Excel linear regression

Figure 5.20 shows a plot of the experimental temperature decay for run 1, after t = 60 min. An excellent linear regression was obtained, which means that U can be regarded as a constant value. The adiabatic temperature rise curves were calculated using Eq. (5.77) (plots are shown in Fig. 5.19). The adiabatic curves are now ready for a kinetic analysis.

The terms Po, Pa, Pt, Pat, Paa, and Pt,t, are adjustable parameters whose values are determined by using linear regression to fit the data to the equation. Such equations are empirical models of the response surface because they have no basis in a theoretical understanding of the relationship between the response and its factors. An empirical model may provide an excellent description of the response surface over a wide range of factor levels. It is more common, however, to find that an empirical model only applies to the range of factor levels for which data have been collected. 

A non-linear regression analysis is employed using die Solver in Microsoft Excel spreadsheet to determine die values of and in die following examples. Example 1-5 (Chapter 1) involves the enzymatic reaction in the conversion of urea to ammonia and carbon dioxide and Example 11-1 deals with the interconversion of D-glyceraldehyde 3-Phosphate and dihydroxyacetone phosphate. The Solver (EXAMPLEll-l.xls and EXAMPLEll-3.xls) uses the Michaehs-Menten (MM) formula to compute v i- The residual sums of squares between Vg(,j, and v j is then calculated. Using guessed values of and the Solver uses a search optimization technique to determine MM parameters. The values of and in Example 11-1 are ... 

Concentrations of terbacil and its Metabolites A, B and C are calculated from a calibration curve for each analyte run concurrently with each sample set. The equation of the line based on the peak height of the standard versus nanograms injected is generated by least-squares linear regression analysis performed using Microsoft Excel. 

Famoxadone, IN-JS940, and IN-KZ007 residues are measured in soil (p-g kg ), sediment (p-gkg ), and water (pgL ). Quantification is based on analyte response in calibration standards and sample extract analyses determined as pg mL Calibration standard runs are analyzed before and after every 1 samples in each analytical set. Analyte quantification is based on (1) linear regression analysis of (y-axis) analyte concentration (lagmL Q and (x-axis) analyte peak area response or (2) the average response factor determined from the appropriate calibration standards. The SLOPE and INTERCEPT functions of Microsoft Excel are used to determine slope and intercept. The AVERAGE and STDEV functions of Microsoft Excel are used to determine average response factors and standard deviations. 

The objectives in this chapter are two. The first one is to briefly review the essentials of linear regression and to present them in a form that is consistent with our notation and approach followed in subsequent chapters addressing nonlinear regression problems. The second objective is to show that a large number of linear regression problems can now be handled with readily available software such as Microsoft Excel and SigmaPlot . 

Problems that can be described by a multiple linear regression model (i.e., they have a single response variable, 1) can be readily solved by available software. We will demonstrate such problems can be solved by using Microsoft Excel and SigmaPlot . 

As shown in Figure 6.21, excellent linearity was obtained, as represented by the high coefficient of correlation obtained for the least square linear regression. Similar results were obtained for the evaluation of autosampler accuracy when other analytes (propyl paraben and rhodamine 110 chloride) were employed in the determinations. Liu et al.9 conducted similar evaluations for the samples employed in the evaluation of the drug release rate profile of OROS with similar results to those discussed above. 

In an excellent paper, Zhao et al. [29] assembled a carefully reviewed literature set of human absorption data on 241 drugs. They showed that a linear regression model built with 5 Abraham descriptors could fit percent human absorption data reasonably well (r2 = 0.83, RMSE = 14%). The descriptors are excess molar refraction (E), polarizability (S), hydrogen bond acidity (A), hydrogen bond basicity (B), and McGowan volume (V), all related to lipophilicity, hydrophilicity, and size. In a follow-on paper, data on rat absorption for 151 drugs was collected from the literature and modeled using the Abraham descriptors [30]. A model with only descriptors A and B had r2 = 0.66, RMSE = 15%. 

We have encountered Excel s LINEST as a tool for linear regression. Unfortunately, LINEST cannot be generalised from vectors to matrices. To deal with matrices, we do not have an option but to use equations (4.59) and (4.61). It is possible to do so, but not as convenient as in Matlab. 

A simple linear regression is very easily computed with an ordinary computer spreadsheet program such as Lotus 1-2-3 or Microsoft Excel. The method involves calculating first the average values of x and y, then the values of Co and Ci, and then the estimated value of y ... 

It was found that the requirements were satisfied for application of the linear regression technique to species mass concentrations in a multicomponent aerosol. The results of 254 particle size distributions measured at China Lake in 1979 indicate that the normalized fine aerosol volume distribution remained approximately constant. The agreement between the calculated and measrued fine particle scattering coefficients was excellent. The measured aerosol sulfur mass distribution usually followed the total distribution for particles less than 1 ym. It was assumed that organic aerosol also followed the total submicron distribution. 

Li etal. discuss the use of on-line Raman spectroscopy to dynamically model the synthesis of aspirin, one of the most documented and well-understood reactions in organic chemistry. That makes it an excellent choice for building confidence in the sampling interface, Raman instrumentation, and analysis procedures. The researchers used wavelets during analysis to remove fluorescent backgrounds in the spectra and modeled the concentrations with multiple linear regression.53... 

To establish chiral separation method for donepezil hydrochloride enantiomers by capillary electrophoresis (CE) and to determine the two enantiomers in plasma [39], alkalized plasma was extracted by isopropa-nol-n-hexane (3 97) and L-butefeina was used as the IS. Enantioresolution was achieved using 2.5% sulfated-beta-cyclodextrin as chiral selector in 25 mmol/1 triethylammonium phosphate solution (pH 2.5) on the uncoated fused-silica capillary column (70 cm x 50 fim i.d.). The feasibility of the method to be used as quantitation of donepezil HC1 enantiomers in rabbit plasma was also investigated. Donepezil HC1 enantiomers were separated at a baseline level under the above condition. The linearity of the response was evaluated in the concentration range from 0.1 to 5 mg/1. The linear regression analysis obtained by plotting the peak area ratio (A(s)/A(i)) of the analyte to the IS versus the concentration (C) showed excellent correlation coefficient The low limit of detection was 0.05 mg/1. The inter- and intra-day precisions (RSD) were all less than 20%. Compared with chiral stationary phase by HPLC, the CE method is simple, reliable, inexpensive, and suitable for studying the stereoseletive pharmacokinetics in rabbit. 

The EC 10 was calculated using a non linear regression procedure that is available as an Excel macro at the following link http //eric.vindimian.9online.fr... 

Excel provides some built-in tools for fitting models to data sets. By far the most common routine method for experimental data analysis is linear regression, from which the best-fit model is obtained by minimizing the least-squares error between the y-test data and an array of predicted y data calculated according to a linear... 

Figure 2.3. Linear regression analysis with Excel. Simple linear regression analysis is performed with Excel using Tools -> Data Analysis -> Regression. The output is reorganized to show regression statistics, ANOVA residual plot and line fit plot (standard error in coefficients and a listing of the residues are not shown here).

Linear regression using the Excel Data Analysis Add-in... 

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