A Study on Multiple Linear Regression Using Matrix Calculus

Mahaboob, B.; Praveen, J. Peter; Rao, Bopeng; Harnath, Y.; Narayana, C.; Prakash, Gyan

doi:10.37418/amsj.9.7.52

Cited by 6 publications

(5 citation statements)

References 6 publications

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“…In order to estimate the actual value of the attenuation coefficient, estimation models are needed based on the measurement results of several different specimen thicknesses, as shown in Figure 7 above. In this case, the estimation model was in the form of a nonlinear regression equation, as follows [26,27]:…”

Section: Discussionmentioning

confidence: 99%

Decomposition Technique for Bio-Transmittance Imaging Based on Attenuation Coefficient Matrix Inverse

Priambodo,

Aminoto,

Basari

2024

J. Imaging

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Human body tissue disease diagnosis will become more accurate if transmittance images, such as X-ray images, are separated according to each constituent tissue. This research proposes a new image decomposition technique based on the matrix inverse method for biological tissue images. The fundamental idea of this research is based on the fact that when k different monochromatic lights penetrate a biological tissue, they will experience different attenuation coefficients. Furthermore, the same happens when monochromatic light penetrates k different biological tissues, as they will also experience different attenuation coefficients. The various attenuation coefficients are arranged into a unique k×k-dimensional square matrix. k-many images taken by k-many different monochromatic lights are then merged into an image vector entity; further, a matrix inverse operation is performed on the merged image, producing N-many tissue thickness images of the constituent tissues. This research demonstrates that the proposed method effectively decomposes images of biological objects into separate images, each showing the thickness distributions of different constituent tissues. In the future, this proposed new technique is expected to contribute to supporting medical imaging analysis.

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Section: Discussionmentioning

confidence: 99%

Decomposition Technique for Bio-Transmittance Imaging Based on Attenuation Coefficient Matrix Inverse

Priambodo,

Aminoto,

Basari

2024

J. Imaging

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“…Before the multiple regression analysis, researchers examined data credibility for regression using pairwise Pearson's correlation between the independent variables and multicollinearity using variance inflation factors, and checked whether an explanatory variable is correlated with the error term using Durbin and Wu-Hausman test. Multiple regression was also preferred over other models because it assesses the four explanatory variables simultaneously instead of separately [ [ 82 , 83 ]; [ [ 84 , 85 ]]. Multiple regression modeling could analyze these four explanatory variables [ [ 86 ]; [ [ [87] , [88] , [89] ]].…”

Section: Methodsmentioning

confidence: 99%

The christian religious education teachers’ attitudes toward the five-stage lesson plan framework in Kenya: A gender-based analysis

Saoke

Musafiri²,

Ndwiga

et al. 2023

Heliyon

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“…In multiple linear regression (MLR), the dependent variable Y is sometimes affected by more than one independent variable. A linear model that relates Y to several estimators can be expressed by Equation 7 [20].…”

Section: Multiple Linear Regression Modelmentioning

confidence: 99%

“…and Comp. Eng., 1(1), [14][15][16][17][18][19][20][21][22][23]2022 E.K. Akpınar, M. Daş theoretical framework helps to understand a particular phenomenon better.…”

Section: Introductionmentioning

confidence: 99%

Modeling of a solar air collector heat transfer coefficient with regression algorithms

Akpınar¹,

Daş²

2022

FUJECE

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Solar air collectors (SAC) are thermodynamic systems that convert solar energy into useful fluid energy. SACs are very common in heating, cooling, food drying, and many other low-temperature applications. In this study, the heat transfer coefficient in the SAC was calculated according to Newton's cooling law. The obtained values and the thermal performance of the SAC were examined during the sunshine period. At the same time, SAC heat transfer coefficient models were made with the help of regression algorithms (multiple linear regression, simple linear regression) using SAC temperature data obtained by experimental measurements (inlet fluid, outlet fluid, and absorber plate) and solar radiation data on the SAC. As a result of the modeling, linear mathematical equations expressing the heat transfer coefficient for SACs were obtained. Obtained experimental and model data were compared. SAC heat transfer coefficient values were modeled with a mean absolute error of 0.6.

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A Study on Multiple Linear Regression Using Matrix Calculus

Cited by 6 publications

References 6 publications

Decomposition Technique for Bio-Transmittance Imaging Based on Attenuation Coefficient Matrix Inverse

Decomposition Technique for Bio-Transmittance Imaging Based on Attenuation Coefficient Matrix Inverse

The christian religious education teachers’ attitudes toward the five-stage lesson plan framework in Kenya: A gender-based analysis

Modeling of a solar air collector heat transfer coefficient with regression algorithms

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