Regression significance

H. pylori also is indicated in the treatment of mucosa-associated lymphoid tissue lymphomas of the stomach, which can regress significantly after such treatment. 

Possibly the single most important figure in 20th-century statistics is R.A. Fisher. He made many original contributions to almost every branch of statistics including correlation, regression, significance tests, the theory of estimation, analysis of variance... 

Reversible Hodgkin s lymphoma associated with Epstein-Barr virus infection during azathioprine therapy for systemic lupus erythematosus in a 47-year-old woman was attributed to azathioprine, which she had taken for several years [136 ]. A locally invasive mass associated with lymphadenop-athy in the neck regressed significantly after withdrawal of azathioprine, and after about 5 months had almost completely resolved without the need for chemotherapy. 

Fig. 9. The two materials, A and B, have overlapping 95% confidence limits at the LD q level. Because the slopes of the dose—mortahty regression lines for both materials are similar, there is no statistically significant difference in mortahty at the LD q and LD q levels. Both materials may be assumed to be lethahy equitoxic over a wide range of doses, under the specific conditions of the test.

Fig. 10. Two materials, A and B, have statistically similar LD q values but, because of differences ia the slopes of the dose—mortaUty regression lines, there are significant differences ia mortaUty at the LD q and LD jq levels. Material A is likely to present problems with acute overexposure to large numbers of iadividuals ia an exposed population when lethal levels are reached. With Material B, because of the shallow slope, problems may be encountered at low...

Fig. 12. The relationship between the mean oceanic residence time, T, yr, and the seawater—cmstal rock partition ratio,, of the elements adapted from Ref. 29. , Pretransition metals I, transition metals , B-metals , nonmetals. Open symbols indicate T-values estimated from sedimentation rates. The sohd line indicates the linear regression fit, and the dashed curves show the Working-Hotelling confidence band at the 0.1% significance level. The horizontal broken line indicates the time required for one stirring revolution of the ocean, T. ...

Analysis of such a correlation may reveal the significant variables and interactions, and may suggest some model, say of the L-H type, that could be analyzed in more detail by a regression process. The variables Xi could be various parameters of heterogeneous processes as well as concentrations. An application of this method to isomerization of /i-pentane is given by Kittrel and Erjavec (Ind. Eng. Chem. Proc. Des. Dev., 7,321 [1968]). 

We now consider a type of analysis in which the data (which may consist of solvent properties or of solvent effects on rates, equilibria, and spectra) again are expressed as a linear combination of products as in Eq. (8-81), but now the statistical treatment yields estimates of both a, and jc,. This method is called principal component analysis or factor analysis. A key difference between multiple linear regression analysis and principal component analysis (in the chemical setting) is that regression analysis adopts chemical models a priori, whereas in factor analysis the chemical significance of the factors emerges (if desired) as a result of the analysis. We will not explore the statistical procedure, but will cite some results. We have already encountered examples in Section 8.2 on the classification of solvents and in the present section in the form of the Swain et al. treatment leading to Eq. (8-74). 

One asterisk indicates significance at 95%, two asterisks at 99% level. NS, not significant at 95% level. Calculated by dividing mean square of line by mean square for error in this case deviations from double regression are used as an estimate of error. Significance determined from tables cf., e.g., G. W. Snedecor, Statistical Methods, 4th Edn. Iowa State College Press, Ames, 1946. 

The resulting fit is shown in Figure 12.2c. The regression is linear with a slope not significantly different from unity (slope = 0.95 0.1). The intercept yields the KB value in this case, 1 pM. 

This regression is linear, with a slope of 0.96 0.05. This slope is not significantly different from unity. Thus, the data points are refit to a linear regression with a slope of unity. The intercept of this regression... 

Significant surface regression of polymers appears to start at about 340°C. 

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