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Modern Predictive Analytics and Big Data Systems Engineering
Published in Anna M. Doro-on, Handbook of Systems Engineering and Risk Management in Control Systems, Communication, Space Technology, Missile, Security and Defense Operations, 2023
When we use OLS regression, we estimate regression coefficients so that they minimize the sum of the squared residuals, where residuals are differences between the observed and predicted response values (Miller 2015). The main consideration of linear regression is concerning the dependent variable y that can be estimated by a linear composition of the independent variables x and considering β is a p-dimensional vector of unknown constants: y=βx+εE(ε|x)=0
Exchange Rate Modeling and Decision Support
Published in Yi Chen, Yun Li, Computational Intelligence Assisted Design, 2018
In this chapter, the Mendel-GA will be applied to the studies of empirical analysis on exchange rate determination, which can provide an evolutionary and computational method for the exchange rate determination problem. Specifically, this work attempts to compare the performance of the Mendel-GA and traditional estimation methods, for instance, ordinary least square (OLS) and linear least squares (LS) estimation. OLS and LS are methods for estimating the unknown parameters in a linear regression model. These methods minimize the sum of squared distances between the observed responses in the data set and the responses predicted by the linear approximation. Compared with OLS and LS, the Mendel-GA, through the evolutionary process, can address linear and nonlinear models with higher complexity and can be used as an active optimization solver for switching from one prediction model to another.
Data Analysis
Published in Marian (Editor-in-Chief) Muste, Dennis A. Lyn, David M. Admiraal, Robert Ettema, Vladimir Nikora, Marcelo H. Garcia, Experimental Hydraulics: Methods, Instrumentation, Data Processing and Management, 2017
Marian (Editor-in-Chief) Muste, Dennis A. Lyn, David M. Admiraal, Robert Ettema, Vladimir Nikora, Marcelo H. Garcia
The residuals, ei’s, form the basis for the determination of the bk’s, which are obtained by minimizing a measure of fit. The most common method is the ordinary least squares (OLS) which minimizes the sum of the squared residuals, ∑iei2. Under certain standard assumptions, OLS has desirable statistical properties such as the so-called best linear unbiased estimate or BLUE. Ryan (2009) points out that the BLUE characteristic will not apply for OLS applied to an incorrect model. As will be seen in the discussion of Bayesian linear regression (Section 6.7.1, Volume I), OLS can also be justified from a maximum likelihood argument. Criteria other than OLS are available (Ryan, 2009), mainly so as to decrease sensitivity to outliers (robust regression) and to address the problem of highly correlated regressors also known as multicollinearity (e.g., through ridge regression). In the machine learning context, ridge regression is viewed as an example of a regularization or shrinkage technique that seeks a smoother fit less sensitive to noisy data through a measure of fit (other than OLS) that penalizes large values of bk’s.
Fitness for duty prediction model for bus driver of batik solo trans based on physical, mental, and work aspects
Published in Cogent Engineering, 2022
Bambang Suhardi, Anisa Rosyidasari, Rahmaniyah Dwi Astuti, Iksan Adiasa
A correlation test is used to find out the correlation between variables. These variables included age, weight, height, sleep duration, sleep quality, cigarette consumption, caffeine consumption, shift, PVT value, VAS, KSS, as well as whether the driver was fit or not. The logistic regression test aimed to know whether the dependent variable in the form of driver’s job readiness based on physical tests can be predicted using the independent variable. Logistic regression is an approach to making predictive models such as linear regression, commonly referred to as Ordinary Least Squares (OLS) regression (Menard, 2000). Generally, the dependent variable has been marked with the letter Y, while the independent variable was the letter X. Algebraic equation models such as OLS that we usually use are as follows (Hosmer et al., 2013):
Trip chaining of bicycle and car commuters: an empirical analysis of detours to secondary activities
Published in Transportmetrica A: Transport Science, 2022
Florian Schneider, Winnie Daamen, Serge Hoogendoorn
The model performance was assessed using R squared as a simple measure of goodness of fit. Indicating how well a postulated model fits the data, the R squared is a standard statistic of OLS models. Very recently, Gelman et al. (2019) defined a similar measure for Bayesian regression models. Similarly to the conventional R squared, this Bayesian R squared can be considered as the part of the variance that is explained by the postulated model. We calculated the Bayesian R squared using the bayes_R2 function from the R rstanarm package. Both R squared values will be provided in the results section. To determine the effects of all main and interaction effects, four models were estimated in which we omitted different categories of each categorical variable (see Table 1). This entails the use of four different design matrices to . In model 1, for instance, the dummy variables for the main effects of bicycle, grocery, older than 65 years, female, suburban/rural and evening were omitted. Accordingly, model 2 estimated these main effects by omitting a complementary category of the respective categorical variables. As interaction terms could only be calculated for the travel mode that is included in the respective model, model 3 and 4 were necessary to estimate the missing interaction effects.
Quantification of health and environmental risks due to radionuclides in limestone mining regions of Ariyalur, South India
Published in Human and Ecological Risk Assessment: An International Journal, 2022
E. Kumar, T. Subramani, Peiyue Li, D. Karunanidhi
Ordinary least squares (OLS) are one of the linear least-squares methods to establish a linear regression of the relationship between a response variable and multiple explanatory variables. It is expressed in the form given by Eq. (8) (Ciotcoli et al. 2017; He et al. 2020; Li et al. 2021; Wang et al. 2020) where y is the response variable and x1, x2…,xn are the multiple explanatory variables. λi are the coefficients variables computed by the spatial regression tool. It is used to define or represent the strength variables and the type of relationship between x and y variables. OLS is named for global regression of the data (Ciotcoli et al. 2017).