Testing Single-Equation Least Squares Regression Models for Autocorrelated Disturbances

Econometrica ◽  
1966 ◽  
Vol 34 (3) ◽  
pp. 646 ◽  
Author(s):  
Richard C. Henshaw
Keyword(s):  
Least Squares ◽  
Regression Models ◽  
Single Equation ◽  
Least Squares Regression

A Calibration Tutorial for Spectral Data. Part 1: Data Pretreatment and Principal Component Regression Using Matlab

1996 ◽  
Vol 4 (1) ◽  
pp. 225-242 ◽  
Author(s):  
Paul Geladi ◽  
Harald Martens
Keyword(s):  
Least Squares ◽  
Spectral Data ◽  
Partial Least Squares ◽  
Regression Models ◽  
Principal Component Regression ◽  
Principal Component ◽  
Ordinary Least Squares ◽  
Least Squares Regression ◽  
Statistical Parameters ◽  
Calibration Samples

Regression and calibration play an important role in analytical chemistry. All analytical instrumentation is dependent on a calibration that uses some regression model for a set of calibration samples. The ordinary least squares (OLS) method of building a multivariate linear regression (MLR) model has strict limitations. Therefore, biased or regularised regression models have been introduced. Some selected ones are ridge regression (RR), principal component regression (PCR) and partial least squares regression (PLS or PLSR). Also, artificial neural networks (ANN) based on back-propagation can be used as regression models. In order to understand regression models more is needed than just a set of statistical parameters. A deeper understanding of the underlying chemistry and physics is always equally important. For spectral data this means that a basic understanding of spectra and their errors is useful and that spectral representation should be included in judging the usefulness of the data treatment. A “constructed” spectrometric example is introduced. It consists of real spectrometric measurements in the range 408–1176 nm for 26 calibration samples and 10 test samples. The main response variable is litmus concentration, but other constituents such as bromocresolgreen and ZnO are added as interferents and also the pH is changed. The example is introduced as a tutorial. All calculations are shown in detail in Matlab. This makes it easy for the reader to follow and understand the calculations. It also makes the calculations completely traceable. The raw data are available as a file. In Part 1, the emphasis is on pretreatment of the data and on visualisation in different stages of the calculations. Part 1 ends with principal component regression calculations. Partial least squares calculations and some ANN results are presented in Part 2.

scholarly journals NIR-chemometric approaches for evaluating carbonization characteristics of hydrothermally carbonized lignin

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Sung-Wook Hwang ◽  
Un Taek Hwang ◽  
Kyeyoung Jo ◽  
Taekyeong Lee ◽  
Jinseok Park ◽  
...  
Keyword(s):  
Least Squares ◽  
Infrared Spectra ◽  
Regression Models ◽  
Near Infrared ◽  
Prediction Models ◽  
Hydrothermal Carbonization ◽  
Ordinary Least Squares ◽  
Least Squares Regression ◽  
Near Infrared Spectra ◽  
Mean Square Errors

AbstractThe aim of this study is to establish prediction models for the non-destructive evaluation of the carbonization characteristics of lignin-derived hydrochars as a carbon material in real time. Hydrochars are produced via the hydrothermal carbonization of kraft lignins for 1–5 h in the temperature range of 175–250 °C, and as the reaction severity of hydrothermal carbonization increases, the hydrochar is converted to a more carbon-intensive structure. Principal component analysis using near-infrared spectra suggests that the spectral regions at 2132 and 2267 nm assigned to lignins and 1449 nm assigned to phenolic groups of lignins are informative bands that indicate the carbonization degree. Partial least squares regression models trained with near-infrared spectra accurately predicts the carbon content, oxygen/carbon, and hydrogen/carbon ratios with high coefficients of determination and low root mean square errors. The established models demonstrate better prediction than ordinary least squares regression models.

Prediction of Long-Residue Properties of Potential Blends from Mathematically Mixed Infrared Spectra of Pure Crude Oils by Partial Least-Squares Regression Models

2009 ◽  
Vol 23 (4) ◽  
pp. 2164-2168 ◽  
Author(s):  
Peter de Peinder ◽  
Tom Visser ◽  
Derek D. Petrauskas ◽  
Fabien Salvatori ◽  
Fouad Soulimani ◽  
...  
Keyword(s):  
Least Squares ◽  
Partial Least Squares ◽  
Infrared Spectra ◽  
Regression Models ◽  
Partial Least Squares Regression ◽  
Crude Oils ◽  
Least Squares Regression

The Long Shadow of Ferguson: Legitimacy, Legal Cynicism, and Public Perceptions of Police Militarization

2018 ◽  
Vol 65 (2) ◽  
pp. 151-182 ◽  
Author(s):  
Richard K. Moule ◽  
Bryanna Hahn Fox ◽  
Megan M. Parry
Keyword(s):  
Least Squares ◽  
Regression Models ◽  
National Sample ◽  
Ordinary Least Squares ◽  
Public Perceptions ◽  
Least Squares Regression ◽  
Legal Socialization ◽  
Legal Cynicism ◽  
Perceptions Of Police ◽  
Influence Perceptions

This study examines public perceptions of police militarization, specifically whether individuals believe police are too militarized, and support for practices associated with militarization. Drawing on concepts found in the legal socialization literature—legitimacy and legal cynicism—this study tests hypotheses regarding whether these constructs influence perceptions of militarization. Using a national sample of 702 American adults, a series of ordinary least squares regression models are used to analyze the relationships between legitimacy, cynicism, and perceptions of police militarization. Results suggested that higher levels of legitimacy reduced beliefs that police are too militarized while also increasing support for practices associated with militarization. Cynicism increased beliefs that the police are too militarized, but had no effect on support for militarization. Perceptions of militarization are thus influenced by legal socialization.

Linear regression models for biomass table construction, using cluster samples

1989 ◽  
Vol 19 (5) ◽  
pp. 664-673 ◽  
Author(s):  
Andrew J. R. Gillespie ◽  
Tiberius Cunia
Keyword(s):  
Least Squares ◽  
Regression Models ◽  
Predictor Variable ◽  
Ordinary Least Squares ◽  
Cluster Sampling ◽  
Parameter Estimates ◽  
Least Squares Regression ◽  
Linear Regression Models ◽  
Estimation Procedures ◽  
Biased Estimates

Biomass tables are often constructed from cluster samples by means of ordinary least squares regression estimation procedures. These procedures assume that sample observations are uncorrelated, which ignores the intracluster correlation of cluster samples and results in underestimates of the model error. We tested alternative estimation procedures by simulation under a variety of cluster sampling methods, to determine combinations of sampling and estimation procedures that yield accurate parameter estimates and reliable estimates of error. Modified, generalized, and jack-knife least squares procedures gave accurate parameter and error estimates when sample trees were selected with equal probability. Regression models that did not include height as a predictor variable yielded biased parameter estimates when sample trees were selected with probability proportional to tree size. Models that included height did not yield biased estimates. There was no discernible gain in precision associated with sampling with probability proportional to size. Random coefficient regressions generally gave biased point estimates with poor precision, regardless of sampling method.

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