a multiple linear regression model

The link between the indices of twelve atmospheric teleconnection patterns (mostly Northern Hemispheric) and gridded European temperature data is investigated by means of multiple linear regression models for each grid cell and month. Furthermore index-specific signals are calculated to estimate the contribution to temperature anomalies caused by each individual teleconnection pattern. To this extent, an observational product of monthly mean temperature (E-OBS), as well as monthly time series of teleconnection indices (CPC, NOAA) for the period 1951–2010 are evaluated. The stepwise regression approach is used to build grid cell based models for each month on the basis of the five most important teleconnection indices (NAO, EA, EAWR, SCAND, POLEUR), which are motivated by an exploratory correlation analysis. The temperature links are dominated by NAO and EA in Northern, Western, Central and South Western Europe, by EAWR during summer/autumn in Russia/Fenno-Scandia and by SCAND in Russia/Northern Europe; POLEUR shows minor effects only. In comparison to the climatological forecast, the presented linear regression models improve the temperature modelling by 30–40 % with better results in winter and spring. They can be used to model the spatial distribution and structure of observed temperature anomalies, where two to three patterns are the main contributors. As an example the estimated temperature signals induced by the teleconnection indices is shown for February 2010

Multiple Linear Regression Applications in Real Estate Pricing

In this paper, we attempt to predict the price of a real estate individual homes sold in North West Indiana based on the individual homes sold in 2014. The data/information is collected from realtor.com. The purpose of this paper is to predict the price of individual homes sold based on multiple regression model and also utilize SAS forecasting model and software. We also determine the factors influencing housing prices and to what extent they affect the price. Independent variables such square footage, number of bathrooms, and whether there is a finished basement,. and whether there is brick front or not and the type of home: Colonial, Contemporary or Tudor. How much does each type of home (Colonial, Contemporary, Tudor) add to the price of the real estate

Quantum Circuit Design Methodology for Multiple Linear Regression

Multiple linear regression assumes an imperative role in supervised machine learning. In 2009, Harrow et al. [Phys. Rev. Lett. 103, 150502 (2009)] showed that their HHL algorithm can be used to sample the solution of a linear system $\mathbf{Ax=b}$ exponentially faster than any existing classical algorithm, with some manageable caveats. The entire field of quantum machine learning gained considerable traction after the discovery of this celebrated algorithm. However, effective practical applications and experimental implementations of HHL are still sparse in the literature. Here, we demonstrate a potential practical utility of HHL, in the context of regression analysis, using the remarkable fact that there exists a natural reduction of any multiple linear regression problem to an equivalent linear systems problem. We put forward a $7$-qubit quantum circuit design, motivated from an earlier work by Cao et al. [Mol. Phys. 110, 1675 (2012)], to solve a $3$-variable regression problem, using only elementary quantum gates. We also implement the Group Leaders Optimization Algorithm (GLOA) [Mol. Phys. 109 (5), 761 (2011)] and elaborate on the advantages of using such stochastic algorithms in creating low-cost circuit approximations for the Hamiltonian simulation. We believe that this application of GLOA and similar stochastic algorithms in circuit approximation will boost time- and cost-efficient circuit designing for various quantum machine learning protocols. Further, we discuss our Qiskit simulation and explore certain generalizations to the circuit design.Comment: 14 pages, 7 figure

A Mathematical Programming Approach for Integrated Multiple Linear Regression Subset Selection and Validation

Subset selection for multiple linear regression aims to construct a regression model that minimizes errors by selecting a small number of explanatory variables. Once a model is built, various statistical tests and diagnostics are conducted to validate the model and to determine whether the regression assumptions are met. Most traditional approaches require human decisions at this step. For example, the user adding or removing a variable until a satisfactory model is obtained. However, this trial-and-error strategy cannot guarantee that a subset that minimizes the errors while satisfying all regression assumptions will be found. In this paper, we propose a fully automated model building procedure for multiple linear regression subset selection that integrates model building and validation based on mathematical programming. The proposed model minimizes mean squared errors while ensuring that the majority of the important regression assumptions are met. We also propose an efficient constraint to approximate the constraint for the coefficient t-test. When no subset satisfies all of the considered regression assumptions, our model provides an alternative subset that satisfies most of these assumptions. Computational results show that our model yields better solutions (i.e., satisfying more regression assumptions) compared to the state-of-the-art benchmark models while maintaining similar explanatory power

On eigenvalues, case deletion and extremes in regression

This paper presents an approximation for assessing the effect of deleting an observation in the eigenvalues of the correlation matrix of a multiple linear regression modelo Applications in connection with the detection of collinearityinfluential observations are explored

Multiple linear regression based models for solar collectors

Mathematical modelling is the theoretically established tool to investigate and develop solar thermal collectors as environmentally friendly technological heat producers. In the present survey, recent multiple linear regression (MLR) based collector models are presented and compared with one another and with a physically-based model, used successfully in many applications, by means of measured data. The MLR-based models, called MLR model, SMLR model and IMLR model, prove to be rather precise with a modelling error of 4.6%, 8.0% and 4.1%, respectively, which means that all MLR-based models are more or nearly the same accurate as the well- ried physically-based model. The SMLR model is the most, while the IMLR model is the least easy-to-apply MLR-based model with the lowest and the highest computational demand, respectively. Nevertheless, all MLR-based models have lower computational demand than the physically-based model. Accordingly, the MLR-based models are suggested for fast but accurate collector modelling