Abstract
This chapter deals with statistical methods, and more particularly with simple and multiple regression analysis, which are the basic tool when correlating transport demand to factors (such as time, cost, etc.) affecting it. After an overview of fundamentals of statistics such as terms, measures, hypothesis testing, probability distribution, and stationarity, the mathematical expression of the simple and multiple linear regression and the estimation of the various regression coefficients and the error term with the use of the ordinary least squares method are presented. Pearson correlation coefficient, coefficient of determination, and adjusted coefficient of determination as measures for the degree of correlation between one dependent and one or more independent variable(s) are analyzed. Tests of the significance of the coefficients of a regression analysis (Student's t-test and F-test) are presented afterward. Multicollinearity (correlation between independent variables), its detection, and techniques of removal are identified. The various characteristics and properties of residuals of a linear regression are surveyed with the help of the appropriate tests: probability distribution (skewness and kurtosis, Jarque–Bera test), influence of residuals and determination of outliers (Cook's distance), existence or not of serial correlation in the residuals (Durbin–Watson test, Durbin's h-test, Breusch–Godfrey Lagrange Multiplier test, Ljung–Box test). The various tests for the detection of heteroscedasticity in a regression analysis are analyzed: Breusch–Pagan test, Glesjer test, Harvey–Godfrey test, White test, autoregressive conditional heteroscedasticity test. Next, the various criteria for the evaluation of the forecasting accuracy of calibrated models are categorized, among them the Theil's inequality coefficient. All the above analysis, methods, tests, and criteria are extensively put into practice in a specific example of multiple linear regression analysis for the construction of an econometric model for transport demand.
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