ASTM E3080-16

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Designation: E3080 − 16 An American National Standard
Standard Practice for
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Regression Analysis
This standard is issued under the fixed designation E3080; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope 3.1.3.1 Discussion—The confidence level, 1 –α, reflects the
proportion of cases that the confidence interval [L, U] would
1.1 This practice covers regression analysis methodology
containorcoverthetrueparametervalueinaseriesofrepeated
for estimating, evaluating, and using the simple linear regres-
random samples under identical conditions. Once L and U are
sion model to define the relationship between two numerical
given values, the resulting confidence interval either does or
variables.
doesnotcontainit.Inthissense“confidence”appliesnottothe
1.2 The system of units for this practice is not specified.
particular interval but only to the long run proportion of cases
Dimensional quantities in the practice are presented only as
when repeating the procedure many times.
illustrations of calculation methods. The examples are not
3.1.4 confidence level, n—thevalue,1 –α,oftheprobability
binding on products or test methods treated.
associated with a confidence interval, often expressed as a
1.3 This standard does not purport to address all of the
percentage. E2586
safety concerns, if any, associated with its use. It is the
3.1.4.1 Discussion—α is generally a small number. Confi-
responsibility of the user of this standard to establish appro-
dence level is often 95 % or 99 %.
priate safety and health practices and determine the applica-
3.1.5 correlation coeffıcient, n—for a population, ρ, a di-
bility of regulatory limitations prior to use.
mensionless measure of association between two variables X
and Y, equal to the covariance divided by the product of σ
X
2. Referenced Documents
times σ .
Y
2
2.1 ASTM Standards:
3.1.6 correlation coeffıcient, n—for a sample, r,theestimate
E456 Terminology Relating to Quality and Statistics
of the parameter ρ from the data.
E2282 Guide for Defining the Test Result of a Test Method
3.1.7 covariance, n—of a population, cov(X, Y), for two
E2586 Practice for Calculating and Using Basic Statistics
variables, X and Y, the expected value of (X – µ )(Y – µ ).
X Y
3. Terminology
3.1.8 covariance, n—of a sample; the estimate of the pa-
rameter cov(X,Y) from the data.
3.1 Definitions—Unless otherwise noted, terms relating to
quality and statistics are as defined in Terminology E456.
3.1.9 dependent variable, n—a variable to be predicted
3.1.1 characteristic, n—a property of items in a sample or using an equation.
population which, when measured, counted, or otherwise
3.1.10 degrees of freedom, n—the number of independent
observed, helps to distinguish among the items. E2282
data points minus the number of parameters that have to be
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3.1.2 coeffıcient of determination, r,n—square of the
estimated before calculating the variance. E2586
correlation coefficient.
3.1.11 deviation, d, n—the difference of an observed value
3.1.3 confidence interval, n—an interval estimate [L, U] from its mean.
with the statistics L and U as limits for the parameter θ and
3.1.12 estimate, n—sample statistic used to approximate a
with confidence level 1 –α, where Pr(L≤θ≤ U) ≥ 1–α.
population parameter. E2586
E2586
3.1.13 independent variable, n—a variable used to predict
another using an equation.
3.1.14 mean, n—of a population, µ, average or expected
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This practice is under the jurisdiction ofASTM Committee E11 on Quality and
¯
Statistics and is the direct responsibility of Subcommittee E11.10 on Sampling / value of a characteristic in a population – of a sample, X, sum
Statistics.
of the observed values in the sample divided by the sample
Current edition approved Nov. 1, 2016. Published November 2016. DOI:
size. E2586
10.1520/E3080-16.
2
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
3.1.15 parameter, n—see population parameter. E2586
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
3.1.16 population, n—the totality of items or units of
Standards volume information, refer to the standard’s Document Summary page on
the ASTM website. material under consideration. E2586
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E3080 − 16
3.1.17 population parameter, n—summary measure of the 5. Straight Line Regression and Correlation
values of some characteristic of a population. E2586
5.1 Two Variables—The data set includes two variables, X
3.1.
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