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Cognitive Internet of Things
Published in J P Patra, Gurudatta Verma, Cognitive IoT, 2022
Multiple Regression: Simple linear regression model has a continuous outcome and one predictor, whereas a multiple linear regression model has a continuous outcome and multiple predictors (continuous or categorical). A simple linear regression model would have the form: y=α+xβ+ε
Regression II: linear regression
Published in Tiffany Timbers, Trevor Campbell, Melissa Lee, Data Science, 2022
Tiffany Timbers, Trevor Campbell, Melissa Lee
Simple linear regression chooses the straight line of best fit by choosing the line that minimizes the average squared vertical distance between itself and each of the observed data points in the training data. Figure 8.4 illustrates these vertical distances as red lines. Finally, to assess the predictive accuracy of a simple linear regression model, we use RMSPE—the same measure of predictive performance we used with KNN regression.
Data Analysis with Regression Models, Advanced Regression Models, and Machine Learning through Optimization
Published in William P. Fox, Nonlinear Optimization, 2020
We use diagnostic methods to identify violations of the assumption to determine whether variances are too large or too small include plots of residuals versus the mean at different levels of the predictor variable. Recall that in the case of normal linear regression, diagnostics of the model used plots of residuals against fits (fitted values). This implies that some of the same diagnostics can be used in the case of Poisson regression. We will use the residual or deviation plot, deviations versus the model to look for patterns as our main diagnostic method.
Estimation of shear strength parameter of silty sand from SPT-N60 using machine learning models
Published in Geomechanics and Geoengineering, 2022
A. Hossain, T. Alam, S. Barua, M. R. Rahman
Linear regression is a linear approach to model the relationship between a dependent variable and one or more independent variables. For more than one individual variable, the procedure is called multiple linear regression (Freedman 2009). Equation 8 provides the general expression of MLR where s are the attributes, s are the weights, and is the predictor. For a set of data, infinite combinations of weights are possible. The combination which produces the minimum sum of the square of residuals (SSR) is selected. SSR is calculated using Equation 9 where is the actual points and is the predicted values using Equation 8.
Testbed Implementation of a Scalable ARIMA Model for Spectrum Estimation in Cognitive Radio-A Null Hypothesis Approach
Published in IETE Journal of Research, 2021
Debashis Chakraborty, Salil Kumar Sanyal
Residual analysis is used to assess the appropriateness or a measure of fitments of a linear regression model by defining residuals and examining the residual plot graphs. Residual (e) refers to the deviation between the observed values (y) vs. predicted value . Every data point has one residual value and we can plot residuals that could be plotted for the entire number of samples (N). Therefore, Residual analysis is performed in two steps aiming to find out residual correlation, known as Whiteness Test and to find a past correlation, known as Independence Test. Interestingly, the residual test can be performed in both the time and frequency domains. In the time domain, the autocorrelation could be evaluated for all the output samples, whereas cross-correlation is computed between each input sample and corresponding residuals.
Static creep of modified superpave asphalt concrete mixtures using crumb tire rubber, microcrystalline synthetic wax, and nano-silica
Published in International Journal of Pavement Engineering, 2021
Aslam Ali Al-Omari, Mohammad Ali Khasawneh, Taleb Mustafa Al-Rousan, Saja Faris Al-Theeb
Regression is a statistical technique that is used to predict a variable (dependent variable) of interest from several variables (independent variables), and it can be divided into linear and nonlinear regression. Linear regression could be either simple linear regression technique with one independent variable, used to predict the response variable, or multiple linear regression technique with two or more independent variables. There are several assumptions required to run linear regression analysis: linearity between independent and response variables, normality of error distribution, homoscedasticity (equal variances of the errors), and independence between residuals. In this study, multiple linear regression was carried out with 95% confidence level (significance level; α = 0.05) using Minitab software (version 17) to establish models for the prediction of accumulated micro-strain, creep stiffness modulus, and steady state creep slope as a function of the tested variables; Temp, CE, and MT. The MT variable was chosen to be a dummy variable in the analysis.