The document presents an analysis of auto crash variables in Nigeria using multivariate regression techniques. The analysis finds that while the overall multiple regression model is not statistically significant, the relationships between individual variables and number of deaths are significant. Specifically, number of injured people, number of vehicles involved, and month of accident are positively correlated with number of deaths. The analysis suggests other unexplored variables may improve prediction of factors affecting auto crash fatalities.
Parametric Sensitivity Analysis of a Mathematical Model of Two Interacting Po...IOSR Journals
Experts in the mathematical modeling for two interacting technologies have observed the different contributions between the intraspecific and the interspecific coefficients in conjunction with the starting population sizes and the trading period. In this complex multi-parameter system of competing technologies which evolve over time, we have used the numerical method of mathematical norms to measure the sensitivity values of the intraspecific coefficients b and e, the starting population sizes of the two interacting technologies and the duration of trading. We have observed that the two intraspecific coefficients can be considered as most sensitive parameter while the starting populations are called least sensitive. We will expect these contributions to provide useful insights in the determination of the important parameters which drive the dynamics of the technological substitution model in the context of one-at-a-timesensitivity analysis
The document discusses using machine learning techniques to analyze traffic accident data from Porto Alegre, Brazil between 2000-2013. It compares decision trees, random forests, and logistic regression for predicting whether accidents resulted in injuries. Random forests and logistic regression performed similarly and better than decision trees. Motorcycles and accident type were highly predictive of injuries, while factors like weather had low relevance. The models could be improved with additional data on drivers, weather, and traffic conditions.
On improved estimation of population mean using qualitative auxiliary informa...Alexander Decker
This document proposes new estimators for estimating the population mean of a variable using qualitative auxiliary information. It begins with background on using auxiliary information to improve estimation. Previous related work that proposed ratio, product, and combined ratio-product estimators is reviewed.
The document then proposes four new exponential-type estimators: an exponential ratio estimator, an exponential product estimator, an exponential dual-to-ratio estimator, and an exponential ratio-dual-to-ratio estimator. Expressions for the bias and mean squared error of the proposed estimators are derived.
Finally, the document states that a numerical demonstration will be presented to illustrate the improvements of the proposed estimators over previous methods. The goal is to provide better estimators that can be useful in
The International Journal of Engineering and Science (The IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
Application of Semiparametric Non-Linear Model on Panel Data with Very Small ...IOSRJM
-This research work investigated the behaviour of a new semiparametric non-linear (SPNL) model on
a set of panel data with very small time point (T = 1). The SPNL model incorporates the relationship between
individual independent variable and unobserved heterogeneity variable. Five different estimation techniques
namely; Least Square (LS), Generalized Method of Moments (GMM), Continuously Updating (CU), Empirical
Likelihood (EL) and Exponential Tilting (ET) Estimators were employed for the estimation; for the purpose of
modelling the metrical response variable non-linearly on a set of independent variables. The performances of
these estimators on the SPNL model were examined for different parameters in the model using the Least
Square Error (LSE), Mean Absolute Error (MAE) and Median Absolute Error (MedAE) criteria at the lowest
time point (T = 1). The results showed that the ET estimator which provided the least errors of estimation is
relatively more efficient for the proposed model than any of the other estimators considered. It is therefore
recommended that the ET estimator should be employed to estimate the SPNL model for panel data with very
small time point.
A Class of Continuous Implicit Seventh-eight method for solving y’ = f(x, y) ...AI Publications
In this article, we develop a continuous implicit seventh-eight method using interpolation and collocation of the approximate solution for the solution of y’ = f(x, y) with a constant step-size. The method uses power series as the approximate solution in the derivation of the method. The independent solution was then derived by adopting block integrator. The properties of the method was investigated and found to be zero stable, consistent and convergent. The integrator was tested on numerical examples ranging from linear problem, Prothero-Robinson Oscillatory, Growth Model and Sir Model. The results show that the computed solution is closer to the exact solution and also, the absolutes errors perform better than the existing methods.
