scholarly journals Exact adaptive confidence intervals for linear regression coefficients

2019 ◽  
Vol 13 (1) ◽  
pp. 94-119 ◽  
Author(s):  
Peter Hoff ◽  
Chaoyu Yu
Keyword(s):  
Linear Regression ◽  
Confidence Intervals ◽  
Regression Coefficients ◽  
Adaptive Confidence Intervals

A Note on Confidence Intervals and Model Specification

Marketing ZFP ◽  
2019 ◽  
Vol 41 (4) ◽  
pp. 33-42
Author(s):  
Thomas Otter
Keyword(s):  
Confidence Intervals ◽  
Generalized Linear Model ◽  
Statistical Information ◽  
Regression Coefficients ◽  
Model Specification ◽  
Model Parameters ◽  
Exploratory Research ◽  
Empirical Calibration ◽  
Credible Intervals ◽  
Model Structures

Empirical research in marketing often is, at least in parts, exploratory. The goal of exploratory research, by definition, extends beyond the empirical calibration of parameters in well established models and includes the empirical assessment of different model specifications. In this context researchers often rely on the statistical information about parameters in a given model to learn about likely model structures. An example is the search for the 'true' set of covariates in a regression model based on confidence intervals of regression coefficients. The purpose of this paper is to illustrate and compare different measures of statistical information about model parameters in the context of a generalized linear model: classical confidence intervals, bootstrapped confidence intervals, and Bayesian posterior credible intervals from a model that adapts its dimensionality as a function of the information in the data. I find that inference from the adaptive Bayesian model dominates that based on classical and bootstrapped intervals in a given model.

A robust random coefficient regression representation of the chain-ladder method

2021 ◽  
pp. 1-32
Author(s):  
Ioannis Badounas ◽  
Apostolos Bozikas ◽  
Georgios Pitselis
Keyword(s):  
Linear Regression ◽  
Linear Regression Model ◽  
Random Coefficients ◽  
Regression Coefficients ◽  
Varying Coefficients ◽  
Statistical Procedures ◽  
Chain Ladder Method ◽  
Loss Reserving ◽  
Random Coefficient Regression ◽  
Chain Ladder

Abstract It is well known that the presence of outliers can mis-estimate (underestimate or overestimate) the overall reserve in the chain-ladder method, when we consider a linear regression model, based on the assumption that the coefficients are fixed and identical from one observation to another. By relaxing the usual regression assumptions and applying a regression with randomly varying coefficients, we have a similar phenomenon, i.e., mis-estimation of the overall reserves. The lack of robustness of loss reserving regression with random coefficients on incremental payment estimators leads to the development of this paper, aiming to apply robust statistical procedures to the loss reserving estimation when regression coefficients are random. Numerical results of the proposed method are illustrated and compared with the results that were obtained by linear regression with fixed coefficients.

scholarly journals How cann soccer improve statistical learning?

2014 ◽  
Vol 2 (7) ◽  
pp. 83-87
Author(s):  
Enivaldo C. Rocha ◽  
Dalson Britto Figueiredo Filho ◽  
Ranulfo Paranhos ◽  
José Alexandre Silva Jr. ◽  
Denisson Silva
Keyword(s):  
Linear Regression ◽  
Statistical Learning ◽  
Undergraduate Students ◽  
Ordinary Least Squares ◽  
Regression Coefficients ◽  
Least Squares Regression ◽  
Practical Application ◽  
Implementation Cost ◽  
Home Team ◽  
Classical Hypothesis

This paper presents an active classroom exercise focusing on the interpretation of ordinary least squares regression coefficients. Methodologically, undergraduate students analyze Brazilian soccer data, formulate and test classical hypothesis regarding home team advantage. Technically, our framework is simply adapted for others sports and has no implementation cost. In addition, the exercise is easily conducted by the instructor and highly enjoyable for the students. The intuitive approach also facilitates the understanding of linear regression practical application.

scholarly journals ANALISIS FAKTOR-FAKTOR YANG MEMPENGARUHI MINAT BELI KONSUMEN PADA SITUS JUAL-BELI ONLINE

2020 ◽  
Vol 6 (2) ◽  
pp. 179
Author(s):  
I Gede Andri Setiawan ◽  
Sukardi Sukardi
Keyword(s):  
Data Analysis ◽  
Risk Perception ◽  
Linear Regression ◽  
Multiple Linear Regression ◽  
Significant Influence ◽  
Regression Coefficient ◽  
Regression Coefficients ◽  
Test Results ◽  
Price Perception ◽  
Usefulness Perception

