whether a pure component or mixture is being considered. For mixtures, simple molar average pseiidocritical temperature (Kay s rule), pressure, and density, and molar average molecular weight are used. The vapor density can be predicted by the methods previously discussed. Errors of above 5 percent are common for hydrocarbons and their mixtures. Experimental densities will reduce the errors slightly. 

To estimate the model (St), the 550 response variables in the region from 1100 to 2198 nm of the pure component spectra and a simple baseline offset are supplied to the computer. The resulting output from the validation samples includes the statistical prediction errors, estimated concentrations, concentration residuals, and spectral residuals. 

Uncet tainty in Pure Spectra (Model Diagnostic) The pure-component spectra are estimated from a standard multiple linear regression calculation (Equation 5-16) and. therefore, error estimates are available. The error estimates for all pure spectra at variable are shown in Equation 5.17 ... 

Measurement Residual Plot (Model, Sample and Variable Diagnostic) The spectral residuals for the validation data shown in Figure 5-58 are an order of magnitude smaller and less structured than the residuals obtained when the pure spectra were estimated (Figure 5-33). This can be explained as follows Equation 5.18 shows that the reported concentrations and temperatures (C is used in Equation 3.18) are used in the computation of the calibration residuals. Therefore, errors in the reported concentrations and temperatures contribute to the calibration residuals in addition to model inadequacy. In contrast. estimated concentrations and temperatures (C is u.sed in Equation 5-13)... 

It can be seen that this model contains all main effects, all quadratic terms in the design variables, all interactions among the design variables, and all interactions between the design and the environmental variables. An estimate of the pure experimental error can be obtained from the replication at the four center points. 

At pH 7 (the method describes determinations at pH 5 and 7) protein began to precipitate after 15 to 20 minutes incubation with p-chloromercuribenzoate, turning the procedure impracticable. The enzyme preparations used in our work had been lyophilized and stored for variable lengths of time their specific activity had not decreased with storage. As the preparations were about 85% pure, a systematic error is present in our determinations. Marshall, Metzenberg, and Cohen (30) have reported that the reaction of the enzyme with hydroxymercuri-benzoate was complete in approximately 80 minutes with the concentration of reagents which were used. Between 41 and 44 moles of SH... 

Blocking is used to increase the power of an experiment by removing known sources of variability from the estimate of error. Blocks can include panelists, replications, treatment, or anything else that is a known source of variation. By grouping experimental units into blocks, a more accurate measure of pure or experimental error is obtained. 

Principal components analysis (see also p. 16) involves an examination of set of data as points in n-dimensional space (corresponding to n original tests) and determines (first) the direction that accounts for the biggest variability in the data (first principal component). The process is repeated until n principal components are evaluated, but not all of these are of practical importance because some may be attributable purely to experimental error. The number of significant principal components shows the number of independent properties being measured by the tests considered. 

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