Linear Regression Analysis

By Michael B. Miller. 2013

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Citations in the corpus

PAC-Bayesian Theory Meets Bayesian Inference (2016, neutral): “Note that a proof of equality E w ∼ ˆ ρ w T Φ T Φw = tr Φ T Φ A − 1 + (cid:98) w T Φ T Φ (cid:98) w (Line ♣ below), known as the “expectation of the quadratic form”, can be found in Seber and Lee [41, Theorem 1.5].”
Backpropagation algorithms and Reservoir Computing in Recurrent Neural Networks for the forecasting of complex spatiotemporal dynamics (2019, methodology): “The matrix W o , h ∈ R d o × d h is trained with regularized least-squares regression with Tikhonov regularization to alleviate overfitting (Tikhonov & Arsenin, 1977; Yan & Su, 2009) following the same recipe as in Pathak, Hunt et al. (2018).”
A study over the general formula of regression sum of squares in multiple linear regression (2020, methodology): “Seber defined linear regression analysis, LRA, as a common technique of estimating the relationship between any two random variables, the explanatory variable X, and the dependent variable Y such as height and weight, income and intelligence quotient, ages of husband and wife [4].”
Analysis of regression confidence intervals and Bayesian credible intervals for uncertainty quantification (2012, background): “When s2 is known, the distribution of estimates b of the unknown true parameters b is multivariate Gaussian, i.e., [Draper and Smith, 1998, p. 94; Seber and Lee, 2003, p. 47], b Np b; XTC 1ɛ X 1 ∝ exp 1 2 b b TXTC 1ɛ X b b : ð8Þ Ideally X in (8) is the same as in (6), but in reality alternative…”
A new fuzzy linear regression approach for dissolved oxygen prediction (2015, methodology): “The first is known as ‘possibilistic’ fuzzy regression, developed by Tanaka et al. (1982), which is a linear programming approach that aims to minimize the fuzziness of the system.”
Understanding Robust Corrections in Structural Equation Modeling (2014, background): “The mathematical developments presented in this section assume that the reader is familiar with regression presented in matrix form (e.g., Christensen, 2002; Neter et al., 1996; Seber & Lee, 2003).”
Expert Systems With Applications (methodology): “Examples of methodologies for regression analysis in the literature include linear regression ( Seber & Lee, 2012 ), automated learning of algebraic models for optimisation (ALAMO) ( Cozad, Sahinidis, & Miller, 2014; Zhang & Sahinidis, 2013 ), support vector regression (SVR) ( Smola & Schlkopf,…”
Precision Agriculture Techniques and Practices: From Considerations to Applications (2019, methodology): “The linear regression found a relation between the two parameters by fitting the equation of the line using the observed dataset [69].”
Supplementary Material for “ Statistical test for consistent estimation of causal effects in linear non-Gaussian models ” (2012, unknown): “…Zˆc + r v v = Z˜c + E w b + ˜ r v The coefficients˜c of the second regression can be expressed in terms of the coefficientsˆc and b as˜c = ˆ c − (Z T Z) −1 Z T E w b (Seber and Lee, 2003, p. 54), which yields for the second regression v = Z(ˆ c − (Z T Z) −1 Z T E w b) + E w b + ˜ r v = Zˆc + (I −…”
Thirty Years of Machine Learning: The Road to Pareto-Optimal Wireless Networks (2019, methodology): “Based on the specific form of regression function, regression analysis methods can be classified as ordinary linear regression [189], logistic regression [190], polynomial regression [191], etc.”
New Confidence Intervals and Bias Comparisons Show That Maximum Likelihood Can Beat Multiple Imputation in Small Samples (2013, methodology): “Breaking this into components, we see that the first component is a quadratic form whose expectation can be calculated using a standard matrix identity (Seber & Lee, 2003, pp. 9–12), Δ .”
Seeing the forest beyond the trees (2015, methodology): “The so-called geostatistical regression (GR) (Johnson & Hoeting, 2011) utilizing the generalized least squares (GLS) method shows that none of the trends provided by Mitchard et al. (2014) is significant under this approach (Seber & Lee, 2012).”