Study of linear regression based on least squares and fuzzy least absolutes deviations and its application in geography

Dehghan, Mohammad Hossein; Hamidi, Farhad; Salajegheh, Mahsa

doi:10.1109/cfis.2015.7391667

Cited by 8 publications

(6 citation statements)

References 6 publications

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“…Simple linear regression is a basic statistical analysis method used to study the linear relationship between an independent variable and a dependent variable. In this method, firstly it assumes a linear relationship between the independent variable and the dependent variable, that is, the value of the dependent variable can be linearly predicted by the value of the independent variable [10,11].…”

Section: Simple Linear Regressionmentioning

confidence: 99%

Research on the Selection of the most Popular Product Categories in TikTok based on Linear Regression

Chen

2024

SHS Web Conf.

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In the e-commerce industry, live streaming has become an increasingly popular way to promote and sell products. With the rise of social media platforms like Facebook, Instagram, and TikTok, more and more businesses are using live streaming to engage with their customers and boost sales. This study investigates the relationship between sales and the number of live viewers to find out the most popular partition for live sales of TikTok’s e-commerce by employing simple linear regression, deseasonalization, and variable transformation techniques to optimize the models. This study improves the accuracy and interpretability of regression models in the e-commerce industry, specifically focusing on the relationship between real-time viewership and Gross Merchandise Volume (GMV). The findings indicate that removing seasonality and applying log-to-log transformation provide more reliable and accurate models, ultimately helping businesses better understand and optimize their sales strategies.

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Section: Simple Linear Regressionmentioning

confidence: 99%

Research on the Selection of the most Popular Product Categories in TikTok based on Linear Regression

Chen

2024

SHS Web Conf.

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“…Regression models can be linear or nonlinear, and one of the most common machine learning algorithms is linear regression. First suggested by Sir Francis Galton in 1894, linear regression is used to evaluate and quantify the relationship between observed variables 54–56 . For any of the available regression models, the response variable's mean value for the given independent variable values is the key quantity.…”

Section: Regression Modelsmentioning

confidence: 99%

“…First suggested by Sir Francis Galton in 1894, linear regression is used to evaluate and quantify the relationship between observed variables. [54][55][56] For any of the available regression models, the response variable's mean value for the given independent variable values is the key quantity. Model realization is a multiple-step process, as shown below in Figure 6.…”

Section: Regression Modelsmentioning

confidence: 99%

Machine learning‐based regression models for predicting signal quality of dense wavelength division multiplexing (DWDM) optical communication network

Masih

Kaur

2023

Int J Communication

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Summary Over the years, optical communication systems have been a significant source of fast and secure communication. However, factors like noise and mitigation error can degrade the bit error rate (BER) and quality factor (Q factor) of optical communication systems. Predicting the optimal threshold, Q factor, and BER is usually a difficult task. Therefore, in this paper, machine learning‐based linear regression, least absolute shrinkage and selection operator (LASSO) regression, and Ridge regression have been used for a dense wavelength division multiplexing (DWDM)‐based optical communication network to predict the signal quality. These techniques have been used to predict the desired BER, Q factor, threshold, and eye height of the system. To demonstrate this research concept, a DWDM‐based optical communication network of 50 km length is designed and simulated using Optisystem‐14.0. After data preparation, regression models have been developed and validated through diagnostic plots. Results show that mean square error (MSE) has a significant decline with an increase in the number of epochs for all four models. LASSO and Ridge regression have effectively resolved the issue of overfitting, which occurred in the linear regression case. Furthermore, the mean MSE plot proved the significant reduction of mean MSE in the case of LASSO regression. Results show that min BER for LASSO regression came out to be −173,627.14, providing a robust and cost‐efficient process.

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“…Some of the main works in this class are of D'Urso [14], who proposed regression models for crisp/fuzzy input-output data, and D'Urso et al [16] that proposed robust fuzzy linear regression model using least median squares-WLS estimation procedure to deal with data that contains outliers. The work of Dehghan et al [20] may also be attributed to this group as it uses LS and least absolute deviations methods to compare classical and fuzzy regressions using numerical examples of geographical data with symmetric fuzzy observations. Another notable work of Coppi et al [13] proposed an iterative procedure with LS estimations for a regression mode to study the connection between crisp inputs and fuzzy output observations.…”

Section: Linear Regression Analysis Problem Over Fuzzy Datamentioning

confidence: 99%

Outlier Detection Algorithms Over Fuzzy Data with Weighted Least Squares

Nikolova

Rodríguez

Symes

et al. 2021

Int. J. Fuzzy Syst.

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In the classical leave-one-out procedure for outlier detection in regression analysis, we exclude an observation, then construct a model on the remaining data. If the difference between predicted and observed value is high we declare this value an outlier. As a rule, those procedures utilize single comparison testing. The problem becomes much harder when the observations can be associated with a given degree of membership to an underlying population and the outlier detection should be generalized to operate over fuzzy data. We present a new approach for outlier that operates over fuzzy data using two inter-related algorithms. Due to the way outliers enter the observation sample, they may be of various order of magnitude. To account for this, we divided the outlier detection procedure into cycles. Furthermore, each cycle consists of two phases. In Phase 1 we apply a leave-one-out procedure for each nonoutlier in the data set. In Phase 2, all previously declared outliers are subjected to Benjamini-Hochberg step-up multiple testing procedure controlling the false discovery rate, and the non-confirmed outliers can return to the data set. Finally, we construct a regression model over the resulting set of non-outliers. In that way we ensure that a reliable and high-quality regression model is obtained in Phase 1 because the leaveone-out procedure comparatively easily purges the dubious observations due to the single comparison testing. In the same time, the confirmation of the outlier status in relation to the newly obtained high-quality regression model is much harder due to the multiple testing procedure applied hence only the true outliers remain outside the data sample. The two phases in each cycle are a good trade-off between the desire to construct a high-quality model (i.e. over informative data points) and the desire to use as much data points as possible (thus leaving as much observations as possible in the data sample). The number of cycles is user-defined, but the procedures can finalize the analysis in case a cycle with no new outliers is detected. We offer one illustrative example and two other practical case studies (from real-life thrombosis studies) that demonstrate the application and strengths of our algorithms. In the concluding section, we discuss several limitations of our approach and also offer directions for future research. Keywords: regression analysis, leave-one-out method, degree of membership, multiple testing, Benjamini-Hochberg step-up multiple testing, false-discovery rate Highlights: -We develop algorithms for outlier rejection over fuzzy samples using weighted least squares that operate in a given number of cycles -Each cycle has two phases -use single testing leave-one-out procedure for initial purging of data, then confirm the previous outlier status with multiple testing -We offer one illustrative example and two examples from a case study in thrombosis research to show the strength of our cycle-based approach

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Study of linear regression based on least squares and fuzzy least absolutes deviations and its application in geography

Cited by 8 publications

References 6 publications

Research on the Selection of the most Popular Product Categories in TikTok based on Linear Regression

Research on the Selection of the most Popular Product Categories in TikTok based on Linear Regression

Machine learning‐based regression models for predicting signal quality of dense wavelength division multiplexing (DWDM) optical communication network

Outlier Detection Algorithms Over Fuzzy Data with Weighted Least Squares

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