ASTM_E_3080_-_17.pdf

Designation:E308017An American National StandardStandard Practice forRegression Analysis1This standard is issued under the fixed designation E3080;the number immediately following the designation indicates the year oforiginal adoption or,in the case of revision,the year of last revision.A number in parentheses indicates the year of last reapproval.Asuperscript epsilon()indicates an editorial change since the last revision or reapproval.1.Scope1.1 This practice covers regression analysis methodologyfor estimating,evaluating,and using the simple linear regres-sion model to define the statistical relationship between twonumerical variables.1.2 The system of units for this practice is not specified.Dimensional quantities in the practice are presented only asillustrations of calculation methods.The examples are notbinding on products or test methods treated.1.3 This standard does not purport to address all of thesafety concerns,if any,associated with its use.It is theresponsibility of the user of this standard to establish appro-priate safety,health,and environmental practices and deter-mine the applicability of regulatory limitations prior to use.1.4 This international standard was developed in accor-dance with internationally recognized principles on standard-ization established in the Decision on Principles for theDevelopment of International Standards,Guides and Recom-mendations issued by the World Trade Organization TechnicalBarriers to Trade(TBT)Committee.2.Referenced Documents2.1 ASTM Standards:2E178 Practice for Dealing With Outlying ObservationsE456 Terminology Relating to Quality and StatisticsE2586 Practice for Calculating and Using Basic Statistics3.Terminology3.1 DefinitionsUnless otherwise noted,terms relating toquality and statistics are as defined in Terminology E456.3.1.1 coeffcient of determination,r2,nsquare of thecorrelation coefficient.3.1.2 degrees of freedom,nthe number of independentdata points minus the number of parameters that have to beestimated before calculating the variance.E25863.1.3 residual,nobserved value minus fitted value,when amodel is used.3.1.4 predictor variable,X,na variable used to predict aresponse variable using a regression model.3.1.4.1 DiscussionAlso called an independent or explana-tory variable.3.1.5 regression analysis,na statistical procedure used tocharacterize the association between two numerical variablesfor prediction of the response variable from the predictorvariable.3.1.6 response variable,Y,na variable predicted from aregression model.3.1.6.1 DiscussionAlso called a dependent variable.3.1.7 sample correlation coeffcient,r,na dimensionlessmeasure of association between two variables estimated fromthe data.3.1.8 sample covariance,sxy,nan estimate of the associa-tion of the response variable and predictor variable calculatedfrom the data.3.2 Definitions of Terms Specific to This Standard:3.2.1 intercept,nof a regression model,0,the value ofthe response variable when the predictor variable is zero.3.2.2 regression model parameter,na descriptive constantdefining a regression model that is to be estimated.3.2.3 residual standard deviation,nof a regression model,the square root of the residual variance.3.2.4 residual variance,nof a regression model,2,thevariance of the residuals(see residual).3.2.5 slope,nof a regression model,1,the incrementalchange in the response variable due to a unit change in thepredictor variable.3.3 Symbols:b0=intercept estimate(5.2.2)b1=slope estimate(5.2.2)0=intercept parameter in model(5.1.2)1=slope parameter in model(5.1.2)1This practice is under the jurisdiction ofASTM Committee E11 on Quality andStatistics and is the direct responsibility of Subcommittee E11.10 on Sampling/Statistics.Current edition approved Nov.1,2017.Published January 2018.Originallyapproved in 2019.Last previous edition approved in 2016 as E3080 16.DOI:10.1520/E3080-17.2For referenced ASTM standards,visit the ASTM website,www.astm.org,orcontact ASTM Customer Service at serviceastm.org.For Annual Book of ASTMStandards volume information,refer to the standards Document Summary page onthe ASTM website.Copyright ASTM International,100 Barr Harbor Drive,PO Box C700,West Conshohocken,PA 19428-2959.United StatesThis international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for theDevelopment of International Standards,Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade(TBT)Committee.1 E=general point estimate of a parameter(5.4.2)ei=residual for data point i(5.2.5)=residual parameter in model(5.1.3)F=F statistic(X1.3.2)h=index for any value in data range(5.4.5)i=index for a data point(5.2.1)n=number of data points(5.2.1)r=sample correlation coefficient(5.3.2.1)r2=coefficient of determination(5.3.2.2)S(b0,b1)=sum of squared deviations of Yito the regressionline(X1.1.2)sb1=standard error of slope estimate(5.4.3)sb0=standard error o