Simple linear regression and the method of least squares

1977 ◽  
pp. 255-274 ◽  
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Simple Linear Regression ◽  
Method Of Least Squares

On Consistency of Estimators in Simple Linear Regression Models

2002 ◽  
Vol 53 (3-4) ◽  
pp. 261-264 ◽  
Author(s):  
Anindya Roy ◽  
Thomas I. Seidman
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Regression Models ◽  
Sufficient Condition ◽  
Simple Linear Regression ◽  
Linear Regression Models ◽  
Least Squares Estimators

We derive a property of real sequences which can be used to provide a natural sufficient condition for the consistency of the least squares estimators of slope and intercept for a simple linear regression models.

scholarly journals On Least Squares Estimation in a Simple Linear Regression Model with Periodically Correlated Errors: A Cautionary Note

2016 ◽  
Vol 41 (3) ◽  
Author(s):  
Abdullah A. Smadi ◽  
Nour H. Abu-Afouna
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Least Squares ◽  
Autoregressive Model ◽  
Relative Efficiency ◽  
Generalized Least Squares ◽  
Correlated Errors ◽  
Simple Linear Regression ◽  
Simple Regression Model ◽  
Autocorrelated Errors

In this research the simple linear regression (SLR) model with autocorrelated errors is considered. Traditionally, correlated errors are assumed to follow the autoregressive model of order one (AR(1)). Beside this model we will also study the SLR model with errors following the periodic autoregressive model of order one (PAR(1)). The later model is useful for modeling periodically autocorrelated errors. In particular, it is expected to beuseful when the data are seasonal. We investigate the properties of the least squares estimators of the parameters of the simple regression model when the errors are autocorrelated and for various models. In particular, the relative efficiency of those estimates are obtained and compared for the white noise, AR(1) and PAR(1) models. Also, the generalized least squares estimates for the SLR with PAR(1) errors are derived. The relative efficiency of the intercept and slope estimates based on both methods is investigated via Monte-Carlo simulation. An application on real data set is also provided.It should be emphasized that once there are sufficient evidences that errors are autocorrelated then the type of this autocorrelation should be uncovered. Then estimates of model’s parameters should be obtained accordingly, using some method like the generalized least squares but not the ordinary least squares.

scholarly journals Regresión lineal de mínimos cuadrados para la carga y descarga de un condensador

2015 ◽  
Vol 6 (1) ◽  
pp. 34
Author(s):  
José Libardo Santiago-Angarita ◽  
Olga Lucy Rincón-Leal
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Current Source ◽  
Mathematical Software ◽  
Method Of Least Squares ◽  
In Series ◽  
Experimental Errors ◽  
Loading And Unloading ◽  
Lineal Regression ◽  
A Current

ResumenEl objetivo es determinar experimentalmente el proceso de carga y descarga de un condensador estando conectado en serie con una resistencia y una fuente de corriente  continua, utilizando para ello los métodos numéricos en el proceso de ajuste de curvas a través de la regresión lineal de mínimos cuadrados, y con ayuda del software matemático Matlab se realizó la construcción de las respectivas curvas. Se estableció una relación entre el voltaje y el tiempo, formándose así una gráfica exponencial; se dedujeron las relaciones existentes y el comportamiento del fenómeno, dadas las ecuaciones y con la ayuda de lasegunda Ley de Kirchhoff; se determinaron las contantes de tiempo utilizando el método de regresión lineal de mínimos cuadrados, encontrándose un error experimental del 5 % con respecto a la constate de tiempo teórica RC.Palabras Claves: Condensador, resistencia y regresión lineal.ABSTRACTThe objective is to determine experimentally S. Process Loading and unloading of un capacitor being connected in series with a resistor and a current source , using para This numerical methods in the process of adjustment curves Through linear regression Least Squares , with the help of mathematical software Matlab building the respective curves was performed.A relationship between the voltage and time, thus forming exponential graph A is established; the relationships and the behavior of the phenomenon were deducted, given the equations and with the help of the Second Law of Kirchhoff; the Time constants were determined using the method of least squares linear regression, experimental errors UN meeting 5% with respect to the I Theoretical RC time constant.Keywords: Condenser, resistance and lineal regression.

scholarly journals IMPACT OF TRANSFER PRICING ON FOREIGN DIRECT INVESTMENT IN ROMANIA

2021 ◽  
Vol 14(63) (2) ◽  
pp. 141-150
Author(s):  
Ileana Tache ◽  
◽  
Mihaela Paraschiva Luca ◽  
Keyword(s):  
Foreign Direct Investment ◽  
Linear Regression ◽  
Least Squares ◽  
Direct Investment ◽  
Least Squares Method ◽  
Transfer Pricing ◽  
Point Of View ◽  
Simple Linear Regression ◽  
Statistical Point ◽  
The Impact

The purpose of the study presented in this paper is to analyse the impact of transfer pricing on foreign direct investment (FDI) in Romania. For attaining this goal, we performed a simple linear regression by the least squares method to study the impact of adjustments of tax obligations in the field of transfer pricing on foreign direct investment in the period 2011-2019.We have proved, from a statistical point of view, that there is a relationship between foreign direct investment and adjustments to tax liabilities resulting from transfer pricing

scholarly journals Prediction of Lard in Palm Olein Oil Using Simple Linear Regression (SLR), Multiple Linear Regression (MLR), and Partial Least Squares Regression (PLSR) Based on Fourier-Transform Infrared (FTIR)

