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The Importance of the Regression Coefficient
Published in Bruce Ratner, Statistical and Machine-Learning Data Mining, 2017
This answer is correct only when the predictor variables are uncorrelated, a rare occurrence in most models. With uncorrelated predictor variables in a regression model, there is a rank order correspondence between the magnitude of the standardized coefficient and reduction in prediction error. Thus, the magnitude of the standardized coefficient can rank the predictor variables in order of most to least important. Unfortunately, there is no rank order correspondence with correlated predictor variables. Thus, the magnitude of the standardized coefficient of correlated predictor variables cannot rank the variables regarding predictive importance. The proof of these facts is beyond the scope of this chapter [4].
Aviation Forecasting and Regression Analysis
Published in Bijan Vasigh, Ken Fleming, Thomas Tacker, Introduction to Air Transport Economics, 2018
Bijan Vasigh, Ken Fleming, Thomas Tacker
The third major table contained in all regression output is a table of coefficients. This is displayed for the demand forecast from Orlando to Los Angeles in Table 10.23. The coefficients table allows the researcher to construct a linear equation that can be used for forecasting, and it also determines whether the individual variables are statistically significant. The first column of the coefficients table lists all the independent variables used in the analysis, plus the constant. The constant term is usually interpreted as the value of the dependent variable when all the other independent variables are set to zero. Columns 2 and 4 both display values for the coefficients. The standardized values (column 4) are generally used to compare the respective size of the impacts of the independent variables on the dependent variable. This is accomplished by calculating them in standardized units—that is, the standardized coefficient is the unstandardized value of the coefficient multiplied by the ratio of the standard deviation of the independent variable to the standard deviation of the dependent variable. Therefore, a standardized coefficient of 1.14, as the one for GDP, means that a 1.0 standard deviation change in the independent variable will lead to a 1.14 standard deviation change in the dependent variable. Similar interpretations apply to the other standardized coefficients. But, since the unstandardized values are the coefficients that are directly applicable to forecasting actual values, the unstandardized beta values are the coefficients that are used in the forecast equation. However, and as a final step prior to forming a demand equation, each independent variable needs to be tested to see if it is statistically significant.
Forecasting in the air transport industry
Published in Bijan Vasigh, Ken Fleming, Thomas Tacker, Introduction to Air Transport Economics, 2018
Bijan Vasigh, Ken Fleming, Thomas Tacker
The third major table contained in all regression output is a table of coefficients. This is displayed for the demand forecast from Orlando to Los Angeles in Table 10.24. The coefficients table allows the researcher to construct a linear equation that can be used for forecasting. It also determines if the individual variables are statistically significant. The first column of the coefficients table lists all the independent variables used in the analysis plus the constant. The constant term is usually interpreted as the value of the dependent variable when all the other independent variables are set to zero. Columns two and four both display values for the coefficients. The standardized values (column four) are generally used to compare the respective size of the impacts of the independent variables on the dependent variable. This is accomplished by calculating them in standardized units; that is, the standardized coefficient is the unstandardized value of the coefficient multiplied by the ratio of the standard deviation of the independent variable to the standard deviation of the dependent variable. Therefore, a standardized coefficient of 1.14, as the one for GDP, means that a 1 standard deviation change in the independent variable will lead to a 1.14 standard deviation change in the dependent variable. Similar interpretations apply to the other standardized coefficients. But, since the unstandardized values are the coefficients that are directly applicable to forecasting actual values, the unstandardized beta values are the coefficients that are used in the forecast equation. However, and as a final step prior to forming a demand equation, each independent variable needs to be tested to see if it is statistically significant.
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
Meteorological factors select the meteorological data from 11:00 - 14:00 on the measurement day to further reduce the interference of time changes on the data. The standardized coefficient is often used to describe the relative importance of independent variables. The greater the absolute value of the standardized coefficient Beta, the greater the influence of spatial form factors on meteorological factors. The stepwise regression results of meteorological and spatial form factors are shown in Table 9, and the relationship model is shown in Table 12. According to the standardized coefficient of the model, combined with the significance level of each variable, the importance of independent variables can be arranged in the following order high to low: Ta: Ht, ADw, PSVF, ADt; v: Ht, Hs/Wr, AD; RH: PSVF, ADw, PSR.
Traffic congestion and its urban scale factors: Empirical evidence from American urban areas
Published in International Journal of Sustainable Transportation, 2022
Md. Mokhlesur Rahman, Pooya Najaf, Milton Gregory Fields, Jean-Claude Thill
Following established practice, standardized regression coefficients are used to determine the relative strength of the effect of any variable on any other variable in the SEM. In particular, a higher value of the coefficient indicates a stronger effect of the independent variable on the dependent variables compared with other covariates. These standardized coefficients have standard deviation as their units to compare and determine the relative influence of variables. Thus, this standardized coefficient indicates how a unit change in the independent variable (i.e., 1 standard deviation) increases or decreases the dependent variable.
Parametric modelling of a wire electrical discharge machining process using path analysis approach
Published in International Journal of Modelling and Simulation, 2022
Baneswar Sarker, Shankar Chakraborty
For estimating the corresponding path coefficients, MLE is selected. The pre-conditions for implementing MLE are satisfied here as all the variables are normal, while the dependent variables are continuous. For normal data, the coefficients computed by both the MLE and OLS techniques would be equal, thus equating the unstandardized estimates computed by MLE with the regression weights estimated by the OLS method. Hence, the unstandardized coefficient of any independent variable implies the quantitative change in the value of the dependent variable for a unit increase of the independent variable while maintaining the values of other independent variables as constant. These coefficients are also utilized to formulate a linear combination consisting of all the independent variables’ relationships for each dependent variable. The standardized coefficient of an independent variable, derived after dividing the product of the standard deviation of the independent variable and its unstandardized coefficient, by the standard deviation of that dependent variable, enables comparative analysis between the independent variables. The standardized coefficient signifies the change in the value of a dependent variable, in terms of its standard deviation, with one standard deviation change in the independent variable. The absolute values of the standardized coefficients can describe the influence of each independent variable on each of the dependent variables. The higher the absolute value, the more significant is the influence of an independent variable on a dependent variable. Hence, the standardized variables allow comparison on the basis of the absolute standardized coefficient values. In this paper, model construction and path relation estimation are conducted for parametric study and modelling of the said WEDM process with the help of IBM SPSS AMOS 21 Graphics software.