Material strength investigations provide a rich area of application for statistical meth ods.The article “Effects of Aggregates and Microfillers on the Flexural Properties ofConcrete” (Magazine of Concrete Research, 1997: 81–98) reported on a study ofstrength properties of high-performance concrete obtained by using superplasticizersand certain binders. The compressive strength of such concrete had previouslybeen investigated, but not much was known about flexural strength (a measure ofability to resist failure in bending). The accompanying data on flexural strength (inMegaPascal, MPa, where 1 Pa (Pascal) 5 1.45 3 1024 psi) appeared in the articlecited:5.9 7.2 7.3 6.3 8.1 6.8 7.0 7.6 6.8 6.5 7.0 6.3 7.9 9.08.2 8.7 7.8 9.7 7.4 7.7 9.7 7.8 7.7 11.6 11.3 11.8 10.7Suppose we want an estimate of the average value of flexural strength for all beamsthat could be made in this way (if we conceptualize a population of all such beams,we are trying to estimate the population mean). It can be shown that, with a highdegree of confidence, the population mean strength is between 7.48 MPa and8.80 MPa; we call this a confidence interval or interval estimate. Alternatively, thisdata could be used to predict the flexural strength of a single beam of this type. Witha high degree of confidence, the strength of a single such beam will exceed7.35 MPa; the number 7.35 is called a lower prediction bound.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Material strength investigations provide a rich area of application for statistical meth ods.
The article “Effects of Aggregates and Microfillers on the Flexural Properties of
Concrete” (Magazine of Concrete Research, 1997: 81–98) reported on a study of
strength properties of high-performance concrete obtained by using superplasticizers
and certain binders. The compressive strength of such concrete had previously
been investigated, but not much was known about flexural strength (a measure of
ability to resist failure in bending). The accompanying data on flexural strength (in
MegaPascal, MPa, where 1 Pa (Pascal) 5 1.45 3 1024 psi) appeared in the article
cited:
5.9 7.2 7.3 6.3 8.1 6.8 7.0 7.6 6.8 6.5 7.0 6.3 7.9 9.0
8.2 8.7 7.8 9.7 7.4 7.7 9.7 7.8 7.7 11.6 11.3 11.8 10.7
Suppose we want an estimate of the average value of flexural strength for all beams
that could be made in this way (if we conceptualize a population of all such beams,
we are trying to estimate the population mean). It can be shown that, with a high
degree of confidence, the population mean strength is between 7.48 MPa and
8.80 MPa; we call this a confidence interval or
data could be used to predict the flexural strength of a single beam of this type. With
a high degree of confidence, the strength of a single such beam will exceed
7.35 MPa; the number 7.35 is called a lower prediction bound.
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