The purpose of this study were to analyze (1) the influence of trust of the purchase interest of online shop consumers, (2) the influence of risk perception of the  purchase  interest  of  online  shop  consumers,  (3)  the  influence  of  use fulness perception of the purchase interest of online shop consumers, (4) the influence of price perception of the purchase interest of online shop consumers. The populations in this research are  student of Ahmad Dahlah University Yogyakarta  Campus  One.  The  method  sample  is  purposif  sampling  with  the number  of  sample  as  much  as  100  respondents  from  three  Faculty  that  is, Economy  Faculty,  Psycology  Faculty,  and  FTDI.  Collecting  data  using questionnaires  that  was  done  validity  test  and  realibity  test.  This  research  was done by using multiple linear regression data analysis. The  results  of  this  study  indicate  that  (1)  the  trust  is  not  significant influence on consumer purchase interest of the sites online shop, this is evidenced by the significant value  is bigger  than the probability alpha value of 0.05 (0,206 > 0.05), and the regression coefficient has a  positive value of 0.062; (2)  the  trust is not significant influence on consumer purchase interest of the sites online shop, this  is  evidenced  by  the  significant  value  is  bigger  than  the  probability  alpha value of 0.05 (0, 0,234 > 0.05), and the regression coefficient has a positive value of  0.057;  (3)  the  usefulness  perception  is  significant  influence  on  consumer purchase interest of the sites online shop, this is evidenced by the significant value is  smaller  than  the  probability  alpha  value  of  0.05  (0.000  <  0.05),  and  the regression coefficients has a positive value of 0.456; (4) the price perception is not significant  influence on consumer purchase interest of the sites online shop, this  is  evidenced  by  the  significant  value  is  bigger  than  the  probability  alpha value of 0.05 (0.066 > 0.05), and the regression coefficient has a  positive value of  0.111;  and  (5)  trust,  risk  perception,  usefulness  perception  and  price perception  together  have  an  effect  on  consumer  purchase  interest  of  the  sites online  shop,  this  is  evidenced  by  the  significant  value  is  smaller  than  the probability alpha value of 0.05 (0.000 < 0.05). The R2 test results in this study was obtained  R2 value  of  0.413.  This  shows  that  purchase  interest  is  influenced  by trust, risk perception, use perception, and price  perception by 41.3%, while the remaining 58.7% is influenced by other factors not observed by the researcher or considered fixed.

scholarly journals . Reflection of individual typological properties in the tremorogram (Predicting the indicators of Rusalov’s test according to the indicators of the tremorogram)

2021 ◽  
Vol 11 (5) ◽  
pp. 213-222
Author(s):  
B. A. Lobasyuk ◽  
L. N. Akimova ◽  
A. N. Stoyanov ◽  
A. V. Zamkovaya
Keyword(s):  
Linear Regression ◽  
Multiple Linear Regression ◽  
Regression Coefficients ◽  
Regression Equations ◽  
Target Feature ◽  
Left Hand ◽  
Right Hand ◽  
Postural Load ◽  
Significant Regression ◽  
The Right

Rationale for choosing. An increase in physiological tremor (Tr) in emotionally saturated situations is reflected not only in fiction, but also in scientific literature. In other words, tremors and emotional responses are interconnected. Purpose. To investigate the reflection of individual-typological properties in a tremorogram using V. M. Rusalov’s mathematical modeling. Material and methods. Tr was recorded using a linear transducer. Tr was recorded under postural load (arms extended forward). The sensor was alternately placed on the outstretched right and left arms in front of oneself, under conditions of “eyes open” (operative rest). The analysis of the tremorogram (TrG) files was carried out after the end of the study using the "Analist - 2" software according to the half - period analysis algorithm. To study the individual psychological characteristics of the personality, we used the method of determining the properties of the temperament by V.M. Rusalov. Each of the many indicators of Rusalov’s test selected in the analysis was considered as a target feature (Y-s), and the amplitudes and frequencies of TrG were considered as influencing variables (sets of X - s) and multiple linear regression equations of the form were built: The parameters of the amplitude and frequency of EEG rhythms were used as Xs. Own research. In multiple regression analysis of the influence of TrG indices of the right hand on the indices of Rusalov’s test, 12 statistically significant regression coefficients were determined, and 11 statistically significant regression coefficients for the left hand. After obtaining the diagnostic equations of multiple linear regression, describing the influence of TrG indicators on the indicators of Rusalov’s test, an attempt was made, using these equations, to obtain the indicators of Rusalov’s test, using the tremor indicators. On average, the% discrepancy between the determined and predicted indicators was 97.42% for the right hand, and 101.98 for the left. Conclusions. 1. With the use of diagnostic equation, it was possible to predict the indicators of psychological testing according to Rusalov’s test by the indicators of tremor of the right and left hands.2. Influence of Rusalov’s test indicators on TrG indicators were less in modulus than the influence of TrG indicators on the indicators of Rusalov’s  test, i.e. did not participate in the control of the mechanisms of TrG generation.3. The results obtained indicate that tremor indicators contain information about the subject-activity and communicative aspects of temperament according to V. M. Rusalov.

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