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22 - 10 - 2014
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Correlation and Regression: Introduction

Correlation and regression are similar and sometimes one may be confused. In some cases it is reasonable to perform both calculations, however, in others only one of them can make sense.

Correlation is used in the situations when we measured two variables (X and Y) for each case and want to quantify how well they are associated. Correlation makes no assumption whether any of variables depend on other; it does not study with the relationship between variables and only describes association between them. In contrast, regression analysis is aimed to describe dependence of a variable on one or more explanatory variables.

Association between variables is, for example, strong correlation between length of the cell and length of the flagellum attachment zone (Zhou Q et al., 2011). Correlation analysis can be applied for a variety of microbiological tasks. In the Table we listed some examples of using correlation analysis in microbiology, and the table illustrates diversity of possible applications of this method:

Selected examples of application of correlation analysis in microbiology

Studied correlations


Between survival of hepatitis A virus in green onion and storage time

Sun et al., 2012

Between size of marine stramenopiles cells and temperature, and between marine stramenopiles and Synechococcus abundances

Lin et al., 2012

Between results of multilocus sequence typing and automated repetitive sequence-based PCR for determining sequence types of Klebsiella pneumoniae

Giske et al., 2012

Between results of determining respiratory activity in Acanthamoeba spp. by 5-cyano-2,3-ditolyl-tetrazolium chloride staining and the survival rates determined by the culture-dependent biocidal assay using the Spearman-Karber method

Kobayashi et al., 2012

Between results of identification of Corynebacterium spp., Arcanobacterium haemolyticum, and Rhodococcus equi strains by conventional methods (API Coryne complemented with 16S rRNA gene sequence analysis) and matrix-assisted laser desorption ionization–time of flight mass spectrometry

Vila et al., 2012

Between viral load of human papillomavirus (HPV) measured by Linear Array HPV genotyping with the gold standard quantitative PCR

Wentzensen et al., 2012

Between results obtained in four university hospital laboratories for the Etest technique for caspofungin and amphotericin-B MICs determination

Ranque et al., 2012

Between phenotypic residual feed intake and rumen microbial structure of beef cattle and specific microbial populations

Carberry et al., 2012

Between the relative abundance of Staphylococcus and total human milk oligosaccharides content

Hunt et al., 2012

Between dsRNA dots and nonstructural proteins and nascent RNAs of Coronaviruses during visual detection

Hagemeijer et al., 2012

Between CFA/III type IVb pili expression and enterotoxigenic Esherichia coli aggregation

Kolappan et al., 2012

Between predicted RpoS activity of Cronobacter sakazakii natural isolates and tolerance to acid, alkaline, osmotic, and oxidative treatments

Álvarez-Ordóñez et al., 2012

In turn, an example of a regression can be cited from the study of Zhao et al. (2000) who evaluated dependence of time-to-detection of growth of Clostridium botulinum on inoculum size of spores, concentration of sodium chloride and initial pH of the medium. This dependence was expressed by an equation of polynomial regression:

log10(time-to-detection) = 4.910 - 0.533Linoc + 0.139NaCl + 0.055Linoc2 - 0.068pH2,

where Linoc = log(inoculum size),

NaCl = percent of sodium-chloride concentration,

pH = initial pH of the medium.

Correlation is not changed if variables are swapped: in case of positive correlation increase in values of variable X will increase the values of variable Y and vice versa. However, regression has strictly one-way casual effect: if activity of antibiotic increases with decrease of incubation temperature, it does not mean that temperature may be influenced anyhow by activity of antibiotic.

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