Simple linear regression analysis

Principal component analysis (PCA) of the soil physico-chemical or the antibiotic resistance data set was performed with the SPSS software. Before PCA, the row MPN values were log-ratio transformed (ter Braak and Smilauer 1998) each MPN was logio -transformed, then, divided by sum of the 16 log-transformed values. Simple linear regression analysis between scores on PCs based on the antibiotic resistance profiles and the soil physico-chemical characteristics was also performed using the SPSS software. To find the PCs that significantly explain variation of SFI or SEF value, multiple regression analysis between SFI or SEF values and PC scores was also performed using the SPSS software. The stepwise method at the default criteria (p=0.05 for inclusion and 0.10 for removal) was chosen. 

Once suitable parameters are available the values of g can be correlated with them by means of either simple linear regression analysis if the model requires only a single variable, or multiple linear regression analysis if it requires two or more variables. Such a correlation results in a SPQR. In this work we consider only those parameters that are defined directly or indirectly from suitable reference sets or, in the case of steric parameters, calculated from molecular geometries. 

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).

The environmental rain data acquired at the site were compiled in Table 2 for each exposure period. Simple linear regression analysis was performed using each of the factors as the independent variable and the difference in corrosion (Aloss in Table 1) as the dependent variable. All of the regression coefficients were significant. The coefficients for the amount of rainfall were considere to be the most important, since delivery of SO, ... 

Table 2.4 Results of simple linear regression analysis of the data in Table 2.3 using Ln-transformed 5-FU clearance as the dependent variable.

Fig. 1 shows such a plot and illustrates that the error in the value of log increases with time, i.e. as the concentration approaches its limiting value at / = oo, and is asymmetrically distributed. As the values of log 4 at long times are less reliable than those determined at short times, it is not formally correct to use a simple linear regression analysis to fit such a logarithmic plot and to determine k bs-Rather a non-linear regression with the data weighted to account for the increase in error with time and its asymmetric distributions should be employed. Nevertheless, it is often adequate to use a simple linear regression provided that only data collected over, say, the first 90% of the reaction (i.e. 3 half-lives) are used (see Fig. 

Simple linear regression analysis provides bivariate statistical tools essential to the applied researcher in many instances. Regression is a methodology that is grounded in the relationship between two quantitative variables (y, x) such that the value of y (dependent variable) can be predicted based oti the value of X (independent variable). Determining the mathematical relationship between these two variables, such as exposure time and lethality or wash time and logic microbial reductions, is very common in applied research. From a mathematical perspective, two types of relationships must be discussed (1) a functional relationship and (2) a statistical relationship. Recall that, mathematically, a functional relationship has the form... 

Based on papilloma multiplicity data in SENCAR mice (17) < -MA was 21 5 h exposure and +MA was a 2 h exposure. Determined from simple linear regression analysis. 

Integrated forms of Eq. (2.82) for first-, second- and general nth-order reactions are given in (2.83)-(2.85), respectively. Since there are only two unknowns, simple linear regression analysis may be used to determine values for k and n. For a first-order reaction (n = 1), one obtains... 

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