This is the comprehensive PPT on regression analysis. It covers the methods of identifying IV, DV, mediator, and moderators. How to interpreter using the parameters, R square, T-test. differentiation between linear and non-lienar regression
Parametric Sensitivity Analysis of a Mathematical Model of Two Interacting Po...IOSR Journals
Experts in the mathematical modeling for two interacting technologies have observed the different contributions between the intraspecific and the interspecific coefficients in conjunction with the starting population sizes and the trading period. In this complex multi-parameter system of competing technologies which evolve over time, we have used the numerical method of mathematical norms to measure the sensitivity values of the intraspecific coefficients b and e, the starting population sizes of the two interacting technologies and the duration of trading. We have observed that the two intraspecific coefficients can be considered as most sensitive parameter while the starting populations are called least sensitive. We will expect these contributions to provide useful insights in the determination of the important parameters which drive the dynamics of the technological substitution model in the context of one-at-a-timesensitivity analysis
The document discusses using machine learning techniques to analyze traffic accident data from Porto Alegre, Brazil between 2000-2013. It compares decision trees, random forests, and logistic regression for predicting whether accidents resulted in injuries. Random forests and logistic regression performed similarly and better than decision trees. Motorcycles and accident type were highly predictive of injuries, while factors like weather had low relevance. The models could be improved with additional data on drivers, weather, and traffic conditions.
On improved estimation of population mean using qualitative auxiliary informa...Alexander Decker
This document proposes new estimators for estimating the population mean of a variable using qualitative auxiliary information. It begins with background on using auxiliary information to improve estimation. Previous related work that proposed ratio, product, and combined ratio-product estimators is reviewed.
The document then proposes four new exponential-type estimators: an exponential ratio estimator, an exponential product estimator, an exponential dual-to-ratio estimator, and an exponential ratio-dual-to-ratio estimator. Expressions for the bias and mean squared error of the proposed estimators are derived.
Finally, the document states that a numerical demonstration will be presented to illustrate the improvements of the proposed estimators over previous methods. The goal is to provide better estimators that can be useful in
The International Journal of Engineering and Science (The IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
Application of Semiparametric Non-Linear Model on Panel Data with Very Small ...IOSRJM
-This research work investigated the behaviour of a new semiparametric non-linear (SPNL) model on
a set of panel data with very small time point (T = 1). The SPNL model incorporates the relationship between
individual independent variable and unobserved heterogeneity variable. Five different estimation techniques
namely; Least Square (LS), Generalized Method of Moments (GMM), Continuously Updating (CU), Empirical
Likelihood (EL) and Exponential Tilting (ET) Estimators were employed for the estimation; for the purpose of
modelling the metrical response variable non-linearly on a set of independent variables. The performances of
these estimators on the SPNL model were examined for different parameters in the model using the Least
Square Error (LSE), Mean Absolute Error (MAE) and Median Absolute Error (MedAE) criteria at the lowest
time point (T = 1). The results showed that the ET estimator which provided the least errors of estimation is
relatively more efficient for the proposed model than any of the other estimators considered. It is therefore
recommended that the ET estimator should be employed to estimate the SPNL model for panel data with very
small time point.
A Class of Continuous Implicit Seventh-eight method for solving y’ = f(x, y) ...AI Publications
In this article, we develop a continuous implicit seventh-eight method using interpolation and collocation of the approximate solution for the solution of y’ = f(x, y) with a constant step-size. The method uses power series as the approximate solution in the derivation of the method. The independent solution was then derived by adopting block integrator. The properties of the method was investigated and found to be zero stable, consistent and convergent. The integrator was tested on numerical examples ranging from linear problem, Prothero-Robinson Oscillatory, Growth Model and Sir Model. The results show that the computed solution is closer to the exact solution and also, the absolutes errors perform better than the existing methods.
This is the comprehensive PPT on regression analysis. It covers the methods of identifying IV, DV, mediator, and moderators. How to interpreter using the parameters, R square, T-test. differentiation between linear and non-lienar regression
The document discusses machine learning techniques for multivariate data analysis using the TMVA toolkit. It describes several common classification problems in high energy physics (HEP) and summarizes several machine learning algorithms implemented in TMVA for supervised learning, including rectangular cut optimization, likelihood methods, neural networks, boosted decision trees, support vector machines and rule ensembles. It also discusses challenges like nonlinear correlations between input variables and techniques for data preprocessing and decorrelation.
