Introduction to Linear Regression Analysis

By Andreas Karlsson. 2007

4,805 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Statistics and Probability

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Citations in the corpus

Stealing Hyperparameters in Machine Learning (2018, methodology): “Therefore, we leverage the linear least square method [30], a widely used method to derive an approximate solution of an overdetermined system, to estimate the hyperparameters.”
Impact of Information and Communication Technology on Economic Growth: Evidence from Developing Countries (2019, background): “In all our estimations (Tables 3–6), weak VIF values (inferior to 2.5) were found, which indicates the absence of any high multicollinearity between the explanatory variables (Montgomery et al. 2001).”
Evaluation of analytical calibration based on least-squares linear regression for instrumental techniques: A tutorial review (2016, background): “However, residuals values fairly distributed between positive and negative values have been suggested as indicator of the deviation in relation to the linearity assumption [25, 31].”
Eigenfunction properties and approximations of selected incidence matrices employed in spatial analyses (2000, neutral): “From ordinary least-squares (OLS) regression theory [25],”
Exploration from Demonstration for Interactive Reinforcement Learning (2016, methodology): “Discrepancy is computed using the externally studentized residual [27].”
Chronic spinal pain and physical–mental comorbidity in the United States: results from the national comorbidity survey replication (2005, methodology): “The association of chronic spinal pain with role disability was assessed using linear regression (Montgomery et al., 2001).”
Support vector machines in remote sensing: A review (2011, neutral): “Relevant papers are then summarized, while juxta-position of general patterns enables us to derive conclusions and recommendations for further investigations.”
Measuring the ghost of competition: Insights from density-dependent habitat selection on the co-existence and dynamics of lemmings (2000, methodology): “The densities of each species were centred and standardized before calculating interaction terms (Montgomery and Peck, 1982; Rodríguez, 1995).”
Robot-enhanced motor learning: accelerating internal model formation during locomotion by transient dynamic amplification (2005, methodology): “Residual analysis for the linear fit was performed by constructing normal probability plots of the residuals for each subject [21].”
Substantial seagrass blue carbon pools in the southwestern Baltic Sea are spatially heterogeneous, mostly autochthonous, and include relics of terrestrial peatlands (2022, background): “< 5 indicate an acceptable level of collinearity, VIFs > 10 warrant further investigation (Montgomery and Peck 1992).”
The Eﬀects of Data Quality on Machine Learning Performance (2022, methodology): “It learns a linear relationship between features added by an inter-cept term [47].”
Selecting random Latin hypercube dimensions and designs through estimation of maximum absolute pairwise correlation (2012, background): “Many analytical techniques that experimenters apply to computer outputs—such as regression modeling and partition trees—suffer when there is multicollinearity among the input variables (Montgomery, Peck, and Vining 2001; Kim and Loh 2003).”
Quantitative Imaging Biomarkers: A Review of Statistical Methods for Technical Performance Assessment (2014, neutral): “underestimation of both the slope and residual error.(27) Several alternatives to simple linear regression are available to address this issue and should be considered for their applicability to the specific QIB.”
Evaluation of Ridge, Elastic Net and Lasso Regression Methods in Precedence of Multicollinearity Problem: A Simulation Study (2021, methodology): “(Montgomery and Peck, 1992; Kutner et al., 2005).”
Model-based process monitoring using robust generalized linear models (2005, methodology): “Commonly used bounded influence functions include Huber’s function, Andrew’s cosine wave function, the Cauchy function, and Tukey’s bi-weight function (for details, see Montgomery et al. 2001).”