Unbiased Least Squares Regression Coefficients for Multiple Linear Regression Mathematical Models

2021 ◽  
Author(s):  
Yuanchun Guo
2021 ◽  
Vol 13 (1) ◽  
Author(s):  
Manuel Molina

El método de los mínimos cuadrados se utiliza para calcular la recta de regresión lineal que minimiza los residuos, esto es, las diferencias entre los valores reales y los estimados por la recta. Se revisa su fundamento y la forma de calcular los coeficientes de regresión con este método. ABSTRACT The shortest distance. Least squares regression. Least squares regression method is used to calculate the linear regression line that minimizes residuals, that is, the differences among real values and those estimated by the line. Its basis and the way of calculating the regression coefficients with this method are reviewed.


2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Siong Fong Sim ◽  
Min Xuan Laura Chai ◽  
Amelia Laccy Jeffrey Kimura

Fourier-transform infrared (FTIR) offers the advantages of rapid analysis with minimal sample preparation. FTIR in combination with multivariate approach, particularly partial least squares regression (PLSR), has been widely used for adulterant analysis. Limited study has been done to compare PLSR with other regression strategies. In this paper, we apply simple linear regression (SLR), multiple linear regression (MLR), and PLSR for prediction of lard in palm olein oil. Pure palm olein oil was adulterated with lard at different concentrations and subjected to analysis with FTIR. The marker bands distinguishing lard and palm olein oil were determined using Fisher’s weights. The marker regions were then subjected to regression analysis with the models verified based on 100 training/test sets. The prediction performance was measured based on the percentage root mean square error (%RMSE). The absorption bands at 3006 cm−1, 2852 cm−1, 1117 cm−1, 1236 cm−1, and 1159 cm−1 were identified as the marker bands. The bands at 3006 and 1117 cm−1 were found with satisfactory predictive ability, with PLSR demonstrating better prediction yielding %RMSE of 16.03 and 13.26%, respectively.


2009 ◽  
Vol 2009 ◽  
pp. 1-8 ◽  
Author(s):  
Janet Myhre ◽  
Daniel R. Jeske ◽  
Michael Rennie ◽  
Yingtao Bi

A heteroscedastic linear regression model is developed from plausible assumptions that describe the time evolution of performance metrics for equipment. The inherited motivation for the related weighted least squares analysis of the model is an essential and attractive selling point to engineers with interest in equipment surveillance methodologies. A simple test for the significance of the heteroscedasticity suggested by a data set is derived and a simulation study is used to evaluate the power of the test and compare it with several other applicable tests that were designed under different contexts. Tolerance intervals within the context of the model are derived, thus generalizing well-known tolerance intervals for ordinary least squares regression. Use of the model and its associated analyses is illustrated with an aerospace application where hundreds of electronic components are continuously monitored by an automated system that flags components that are suspected of unusual degradation patterns.


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