Multivariate Linear Regression Model for Simulaneous Estimation of Debutanise...NSEAkure
Multivariate Linear Regression Model for Simulaneous Estimation of Debutaniser Products Compostion presentation by Obekpa R.G and Alabi S B @ #Nse conference @ #thedome in AKure
1) ICA can extract sparse and independent features from medical imaging data to build predictive models of conditions like brain trauma.
2) MCCA identifies joint patterns across multiple datasets, like functional MRI scans from a simulated driving experiment.
3) Dimension reduction with PCA improves ICA by addressing issues with high dimensionality, enhancing reproducibility of extracted patterns.
- Multivariate adaptive regression splines (MARS) is a non-parametric regression technique that automatically models non-linearities and interactions between variables. It extends linear models using basis functions including hinge functions.
- MARS builds models in two phases - a forward phase that adds terms and a backward phase that prunes the model. It searches over variables, observations, and model terms to find the best fitting model.
- MARS can model non-linear relationships like those seen in examples where a single independent variable had a nonlinear effect on the response variable. It provides interpretable models using weighted sums of basis functions.
This document outlines the symbols and notation used in various multivariate statistical models. It describes models such as multiple regression, discriminant analysis, factor analysis, principal components analysis, and analysis of variance models. For each model, it shows the graphical representation of the variables involved, indicating which variables are independent, dependent, continuous, categorical, and latent. It provides examples of how multivariate statistical models can be represented using these standardized symbols.
The document discusses using multivariate regression analysis to analyze the factors that determine the sales of pharmaceutical companies. It examines four independent variables - marketing expense, research and development spending, investments, and plant and machinery - and their relationship to the dependent variable of sales revenue. Both multiplicative and additive regression models are used. The multiplicative models find the adjusted R-squared values range from 0.867 to 0.903, indicating the models explain 86.7-90.3% of the variation in sales revenue. The additive models produce adjusted R-squared values of 0.790 to 0.836, meaning 79.0-83.6% of the variation is explained.
This document outlines the history and goals of a company. It discusses how the company was founded 25 years ago with a vision of becoming the leading provider of its product/service. It has since expanded to multiple locations nationally and internationally. The company's current goals are to continue expanding its operations, provide high quality products/services to more customers, and increase customer satisfaction while maintaining its position as the market leader.
The document summarizes a study that developed a multiple regression model to predict the retail price of 2005 GM cars using data on 800 cars. Variables like mileage, engine size, features, and make/model were considered. Initial regression of just price and mileage found mileage explained little of the variation in price and outliers existed. Including other variables in multiple regression improved the predictive ability of the model, with a combination of mileage, cylinders, doors, cruise control, sound system, and leather seats finding the highest correlation. Residual plots helped identify that including make/model as dummy variables further improved the model fit, resulting in an R-squared value of 91.78%. The goal was to describe and predict price based on the explanatory variables.
Reverse Logistics in Different IndustriesPRIYAJNVCTC
The document provides an overview of reverse logistics from the perspectives of operations and challenges. It discusses key aspects of reverse logistics including typical activities, costs, and impact. It notes that reverse logistics is an emerging industry that presents challenges for operations people due to the many stakeholders involved and lack of standardized processes. Best practices discussed include having one group control returns and defined business processes to improve efficiency. The document also provides examples of Flipkart's reverse logistics network and return process.
This document provides an overview of machine learning techniques that can be applied in finance, including exploratory data analysis, clustering, classification, and regression methods. It discusses statistical learning approaches like data mining and modeling. For clustering, it describes techniques like k-means clustering, hierarchical clustering, Gaussian mixture models, and self-organizing maps. For classification, it mentions discriminant analysis, decision trees, neural networks, and support vector machines. It also provides summaries of regression, ensemble methods, and working with big data and distributed learning.
Machine Learning, Deep Learning and Data Analysis IntroductionTe-Yen Liu
The document provides an introduction and overview of machine learning, deep learning, and data analysis. It discusses key concepts like supervised and unsupervised learning. It also summarizes the speaker's experience taking online courses and studying resources to learn machine learning techniques. Examples of commonly used machine learning algorithms and neural network architectures are briefly outlined.
