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Machine Learning
Published in Seyedeh Leili Mirtaheri, Reza Shahbazian, Machine Learning Theory to Applications, 2022
Seyedeh Leili Mirtaheri, Reza Shahbazian
Linear regression is a supervised machine learning algorithm. The output of this learning algorithm is continuous and can therefore be classified into the regression category. The goal of linear regression is to predict the value of a variable based on the value of another variable. The output variable or the variable you want to predict is called the dependent variable. The input variable or the variable you are using to predict the output variable value is called the independent variable. The input variable is also called input features. Linear regression uses a linear equation to predict the output variable. The linear equation of linear regression can be written as the following: y˜=wx+b
Investigating the potential for integrating pure shadow lines into architectural design process
Published in Mário S. Ming Kong, Maria do Rosário Monteiro, Maria João Pereira Neto, Creating Through Mind and Emotions, 2022
Linear regression analysis is a statistical tool that tests the relationship between variables by fitting a linear equation to the data. In the research context, the role of the linear regression analysis is to find the relationship between the degree of purity of the model’s combination and the resulting shadow lines. The four combinations were distributed on the X-axis as independent variables, and the purity of the resulting shadow lines on the Y-axis were considered dependent variables.
Matrices
Published in Bilal M. Ayyub, Richard H. Mccuen, Numerical Analysis for Engineers, 2015
Bilal M. Ayyub, Richard H. Mccuen
The objective of this example is to demonstrate that matrices have a wide variety of applications in engineering, especially in developing prediction models using analytical tools such as regression analysis (Section 10.3 in Chapter 10). Regression analysis is a method used to fit a linear equation to a set of data. This example discusses only the matrix-related part of this analysis.
Nuclear density gauge compaction testing alternatives: synthesis and critical analysis
Published in Journal of Structural Integrity and Maintenance, 2019
Linear regression is also a commonly used methodology to compare test method results that are not the same units of measure. “Linear regression attempts to model the relationship between two variables by fitting a linear equation to observed data. One variable is considered an explanatory variable, and the other is a dependent variable (Yale, 1997)”. Linear regression is used to fit a predictive model to data set with x and y coordinates. With linear regression, the coefficient of determination (R2) is calculated to provide a measure of correlation between the two variables. This is seen when comparing density to stiffness or modulus. R2 is a statistical function that provides data about the exactitude of fit of a model. An R2 of 1.0 indicates that the calculated regression line fits perfectly to the data (Yale, 1997).
Effect of polypropylene fibres on strength and durability performance of M-sand self compacting concrete
Published in Cogent Engineering, 2023
Yamuna Bhagwat, Gopinatha Nayak, Poornachandra Pandit, Aishwarya Lakshmi
Figure 7(b) represents the linear regression results of the V-funnel and T500 test of M-sand self compacted concrete. The coefficient of determination of 0.98 shows the best fit results. The linear regression is used to estimate the required coefficients of dependent variables of the predicted linear equation using one or more independent variables. It is observed from Figure 7(b) that the original V-funnel test results of 7.5, 10.31, 14, 20 are predicted as 7.2696, 10.111, 14.999, 19.35, respectively. V-funnel time can be estimated for the PPF M-sand SCC using the T500 test results using the linear regression results are also shown in Figure 7(b).