Multiple Linear Regression (MLR) and Principal Component Regression (PCR) for Ozone (O3) Concentrations Prediction

The assessment of wood biomass density through multivariate modeling of mid-infrared spectra can be useful for interpreting the relationship between feedstock density and functional groups. This study looked at predicting feedstock density from mid-infrared spectra and interpreting the multivariate models. The wood samples possessed a random cell wall orientation, which would be typical of wood chips in a feedstock process. Principal component regression and multiple linear regression models were compared both before and after conversion of the raw spectra into the 1st derivative. A principal component regression model from 1st derivative spectra exhibited the best calibration statistics, while a multiple linear regression model from the 1st derivative spectra yielded nearly similar performance. Earlywood and latewood based spectra exhibited significant differences in carbohydrate-associated bands (1000 and 1060 cm-1). Only statistically significant principal component terms (alpha less than 0.05) were chosen for regression; likewise, band assignments only originated from statistically significant principal components. Cellulose, lignin, and hemicelllose associated bands were found to be important in the prediction of wood density.

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The Comparison Of Partial Least Squares Regression, Principal Component Regression And Ridge Regression With Multiple Linear Regression For Predicting Pm10 Concentration Level Based On Meteorological Parameters

Journal of Data Science ◽

10.6339/jds.201507_13(3).0003 ◽

2021 ◽

pp. 663-692

Author(s):

Esra Polat ◽

Suleyman Gunay

Keyword(s):

Linear Regression ◽

Multiple Linear Regression ◽

Least Squares ◽

Ridge Regression ◽

Partial Least Squares Regression ◽

Meteorological Parameters ◽

Concentration Level ◽

Principal Component Regression ◽

Principal Component ◽

Least Squares Regression

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Comparative multiple quantitative structure–retention relationships modeling of gas chromatographic retention time of essential oils using multiple linear regression, principal component regression, and partial least squares techniques

Journal of Chromatography A ◽

10.1016/j.chroma.2009.05.016 ◽

2009 ◽

Vol 1216 (27) ◽

pp. 5302-5312 ◽

Cited By ~ 18

Author(s):

Li-Tang Qin ◽

Shu-Shen Liu ◽

Hai-Ling Liu ◽

Juan Tong

Keyword(s):

Linear Regression ◽

Essential Oils ◽

Multiple Linear Regression ◽

Retention Time ◽

Principal Component Regression ◽

Principal Component ◽

Chromatographic Retention ◽

Quantitative Structure ◽

Structure Retention ◽

Least Squares Techniques

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Functional Linear Regression

10.1093/oxfordhb/9780199568444.013.2 ◽

2018 ◽

Author(s):

Hervé Cardot ◽

Pascal Sarda

Keyword(s):

Linear Regression ◽

Least Squares ◽

Linear Models ◽

Estimation Error ◽

Asymptotic Properties ◽

Principal Component Regression ◽

Principal Component ◽

Penalized Least Squares ◽

Open Problems ◽

Functional Linear Regression

This article presents a selected bibliography on functional linear regression (FLR) and highlights the key contributions from both applied and theoretical points of view. It first defines FLR in the case of a scalar response and shows how its modelization can also be extended to the case of a functional response. It then considers two kinds of estimation procedures for this slope parameter: projection-based estimators in which regularization is performed through dimension reduction, such as functional principal component regression, and penalized least squares estimators that take into account a penalized least squares minimization problem. The article proceeds by discussing the main asymptotic properties separating results on mean square prediction error and results on L2 estimation error. It also describes some related models, including generalized functional linear models and FLR on quantiles, and concludes with a complementary bibliography and some open problems.

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Modeling of TEC over the Iberian Peninsula using PCA decomposition and multiple linear regression on space weather parameters

10.5194/egusphere-egu21-7393 ◽

2021 ◽

Author(s):

Anna Morozova ◽

Tatiana Barlyaeva ◽

Teresa Barata

Keyword(s):

Linear Regression ◽

Multiple Linear Regression ◽

Iberian Peninsula ◽

Space Weather ◽

Multiple Linear Regression Model ◽

Principal Component ◽

Electron Content ◽

Time Lags ◽

Total Electron ◽

Weather Parameters

The total electron content (TEC) over the Iberian Peninsula was modeled using a three-step procedure. At the 1st step the TEC series is decomposed using the principal component analysis (PCA) into several daily modes. Then, the amplitudes of those daily modes is fitted by a multiple linear regression model (MRM) using several types of space weather parameters as regressors. Finally, the TEC series is reconstructed using the PCA daily modes and MRM fitted amplitudes.The advantage of such approach is that seasonal variations of the TEC daily modes are automatically extracted by PCA. As space weather parameters we considered proxies for the solar UV and XR fluxes, number of the solar flares, parameters of the solar wind and the interplanetary magnetic field, and geomagnetic indices. Different time lags and combinations of the regressors are tested.The possibility to use such TEC models for forecasting was tested. Also, a possibility to use neural networks (NN) instead of MRM is studied.