This document provides an overview of multivariate analysis techniques, including dependency techniques like multiple regression, discriminant analysis, and MANOVA, as well as interdependency techniques like factor analysis, cluster analysis, and multidimensional scaling. It describes the uses and processes for each technique, such as using multiple regression to predict values, discriminate analysis to classify groups, and factor analysis to reduce variables. The document is signed off with warm wishes from the owner of Power Group.
The document discusses different aspects of interviewing as a marketing research method. It defines interviewing as collecting data by asking questions and following up on answers. There are different types of interviews including individual face-to-face, focus groups, and in-depth interviews. Successful interviews require the respondent to have relevant information, understand what is expected of them, and be motivated to answer accurately. The interviewer's tasks include locating respondents, obtaining the interview, asking questions, and recording responses. Training and supervision of interviewers is important to minimize errors.
This document discusses factors that influence the selection of data analysis strategies and provides a classification of statistical techniques. It notes that the previous research steps, known data characteristics, statistical technique properties, and researcher background all impact strategy selection. Statistical techniques can be univariate, analyzing single variables, or multivariate, analyzing relationships between multiple variables simultaneously. Multivariate techniques are further classified as dependence techniques, with identifiable dependent and independent variables, or interdependence techniques examining whole variable sets. The document provides examples of common univariate and multivariate techniques.
Transform your Business with AI, Deep Learning and Machine LearningSri Ambati
Video: https://www.youtube.com/watch?v=R3IXd1iwqjc
Meetup: http://www.meetup.com/SF-Bay-ACM/events/231709894/
In this talk, Arno Candel presents a brief history of AI and how Deep Learning and Machine Learning techniques are transforming our everyday lives. Arno will introduce H2O, a scalable open-source machine learning platform, and show live demos on how to train sophisticated machine learning models on large distributed datasets. He will show how data scientists and application developers can use the Flow GUI, R, Python, Java, Scala, JavaScript and JSON to build smarter applications, and how to take them to production. He will present customer use cases from verticals including insurance, fraud, churn, fintech, and marketing.
- Powered by the open source machine learning software H2O.ai. Contributors welcome at: https://github.com/h2oai
- To view videos on H2O open source machine learning software, go to: https://www.youtube.com/user/0xdata
Money, income, and prices in bangladesh a cointegration and causality analysisAlexander Decker
This document summarizes a study that examines the causal relationship between money, income, and prices in Bangladesh from 1972/73 to 2009/10. It finds:
1) Money, income, and prices are cointegrated, indicating a long-run relationship.
2) Bivariate analysis finds bidirectional causality between money and income, supporting neither Keynesians nor Monetarists. It finds unidirectional causality from money to prices, supporting Monetarists.
3) Trivariate analysis also finds bidirectional causality between money and income conditional on prices, and unidirectional causality from money to prices conditional on income.
So monetary policy should consider feedback effects between money and income
Bayesian and Non Bayesian Parameter Estimation for Bivariate Pareto Distribut...IJERA Editor
This document summarizes Bayesian and non-Bayesian methods for estimating parameters of the bivariate Pareto distribution based on censored samples. It introduces the bivariate Pareto distribution and describes how censoring can occur in medical studies with paired organs or engineering systems with two components. Maximum likelihood estimators are derived for the bivariate Pareto distribution parameters given censored data. Bayesian parameter estimation is also discussed, where posterior distributions for the parameters are obtained under different prior distribution assumptions. An extensive computer simulation is used to compare the performance of the proposed estimators.
SEMI-PARAMETRIC ESTIMATION OF Px,y({(x,y)/x >y}) FOR THE POWER FUNCTION DISTR...IJESM JOURNAL
The stress-strength model describes the life of a component which has a random strength X and is subjected to random stress Y, in the context of reliability. The component will function satisfactorily whenever X>Y and it fails at the instant the stress applied to it exceeds the strength. R=P(Y<X) is a measure of component reliability .In this paper, we obtain semi parametric estimators of the reliability under stress- strength model for the Power function distribution under complete and censored samples. We illustrate the performance of the estimators using a simulation study.
