Simple Linear Regression

A simple method to evaluate the number of bradyrhizobia on soybean seeds and ...

Soybean seeds are non-sterile and their bacterial population interferes with the enumeration of beneficial bacteria, making it difficult to assess survival under different conditions. Within this context, the principal aims of this work were: (1) to improve a selective media for the enumeration of B.

japonicum recovered from inoculated soybean seeds; (2) to establish the most representative mathematical function for B. japonicum mortality on soybean seeds after inoculation; (3) to evaluate if environmental or physiological conditions modify B.

japonicum mortality on soybean seeds; and (4) to create a new protocol for quality control of soybean inoculants. We successfully evaluated the combination of pentachloronitrobenzene and vancomycin added to the yeast-mannitol medium to inhibit most fungi and Gram-positive soybean microbiota, thus producing reliable counts of B.

japonicum from inoculated soybean seeds. Percentages of recovery and survival factors were obtained and used to construct a two-phase exponential decay non-linear regression function.

High temperature and desiccation decreased these parameters, while the optimization of temperature and the use of osmoprotective compounds with inoculants increased them. The use of this protocol minimized heterogeneity between experiments and may be considered more reliable than the simple expression of direct colony count of bacteria recovered from seeds.

Survey weighting and regression modeling « Statistical Modeling ...

I [Mike] have one specific question about your article in Statistical Science on weighting and multi-level regression models . I have one specific question about the article: do the results for the table 1 regression results use the procedure you describe in section 1? That is, does it include interactions between X and z in the model, or does it use design variables with main effects for the relation (y on z) of interest and simply report the coefficient for y on z? I couldn’t really tell, but perhaps I missed something.

I guess I have another question: on page 157 in the last full paragraph you state that it is not clear why a simple linear regression of y on z in the entire population would be of interest. That implies that it is not of interest. The first line of 1.4 discusses the regression of y on z. If we had all the data in the population, would we not simply compute the simple linear regression parameter estimates and report those as the relationship between y and z (assuming linearity)? If not, what are we trying to estimate with the E(y|z) function? I understand that it would be more interesting to look at y on z and X if we had tons of data, but that did not appear to be the motivation at the start of 1.4.

Related to this, I see that the population proportions of men and women enter into equation (4) through Bayes’ theorem because you don’t have many people of a single height. In the second example (page 158) you might have E(male|white=1) etc. from population data, such as census data in the geographical area. You could use that, couldn’t you, instead of the proportions white among males in the sample and then Bayes’ theorem?

Finally, about implementing this idea, perhaps we need groups of statisticians inside federal agencies to build recommendations for multilevel models for various outcomes and relationships among variables in place of (or in addition to) the survey statisticians developing complicated weights? What do you think?

My reply:

1. The details are given in the second column of p.158. The model does not include interactions, and we just use the coefficient of z.

2. My point on p.157 that you noted is that, once you consider an additional predictor in the model, you have to consider that the regression of y on z might not be linear. In which case, yes, you can certainly create some summary such as the slope that you’d get by regressing y on z given all the data–but it’s not clear why you’d want it. The E(y|z) function is still clearly defined, though, even if nonlinear. There’s a paper by Korn and Graubard in the American Statistician several years ago that discusses this point.

Delicious: Simple linear regression - Wikipedia, the free encyclopedia: [Research]

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