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Supervised Learning
Published in Peter Wlodarczak, Machine Learning and its Applications, 2019
Polynomial regression can be used if there is a nonlinear relationship between the variables x and y. The relationship between the dependent and the independent variable y and x is modeled using a nth degree polynomial. For one single predictor x, the model can be defined as shown in equation 4.17: () yi=β0+β1x1+β2x2+…+βnxn+ε
A Comparative Study of Artificial Intelligence Models for Predicting Interior Illuminance
Published in Applied Artificial Intelligence, 2021
Maryam Arbab, Morteza Rahbar, Mojgan Arbab
The polynomial regression is a form of regression analysis that models the relationship between the independent variable x and the dependent variable y, as an nth-degree polynomial in x (Zhou and Liu 2015). In the presence of a comprehensive database, the polynomial linear regression methods can produce reasonable results concerning the correlation between the model and the analyzed information, which applies to our situation. In developing a correlation method, it is needed to build a comprehensive dataset by conducting many parametric studies and then establish a simple equation using regression analysis. Due to the immense diversity of variables and cases, adequate simulations were conducted to generate a comprehensive dataset. A total number of 5812 simulations were run to have a high-accuracy model for future energy prediction.
A framework of developing machine learning models for facility life-cycle cost analysis
Published in Building Research & Information, 2020
Xinghua Gao, Pardis Pishdad-Bozorgi
Regression analysis is a technique for modelling the relationship between variables (Montgomery, Peck, & Vining, 2012). If the relationship between the independent variables (descriptive attributes) and the dependent variable (target attribute) is linear, then the model is called a linear regression model. A model that involves only one independent variable is called a simple linear regression (SLR) model; a model that involves multiple independent variables is called a multiple linear regression (MLR) model. If the relationship between the independent variable(s), x, and the dependent variable, y, is modelled as an nth degree polynomial in x, it is called a polynomial regression model. Although the polynomial regression model is nonlinear from the data perspective, it is considered a linear machine learning model. This is because the regression function is linear in the unknown parameters that are derived from the data. Therefore, polynomial regression is considered to be a special case of MLR (Montgomery et al., 2012).
A study of rainwater tank adoption in Australian households: selecting the right size for better water-saving performance
Published in Architectural Engineering and Design Management, 2023
Xuechen Gui, Yan Xiong, Zhonghua Gou
Polynomial regression is a form of regression analysis where the relationship between the independent variable x and the dependent variable y is modelled as a polynomial of degree n with respect to x. In general, polynomial regression is considered to be a special case of multiple linear regression (Shen & Lian, 2021). The equation can be written as where y is the water score (estimated by the percentage below the benchmark of 247.5 litres per day per person, which was the average NSW residential potable water consumption pre-BASIX) and x is the average rainwater tank volume of the given water score.