### Standard Practice for Determination of the Slope in the Linear Region of a Test Record

Active Standard ASTM E3076 | Developed by Subcommittee: E08.03

Book of Standards Volume: 03.01

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Significance and Use

5.1 It is often necessary to determine the slope of a linear region within a test record, and for standardization purposes, it is desirable to have a method for determining the slope that is not subjective. There are numerous ASTM standard test methods where the test procedure or analysis requires that slope be determined, but the procedures for doing so are not well defined. Ideally, if multiple laboratories analyze the same data for determination of slope, they should produce the same result. The objective of this standard practice is to eliminate the linear-fit as a source of variability in test results.

1. Scope

1.1 This practice presents an automated, objective linear-fitting method for determining the slope of the linear portion of a test record. The method assumes that there is a linear region early in the test record where the value of the y variable increases roughly in proportion to the x variable and the slope of the record decreases after the linear region. The practice determines the best linear fit to the data based on the least normalized residual and provides metrics for evaluating the quality of the test record and the quality of the resultant fit.

1.2 Data quality metrics are applied that evaluate the level of noise and the digital resolution of the data to determine if the test record is adequate for a linear regression analysis. Fit quality metrics use analysis of residuals in the vicinity of the fit range to determine if the test record is adequately linear and the fit range is sufficiently large.

1.3 For test records that meet the data and fit quality metrics, the practice determines a repeatable slope without the need for operator input that is independent of operator judgment. For test records that fail one or more of the quality metrics, it is recommended that the analyst evaluate the fit to determine if it is acceptable.

1.4 This practice represents a general purpose approach that is applicable for any test standard or method in which a linear fit is desired. It is intended that this practice can be called upon by standard test methods when slope must be determined.

1.5 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use.

1.6 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.

2. Referenced Documents (purchase separately) The documents listed below are referenced within the subject standard but are not provided as part of the standard.

ASTM Standards

E1942 Guide for Evaluating Data Acquisition Systems Used in Cyclic Fatigue and Fracture Mechanics Testing

E2443 Guide for Verifying Computer-Generated Test Results Through The Use Of Standard Data Sets

ICS Code

ICS Number Code 03.120.30 (Application of statistical methods); 17.020 (Metrology and measurement in general)

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DOI: 10.1520/E3076-18

Citation Format

ASTM E3076-18, Standard Practice for Determination of the Slope in the Linear Region of a Test Record, ASTM International, West Conshohocken, PA, 2018, www.astm.org