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Publication# Linear regression analysis of regional mean speed of Athens city network using drone data: A multi-modal approach

Abstract

The work proposes a multi-modal regional mean speed regression analysis for the city network of Athens, Greece. The dataset from pNUEMA experiment is used in the present context. Accumulations and mean speeds of different modes are estimated and compared to each other. Besides, the mean running speeds of all modes are also computed and compared. The mean speed of each mode is assumed to be a linear combination of accumulations of all modes and regression analysis is performed. Ordinary Least Squares (OLS) and Partial Least Squares (PLS) methods are used in the current work. It is noticed that multicollinearity between different modes is weak in the current dataset. The quality of multi-modal regression fits is compared to the uni-modal ones, where the mean speed of a given mode is assumed to be a function of the accumulation of that mode only. It is concluded that multi-modal regression fits outperform their uni-modal counterparts in terms of R2 and Root Mean Squared Relative Error (RMSRE).

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Linear regression

In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.

Regression analysis

In statistical modeling, regression analysis is a set of statistical processes for estimating the relationships between a dependent variable (often called the 'outcome' or 'response' variable, or a 'label' in machine learning parlance) and one or more independent variables (often called 'predictors', 'covariates', 'explanatory variables' or 'features'). The most common form of regression analysis is linear regression, in which one finds the line (or a more complex linear combination) that most closely fits the data according to a specific mathematical criterion.

Segmented regression

Segmented regression, also known as piecewise regression or broken-stick regression, is a method in regression analysis in which the independent variable is partitioned into intervals and a separate line segment is fit to each interval. Segmented regression analysis can also be performed on multivariate data by partitioning the various independent variables. Segmented regression is useful when the independent variables, clustered into different groups, exhibit different relationships between the variables in these regions.

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