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Superpixel-Based Mixed Noise Estimation for Hyperspectral Images Using Multiple Linear Regression

Remote Sensing ◽

10.3390/rs12081324 ◽

2020 ◽

Vol 12 (8) ◽

pp. 1324

Author(s):

Lei Sun ◽

Bujin Li ◽

Yongjian Nian

Keyword(s):

Linear Regression ◽

Multiple Linear Regression ◽

Least Squares Method ◽

Real Life ◽

Principal Component ◽

Noise Estimation ◽

Hyperspectral Images ◽

Spectral Correlation ◽

Local Sample ◽

Mixed Noise

HSIs (hyperspectral images) obtained by new-generation hyperspectral sensors contain both electronic noise and photon noise with comparable power. Therefore, both the SI (signal-independent) component and the SD (signal-dependent) component have to be considered. In this paper, a superpixel-based noise estimation algorithm using MLR (multiple linear regression) is proposed for the above mixed noise to estimate the noise standard deviation of both SI component and SD component. First, superpixel segmentation is performed on the first principal component obtained by MNF (minimum noise fraction)-based dimensionality reduction to generate non-overlapping regions with similar pixels. Then, MLR is performed to remove the spectral correlation, and a system of linear equations with respect to noise variances is established according to the local sample statistics calculated within each superpixel. By solving the equations in terms of the least-squares method, the noise variances are determined. The experimental results show that the proposed algorithm provides more accurate local sample statistics, and yields a more accurate noise estimation than the other state-of-the-art algorithms for simulated HSIs. The results of the real-life data also verify the effectiveness of the proposed algorithm.

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The Research of Wine Quality Evaluation Based on Multiple Linear Regression

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.756-759.2489 ◽

2013 ◽

Vol 756-759 ◽

pp. 2489-2493

Author(s):

Huai Hui Liu ◽

Wen Long Ji ◽

Peng Zhang ◽

Chuan Wen Yao

Keyword(s):

Principal Component Analysis ◽

Linear Regression ◽

Multiple Linear Regression ◽

Linear Regression Model ◽

Quality Evaluation ◽

Evaluation Model ◽

Multiple Linear Regression Model ◽

Principal Component ◽

Wine Grape ◽

Wine Quality

Through the establishment of evaluation model based on principal component analysis, select 8 principal components from nearly 30 indexes of wine grape. Then we establish the multiple linear regression model and analyse the association between physicochemical indexes of wine grape and wine, and the influence of physicochemical indexes of wine grape and wine on wine quality. Finally study whether we could use the physicochemical indexes to evaluate the wine quality.

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Research on Optimization of "Deoxidation Alloying" of Molten Steel Based on Linear Programming

Insight - Material Science ◽

10.18282/ims.v3i1.310 ◽

2020 ◽

Vol 3 (1) ◽

pp. 1

Author(s):

Anna Li ◽

Dongqing Xu

Keyword(s):

Linear Programming ◽

Linear Regression ◽

Multiple Linear Regression ◽

Molten Steel ◽

Programming Model ◽

Linear Regression Analysis ◽

Optimal Solution ◽

Principal Component ◽

Multiple Linear Regression Analysis ◽

Main Factors

Aiming at the optimization of the supporting solution for molten steel "deoxidation alloying", the cost of "deoxidation alloying" is minimized from an economic perspective. Using Excel, Eviews and spss software programming, through factor analysis, clustering dimension reduction, principal component analysis Multiple linear regression analysis and linear programming optimization analysis, the author found out the main factors that affected the yield of alloy elements. This paper establishes a multiple linear regression mathematical model that affects the main factors of alloy elements and yield. According to the reference alloy price, the linear programming model is adopted to find the optimal solution of alloy ingredients.

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