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Siong Fong Sim ◽  
Min Xuan Laura Chai ◽  
Amelia Laccy Jeffrey Kimura
Keyword(s):  
Fourier Transform ◽  
Linear Regression ◽  
Multiple Linear Regression ◽  
Least Squares ◽  
Partial Least Squares ◽  
Partial Least Squares Regression ◽  
Palm Olein ◽  
Least Squares Regression ◽  
Simple Linear Regression ◽  
Olein Oil

Fourier-transform infrared (FTIR) offers the advantages of rapid analysis with minimal sample preparation. FTIR in combination with multivariate approach, particularly partial least squares regression (PLSR), has been widely used for adulterant analysis. Limited study has been done to compare PLSR with other regression strategies. In this paper, we apply simple linear regression (SLR), multiple linear regression (MLR), and PLSR for prediction of lard in palm olein oil. Pure palm olein oil was adulterated with lard at different concentrations and subjected to analysis with FTIR. The marker bands distinguishing lard and palm olein oil were determined using Fisher’s weights. The marker regions were then subjected to regression analysis with the models verified based on 100 training/test sets. The prediction performance was measured based on the percentage root mean square error (%RMSE). The absorption bands at 3006 cm−1, 2852 cm−1, 1117 cm−1, 1236 cm−1, and 1159 cm−1 were identified as the marker bands. The bands at 3006 and 1117 cm−1 were found with satisfactory predictive ability, with PLSR demonstrating better prediction yielding %RMSE of 16.03 and 13.26%, respectively.

Statistical modeling of the novel COVID-19 epidemic in Iraq

2021 ◽  
Vol 10 (s1) ◽  
Author(s):  
Ban Ghanim Al-Ani
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Nonlinear Regression ◽  
Least Squares Method ◽  
Growth Models ◽  
Nonlinear Least Squares ◽  
Weibull Model ◽  
Simple Linear Regression ◽  
Initial Values ◽  
Nonlinear Least Squares Method

Abstract Objectives This study aimed to apply three of the most important nonlinear growth models (Gompertz, Richards, and Weibull) to study the daily cumulative number of COVID-19 cases in Iraq during the period from 13th of March, 2020 to 22nd of July, 2020. Methods Using the nonlinear least squares method, the three growth models were estimated in addition to calculating some related measures in this study using the “nonlinear regression” tool available in Minitab-17, and the initial values of the parameters were deduced from the transformation to the simple linear regression equation. Comparison of these models was made using some statistics (F-test, AIC, BIC, AICc and WIC). Results The results indicate that the Weibull model is the best adequate model for studying the cumulative daily number of COVID-19 cases in Iraq according to some criteria such as having the highest F and lowest values for RMSE, bias, MAE, AIC, BIC, AICc and WIC with no any violations of the assumptions for the model’s residuals (independent, normal distribution and homogeneity variance). The overall model test and tests of the estimated parameters showed that the Weibull model was statistically significant for describing the study data. Conclusions From the Weibull model predictions, the number of cumulative confirmed cases of novel coronavirus in Iraq will increase by a range of 101,396 (95% PI: 99,989 to 102,923) to 114,907 (95% PI: 112,251 to 117,566) in the next 24 days (23rd of July to 15th of August 15, 2020). From the inflection points in the Weibull curve, the peak date when the growth rate will be maximum, is 7th of July, 2020, and at this time the daily cumulative cases become 67,338. Using the nonlinear least squares method, the models were estimated and some related measures were calculated in this study using the “nonlinear regression” tool available in Minitab-17, and the initial values of the parameters were obtained from the transformation to the simple linear regression model.

scholarly journals Gender Pay Gap in the Czech Economy with Accent on ICT Professionals

2021 ◽  
Author(s):  
Lea Nedomová ◽  
Petr Doucek
Keyword(s):  
Regression Analysis ◽  
Czech Republic ◽  
Linear Regression ◽  
Least Squares ◽  
Gender Pay Gap ◽  
Method Of Least Squares ◽  
Pay Gap ◽  
The Czech Republic ◽  
The Subject ◽  
Level Of Significance

The subject of our article is a comparison of the level and development of the gender pay gap between selected EU countries (especially the V4 countries and other selected countries such as Austria and Slovenia) for the period 2009 - 2019. The analysis for the Czech Republic will be then supplemented by a comparison with the development of the gender pay gap in the economy and in ICT Professionals. To approximate the development of wages and GDP, we used the method of linear regression together with the method of least squares. All regression analysis calculations are performed at the 5% level of significance.

Transforming the Method of Least Squares to the Dataflow Paradigm

2021 ◽  
pp. 114-121
Author(s):  
Ilir Murturi
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Linear Algebra ◽  
Control Flow ◽  
Mathematical Statistics ◽  
Regression Equations ◽  
Method Of Least Squares ◽  
The Given ◽  
The Relationship ◽  
Best Fit

In mathematical statistics, an interesting and common problem is finding the best linear or non-linear regression equations that express the relationship between variables or data. The method of least squares (MLS) represents one of the oldest procedures among multiple techniques to determine the best fit line to the given data through simple calculus and linear algebra. Notably, numerous approaches have been proposed to compute the least-squares. However, the proposed methods are based on the control flow paradigm. As a result, this chapter presents the MLS transformation from control flow logic to the dataflow paradigm. Moreover, this chapter shows each step of the transformation, and the final kernel code is presented.

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