Investigations of certain estimators for modeling panel data under violations...Alexander Decker
This document investigates the efficiency of four methods for estimating panel data models (pooling, first differencing, between, and feasible generalized least squares) when the assumptions of homoscedasticity, no autocorrelation, and no collinearity are jointly violated. Monte Carlo simulations were conducted under varying conditions of heteroscedasticity, autocorrelation, collinearity, sample size, and time periods. The results showed that in small samples, the feasible generalized least squares estimator is most efficient when heteroscedasticity is severe, regardless of autocorrelation and collinearity levels. However, when heteroscedasticity is low to moderate with moderate autocorrelation, first differencing and feasible generalized least squares
Parametric sensitivity analysis of a mathematical model of facultative mutualismIOSR Journals
The complex dynamics of facultative mutualism is best described by a system of continuous non-linear first order ordinary differential equations. The methods of 1-norm, 2-norm, and infinity-norm will be used to quantify and differentiate the different forms of the sensitivity of model parameters. These contributions will be presented and discussed.
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
This document presents an exponential-Lindley additive failure rate model (ELAFRM) by combining the hazard functions of an exponential distribution and a Lindley distribution. The key properties of the ELAFRM are derived, including the probability density function, cumulative distribution function, hazard function, moments, and graphical representations. Estimation of the model parameters is also discussed. The document proposes this new ELAFRM distribution and analyzes its mathematical properties.
The document discusses machine learning techniques for multivariate data analysis using the TMVA toolkit. It describes several common classification problems in high energy physics (HEP) and summarizes several machine learning algorithms implemented in TMVA for supervised learning, including rectangular cut optimization, likelihood methods, neural networks, boosted decision trees, support vector machines and rule ensembles. It also discusses challenges like nonlinear correlations between input variables and techniques for data preprocessing and decorrelation.
Multivariate Linear Regression Model for Simulaneous Estimation of Debutanise...NSEAkure
Multivariate Linear Regression Model for Simulaneous Estimation of Debutaniser Products Compostion presentation by Obekpa R.G and Alabi S B @ #Nse conference @ #thedome in AKure
1) ICA can extract sparse and independent features from medical imaging data to build predictive models of conditions like brain trauma.
2) MCCA identifies joint patterns across multiple datasets, like functional MRI scans from a simulated driving experiment.
3) Dimension reduction with PCA improves ICA by addressing issues with high dimensionality, enhancing reproducibility of extracted patterns.
- Multivariate adaptive regression splines (MARS) is a non-parametric regression technique that automatically models non-linearities and interactions between variables. It extends linear models using basis functions including hinge functions.
- MARS builds models in two phases - a forward phase that adds terms and a backward phase that prunes the model. It searches over variables, observations, and model terms to find the best fitting model.
- MARS can model non-linear relationships like those seen in examples where a single independent variable had a nonlinear effect on the response variable. It provides interpretable models using weighted sums of basis functions.
This document outlines the symbols and notation used in various multivariate statistical models. It describes models such as multiple regression, discriminant analysis, factor analysis, principal components analysis, and analysis of variance models. For each model, it shows the graphical representation of the variables involved, indicating which variables are independent, dependent, continuous, categorical, and latent. It provides examples of how multivariate statistical models can be represented using these standardized symbols.
The document discusses using multivariate regression analysis to analyze the factors that determine the sales of pharmaceutical companies. It examines four independent variables - marketing expense, research and development spending, investments, and plant and machinery - and their relationship to the dependent variable of sales revenue. Both multiplicative and additive regression models are used. The multiplicative models find the adjusted R-squared values range from 0.867 to 0.903, indicating the models explain 86.7-90.3% of the variation in sales revenue. The additive models produce adjusted R-squared values of 0.790 to 0.836, meaning 79.0-83.6% of the variation is explained.
This document outlines the history and goals of a company. It discusses how the company was founded 25 years ago with a vision of becoming the leading provider of its product/service. It has since expanded to multiple locations nationally and internationally. The company's current goals are to continue expanding its operations, provide high quality products/services to more customers, and increase customer satisfaction while maintaining its position as the market leader.
The document summarizes a study that developed a multiple regression model to predict the retail price of 2005 GM cars using data on 800 cars. Variables like mileage, engine size, features, and make/model were considered. Initial regression of just price and mileage found mileage explained little of the variation in price and outliers existed. Including other variables in multiple regression improved the predictive ability of the model, with a combination of mileage, cylinders, doors, cruise control, sound system, and leather seats finding the highest correlation. Residual plots helped identify that including make/model as dummy variables further improved the model fit, resulting in an R-squared value of 91.78%. The goal was to describe and predict price based on the explanatory variables.
