Development of a Heart Rate Variability Prediction Equation Through Multiple Linear Regression Analysis Using Physical Characteristics and Heart Rate Variables
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Heart rate variability (HRV) is an effective tool for objectively evaluating physiological stress indices in psychological states. This study aimed to develop multiple linear regression equations to predict HRV variables using physical characteristics, body composition, and heart rate (HR) variables (eg, sex, age, height, weight, body mass index, fat-free mass, percent body fat, resting HR, maximal HR, and HR reserve) in Korean adults. Six hundred eighty adults (male, n = 236, female, n = 444) participated in this study. HRV variable estimation multiple linear regression equations were developed using a stepwise technique. The regression equation’s coefficient of determination for time-domain variables was significantly high (SDNN = adjusted R 2 : 73.6%, P < .001; RMSSD = adjusted R 2 : 84.0%, P < .001; NN50 = adjusted R 2 : 98.0%, P < .001; pNN50 = adjusted R 2 : 99.5%, P < .001). The coefficient of determination of the regression equation for the frequency-domain variables was high without VLF (TP = adjusted R 2 : 75.0%, P < .001; LF = adjusted R 2 : 77.6%, P < .001; VLF = adjusted R 2 : 30.1%, P < .001; HF = adjusted R 2 : 71.3%, P < .001). Healthcare professionals, researchers, and the general public can quickly evaluate their psychological conditions using the HRV variables prediction equation.Keywords:
Stepwise regression
Abstract : Stepwise multiple regression tables are provided separately for males and females. Each table contains a listing for a series of regression equations for each dependent variable. Each dependent variable is first identified by data base number, abbreviated name, and full name. For each listing five columns are presented, each giving the regression constant and coefficient(s) for the best predictive multiple regression including 1, 2, 3, 4, and 5 independent variables, respectively. The last two rows of each listing contain the standard error of the estimate and adjusted coefficient of determination (R-squared) for each of the five sequential models. All models are significantly different from zero at the 0.001 level.
Standardized coefficient
Path coefficient
Stepwise regression
Variables
Table (database)
Regression diagnostic
Listing (finance)
Multiple correlation
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Heart rate variability (HRV) is an effective tool for objectively evaluating physiological stress indices in psychological states. This study aimed to develop multiple linear regression equations to predict HRV variables using physical characteristics, body composition, and heart rate (HR) variables (eg, sex, age, height, weight, body mass index, fat-free mass, percent body fat, resting HR, maximal HR, and HR reserve) in Korean adults. Six hundred eighty adults (male, n = 236, female, n = 444) participated in this study. HRV variable estimation multiple linear regression equations were developed using a stepwise technique. The regression equation’s coefficient of determination for time-domain variables was significantly high (SDNN = adjusted R 2 : 73.6%, P < .001; RMSSD = adjusted R 2 : 84.0%, P < .001; NN50 = adjusted R 2 : 98.0%, P < .001; pNN50 = adjusted R 2 : 99.5%, P < .001). The coefficient of determination of the regression equation for the frequency-domain variables was high without VLF (TP = adjusted R 2 : 75.0%, P < .001; LF = adjusted R 2 : 77.6%, P < .001; VLF = adjusted R 2 : 30.1%, P < .001; HF = adjusted R 2 : 71.3%, P < .001). Healthcare professionals, researchers, and the general public can quickly evaluate their psychological conditions using the HRV variables prediction equation.
Stepwise regression
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2022 International Conference on Machine Learning and Intelligent Systems Engineering (MLISE) (2021)
This paper analyzes the influencing factors of highway passenger and freight traffic, determines its influencing factors, and collects relevant statistical data from 117 different regions. Based on the principle of multiple linear regression method, first all variables are incorporated into the multiple regression equation for simulation. Second, integrate, demonstrate the applicability of the model, and then use the stepwise multiple regression method for model fitting. Based on this idea, the multiple linear regression model is constructed and forecasted for the highway passenger and freight volume. The results show that the stepwise multiple regression is effective. While the number of variables is greatly reduced and the calculation process is simplified, the model's fit is still good, and the problem of collinear between multiple variables is solved, and the regression coefficient of the variable is not consistent with the actual problem, and the result is predicted, It is also consistent with the actual situation and the applicability of the verification method, which can provide application references for road passenger and freight volume forecasting in other related areas.
