An optimal design for the best prediction of a linear regression function

1989 ◽  
Vol 40 (4) ◽  
pp. 369-372
Author(s):  
A. Yu. Zaigraev
Keyword(s):  
Optimal Design ◽  
Linear Regression ◽  
Regression Function ◽  
Linear Regression Function

Experimental Study of Short-Term Creep Characteristics Base on Step Loading-Unloading Method for Hard Rock

2013 ◽  
Vol 774-776 ◽  
pp. 86-93
Author(s):  
Fu Jun Zhang ◽  
Chuan Xiao Liu
Keyword(s):  
Linear Regression ◽  
Axial Strain ◽  
Radial Strain ◽  
Strain Curve ◽  
Regression Function ◽  
Nonlinear Creep ◽  
Linear Regression Function ◽  
Term Creep ◽  
Sandstone Specimen ◽  
Short Term Creep

Based on experimental results of uniaxial compression and short-term creep using 8-step loading-unloading method, fine sandstone specimen, which lower creep limit is 27MPa, present typical brittle breakage properties of hard rock. The correlative coefficients of linear regression function for isochronous stress-strain curve are all higher than 0. 92, and the ratio of long-term strength to instantaneous strength reaches 94. 39%，which indicate that the whole creep of fine sandstone specimen is weak. The average correlative coefficients of linear regression function for isochronous stress- axial strain curve are 3. 92% higher than that of average correlative coefficients of linear regression function for isochronous stress- radial strain curve, so nonlinear creep property of the fine sandstone specimen in axial direction is correspondingly weaker than that in radial direction. Negative Gauss distribution can be applied collectively to nonlinear creep of fine sandstone specimen, which has obvious time effect.With increasing loading, the reduction degrees of average correlative coefficients of linear fitting functions of isochronous stress-axial strain curve and isochronous stress-radial strain curve are 0. 97% and 0. 67% respectively, which indicates the linear correlation decreases commonly. Thus, the degree of nonlinear creep for fine sandstone specimen increases along with loading stress with obvious stress effect.

scholarly journals Temperature dependence of blood surface tension

2007 ◽  
pp. S93-S98
Author(s):  
J Rosina ◽  
E Kvašňák ◽  
D Šuta ◽  
H Kolářová ◽  
J Málek ◽  
...  
Keyword(s):  
Surface Tension ◽  
Linear Regression ◽  
Blood Serum ◽  
Whole Blood ◽  
Healthy Subjects ◽  
Regression Function ◽  
Sediment Surface ◽  
Linear Regression Equation ◽  
Linear Regression Function ◽  
Ring Method

Whole blood surface tension of 15 healthy subjects recorded by the ring method was investigated in the temperature range from 20 to 40 degrees C. The surface tension omega as a function of temperature t ( degrees C) is described by an equation of linear regression as omega(t) = (-0.473 t + 70.105) x 10(-3) N/m. Blood serum surface tension in the range from 20 to 40 degrees C is described by linear regression equation omega(t) = (-0.368 t + 66.072) x 10(-3) N/m and linear regression function of blood sediment surface tension is omega(t) = (-0.423 t + 67.223) x10(-3) N/m.

scholarly journals METODA ZANURZANIA REGRESJI W PRZYPADKU WYSTĘPOWANIA OBSERWACJI NIETYPOWYCH

2019 ◽  
Vol 20 (2) ◽  
pp. 83-92
Author(s):  
Małgorzata Kobylińska
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Least Squares Method ◽  
Regression Function ◽  
Maximum Depth ◽  
Two Dimensional ◽  
Structural Elements ◽  
Linear Regression Function ◽  
Regression Functions

This paper presents the application of the regression maximum depth for the estimation of linear regression function structural elements. For two-dimensional sets including untypical observations, regression functions were developed using the classical least squares method and a method based on the concept of observation depth measure in a sample. The effect of untypical observations on the estimated models has been noted.

scholarly journals Testing Linear Regression Function Adequacy without Replication

1985 ◽  
Vol 13 (4) ◽  
pp. 1482-1489 ◽  
Author(s):  
James W. Neill ◽  
Dallas E. Johnson
Keyword(s):  
Linear Regression ◽  
Regression Function ◽  
Linear Regression Function ◽  
Testing Linear

scholarly journals Automated Grading of Diabetic Retinopathy with Ultra-Widefield Fluorescein Angiography and Deep Learning

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Xiaoling Wang ◽  
Zexuan Ji ◽  
Xiao Ma ◽  
Ziyue Zhang ◽  
Zuohuizi Yi ◽  
...  
Keyword(s):  
Diabetic Retinopathy ◽  
Linear Regression ◽  
Fluorescein Angiography ◽  
Confusion Matrix ◽  
Regression Function ◽  
Diabetic Patients ◽  
Simple Linear Regression ◽  
Generative Adversarial Network ◽  
Data Set ◽  
Linear Regression Function

Purpose. The objective of this study was to establish diagnostic technology to automatically grade the severity of diabetic retinopathy (DR) according to the ischemic index and leakage index with ultra-widefield fluorescein angiography (UWFA) and the Early Treatment Diabetic Retinopathy Study (ETDRS) 7-standard field (7-SF). Methods. This is a cross-sectional study. UWFA samples from 280 diabetic patients and 119 normal patients were used to train and test an artificial intelligence model to differentiate PDR and NPDR based on the ischemic index and leakage index with UWFA. A panel of retinal specialists determined the ground truth for our data set before experimentation. A confusion matrix as a metric was used to measure the precision of our algorithm, and a simple linear regression function was implemented to explore the discrimination of indexes on the DR grades. In addition, the model was tested with simulated 7-SF. Results. The model classification of DR in the original UWFA images achieved 88.50% accuracy and 73.68% accuracy in the simulated 7-SF images. A simple linear regression function demonstrated that there is a significant relationship between the ischemic index and leakage index and the severity of DR. These two thresholds were set to classify the grade of DR, which achieved 76.8% accuracy. Conclusions. The optimization of the cycle generative adversarial network (CycleGAN) and convolutional neural network (CNN) model classifier achieved DR grading based on the ischemic index and leakage index with UWFA and simulated 7-SF and provided accurate inference results. The classification accuracy with UWFA is slightly higher than that of simulated 7-SF.

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