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Generalized Regression Penalty against Complexity
Published in Chong Ho Alex Yu, Data Mining and Exploration, 2022
One common approach to selecting a subset of variables is stepwise regression, which examines the impact of each variable to the model step by step. The variable that cannot contribute much to the variance explained is then thrown out. There are several versions of stepwise regression, such as forward selection, backward elimination, bi-directional, and all-subset. In forward selection, the algorithm starts with a null model, and then each predictor is added into the model one by one. Whatever is found to be significant is kept, and the unimportant one is excluded. Backward elimination is the converse of forward selection. After all variables are input, non-significant variables are removed one by one. In the bi-directional variant, variables go in and out at every step so that the algorithm can evaluate the outcomes by examining many possible combinations. All-subset regression is an extension of the bi-directional method. However, unlike its bi-directional peer that takes only a few combinations into consideration, all-subset regression evaluates all possible combinations of all predictors.
Linear Regression
Published in Simon Washington, Matthew Karlaftis, Fred Mannering, Panagiotis Anastasopoulos, Statistical and Econometric Methods for Transportation Data Analysis, 2020
Simon Washington, Matthew Karlaftis, Fred Mannering, Panagiotis Anastasopoulos
Stepwise regression is a procedure that relies on a user-selected criterion, such as R-squared, adjusted R-squared, F-ratio, or other GOF measures, to select a “best” model among competing models generated by the procedure. Stepwise regression procedures can either be backward or forward. Backward stepwise regression starts by comparing models with large numbers of independent variables (as many as, say, 30 or 40) and sequentially removing one independent variable at each step. The variable removed is the one that contributes least to the GOF criterion. The procedure iterates until a regression model is obtained in the final step. The user can then compare “best” models of different sizes in the computer printout. As one would expect, forward stepwise begins with a simple regression model and sequentially grows the regression by adding the variable with the largest contribution to the GOF criterion.
Simple and Multiple Linear Regression
Published in Alan R. Jones, Best Fit Lines and Curves, and Some Mathe-Magical Transformations, 2018
The really good news is that this is not a different kind of Regression technique to tax our brain cells. Stepwise Regression is a recognised procedure used with Multi-Linear Regression that takes incremental steps in selecting appropriate predictor x-variables or drivers from a range of potential ones. Essentially, there are two procedures, but the principles are the same; it’s more a question of the direction of approach like Top-down or Bottom-up Estimating. In this case we have: Forward Selection, which progressively adds variables to the mix until no further improvement can be made to the Regression Best Fit that is statistically supportable.Backward Elimination, which throws everything into the pot and removes one at a time until no further improvement can be made to the Regression Best Fit that is statistically supportable.
Research on the spatial form effects of thermal comfort on urban waterfront trails in summer – a case study of West Lake in Hangzhou, China
Published in Journal of Asian Architecture and Building Engineering, 2023
Yi Mei, Junke Lu, Dan Han, Lili Xu, Yuhang Han
Spearman correlation analysis initially provides insights into the correlation between variables. However, it has a limitation in that it does not account for collinearity or mutual influence among variables. In order to further investigate the predictive capabilities of the variables, we employed stepwise regression analysis. Stepwise regression is a statistical technique that systematically selects the most significant predictors to construct a regression model. This iterative process aids in identifying the variables that exert the greatest impact on the observed variation in the dependent variable. For the stepwise regression analysis, we employed the backward method to assess the meteorological factors and spatial form factors of the seven spaces. This approach allowed us to determine the parameters that had the most significant impact on the meteorological factors while minimizing the presence of multicollinearity. By examining the standardized coefficients within the model, we were able to determine the relative importance of the parameters influencing the thermal comfort of the waterfront trails in each season. The thermal comfort of the waterfront trails in each season was determined.
Revealing population flow patterns in the Sichuan-Chongqing region, China, during the COVID-19 epidemic in 2020
Published in Annals of GIS, 2022
Jingwei Shen, Zhongyu Huang, Wei Zhou, Dongzhe Zhao
Regression analysis is widely used to infer the relationship between a dependent variable and a series of independent variables. To exclude independent variables that have no significant influence on dependent variables, stepwise regression analysis is intended to be used. Unlike conventional regression analysis that considers all independent variables, stepwise regression is the step-by-step iterative construction of a regression model that involves the selection of independent variables to be used in a final model. Therefore, stepwise regression is able to provide a good explanation of the outcome, and we chose stepwise regression for the analysis of factors affecting regional population flow intensity in this study. R2 and RMSE are widely used indicators for evaluating regression models. Therefore, the performance of the stepwise regression is evaluated by using RMSE and R2 in the article.
Development of subgrade Mr constitutive models based on physical soil properties
Published in Road Materials and Pavement Design, 2018
Ayan Mehrotra, Murad Abu-Farsakh, Kevin Gaspard
Stepwise regression analysis is a popular variable selection technique intended to select the “best” subset of predictor variables. However, the procedures of stepwise regression do not directly account for the final objective of the model selection process. The final objective in this study is selecting an optimal model for each regression coefficient that utilises appropriate soil physical properties that are directly related to the response of the regression coefficient. Stepwise regression analysis can be prone to over-fitting of the models to the input data and/or utilising too many or too few dependent variables for reliable and accurate prediction of the independent variables (Shtatland, Cain, & Barton, 2001). To combat some of the drawbacks of stepwise regression while also keeping the objective of the variable selection process in mind, several different statistical evaluation criteria were used in conjunction with stepwise regression to create a purposeful statistical model with the ability to predict regression coefficients k1, k2, and k3 based on soil physical properties.