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Based on the water level data of many years on the five hydrologic station of the lower yellow river,the paper establishes the regression equation of Aishan station by using the stepwise regression method,verifies the accuracy of the equation by forecasting the water level of Aishan station. Compared with the results of the multiple linear regression method,the results of the stepwise regression method are more precise,which could improve the precision of long-term flood forecasting in the lower Yellow River.
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Plant biochemistry
Ordinary least squares
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Regression analysis is the most common technique used for data analysis in clinical trials. In regression analysis, a regression line is fitted for the response variable (e.g. Viral load at the end of the study) based on few explanatory variables (e.g. Baseline viral load, time since first diagnosis etc.). A regression line Y=a+bX is fitted, where Y is the response variable, X is the explanatory variable, a denotes the intercept and b is the slope (regression coefficient) of the line. The slope indicates the change in the value of Y if X is changed by one unit. Therefore slope is often useful measure of examining the rate of change in variable Y. In clinical trials, comparing slope (rate of change) for two (or more subgroups e.g. Active vs. Placebo) can be the area of interest to assess the effect of medical treatment. SAS® procedure PROC REG does not performs the desired analysis directly but some kind of data manipulation is needed. This paper will discuss the algorithm for comparing the regression coefficients for simple/multiple regression for 2 or more subgroups.
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Standardized coefficient
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The least squares regression minimizing deviations only in dependent variable is not suitable for the regression analysis of environmental monitoring datasets, which are all random variables. Three two-variable linear models, i.e., the least squares regression, the reduced major axis regression, and the least normal square regression, were compared for the regression analysis of anions and cations in rain water samples. The results shown that the reduced major axis regression, rather than the others, was likely to be the model of choice for the regression analysis of random datasets, and a higher value was obtained for the regression coefficient b, showing a better relationship between the variables.
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Local regression
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In the method comparison approach, two measurement errors are observed. The classical regression approach (linear regression) method cannot be used for the analysis because the method may yield biased and inefficient estimates. In view of that, the Deming regression is preferred over the classical regression. The focus of this work is to assess the impact of censored data on the traditional regression, which deletes the censored observations compared to an adapted version of the Deming regression that takes into account the censored data. The study was done based on simulation studies with NLMIXED being used as a tool to analyse the data. Eight different simulation studies were run in this study. Each of the simulation is made up of 100 datasets with 300 observations. Simulation studies suggest that the traditional Deming regression which deletes censored observations gives biased estimates and a low coverage, whereas the adapted Deming regression that takes censoring into account gives estimates that are close to the true value making them unbiased and gives a high coverage. When the analytical error ratio is misspecified, the estimates are as well not reliable and biased.
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Censored regression model
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Robust regression
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The passenger throughput of a regional airport is an important indicator for measuring the development of a region and the basis for achieving the effective allocation of airport resources. Considering the factors affecting the passenger throughput of a western regional airport in China, this paper analyzed the correlation and significance between the factors and the passenger throughput. The stepwise regression method was used to reduce the dimension of original data and obtain the optimal regression model, and the gray model was used to predict the feature parameters. To verify the rationality of the passenger throughput prediction model, multiple linear regression and grey models were used to predict the passenger throughput in the same year and to compare them. The RMSE, MAPE and R2 calculations indicate that: in terms of prediction stability, accuracy and fitting accuracy, the stepwise regression model and multiple linear regression model are better than the gray model, but the multiple linear regression prediction results are large. It means that the combination of stepwise regression and gray model can overcome the shortcomings of a single model, and make the prediction results more scientific and reasonable.
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