Reverse Logistics in Different IndustriesPRIYAJNVCTC
The document provides an overview of reverse logistics from the perspectives of operations and challenges. It discusses key aspects of reverse logistics including typical activities, costs, and impact. It notes that reverse logistics is an emerging industry that presents challenges for operations people due to the many stakeholders involved and lack of standardized processes. Best practices discussed include having one group control returns and defined business processes to improve efficiency. The document also provides examples of Flipkart's reverse logistics network and return process.
This document provides an overview of machine learning techniques that can be applied in finance, including exploratory data analysis, clustering, classification, and regression methods. It discusses statistical learning approaches like data mining and modeling. For clustering, it describes techniques like k-means clustering, hierarchical clustering, Gaussian mixture models, and self-organizing maps. For classification, it mentions discriminant analysis, decision trees, neural networks, and support vector machines. It also provides summaries of regression, ensemble methods, and working with big data and distributed learning.
Machine Learning, Deep Learning and Data Analysis IntroductionTe-Yen Liu
The document provides an introduction and overview of machine learning, deep learning, and data analysis. It discusses key concepts like supervised and unsupervised learning. It also summarizes the speaker's experience taking online courses and studying resources to learn machine learning techniques. Examples of commonly used machine learning algorithms and neural network architectures are briefly outlined.
This document provides an overview of multivariate analysis techniques, including dependency techniques like multiple regression, discriminant analysis, and MANOVA, as well as interdependency techniques like factor analysis, cluster analysis, and multidimensional scaling. It describes the uses and processes for each technique, such as using multiple regression to predict values, discriminate analysis to classify groups, and factor analysis to reduce variables. The document is signed off with warm wishes from the owner of Power Group.
The document discusses different aspects of interviewing as a marketing research method. It defines interviewing as collecting data by asking questions and following up on answers. There are different types of interviews including individual face-to-face, focus groups, and in-depth interviews. Successful interviews require the respondent to have relevant information, understand what is expected of them, and be motivated to answer accurately. The interviewer's tasks include locating respondents, obtaining the interview, asking questions, and recording responses. Training and supervision of interviewers is important to minimize errors.
This document discusses factors that influence the selection of data analysis strategies and provides a classification of statistical techniques. It notes that the previous research steps, known data characteristics, statistical technique properties, and researcher background all impact strategy selection. Statistical techniques can be univariate, analyzing single variables, or multivariate, analyzing relationships between multiple variables simultaneously. Multivariate techniques are further classified as dependence techniques, with identifiable dependent and independent variables, or interdependence techniques examining whole variable sets. The document provides examples of common univariate and multivariate techniques.
Transform your Business with AI, Deep Learning and Machine LearningSri Ambati
Video: https://www.youtube.com/watch?v=R3IXd1iwqjc
Meetup: http://www.meetup.com/SF-Bay-ACM/events/231709894/
In this talk, Arno Candel presents a brief history of AI and how Deep Learning and Machine Learning techniques are transforming our everyday lives. Arno will introduce H2O, a scalable open-source machine learning platform, and show live demos on how to train sophisticated machine learning models on large distributed datasets. He will show how data scientists and application developers can use the Flow GUI, R, Python, Java, Scala, JavaScript and JSON to build smarter applications, and how to take them to production. He will present customer use cases from verticals including insurance, fraud, churn, fintech, and marketing.
- Powered by the open source machine learning software H2O.ai. Contributors welcome at: https://github.com/h2oai
- To view videos on H2O open source machine learning software, go to: https://www.youtube.com/user/0xdata
Money, income, and prices in bangladesh a cointegration and causality analysisAlexander Decker
This document summarizes a study that examines the causal relationship between money, income, and prices in Bangladesh from 1972/73 to 2009/10. It finds:
1) Money, income, and prices are cointegrated, indicating a long-run relationship.
2) Bivariate analysis finds bidirectional causality between money and income, supporting neither Keynesians nor Monetarists. It finds unidirectional causality from money to prices, supporting Monetarists.
3) Trivariate analysis also finds bidirectional causality between money and income conditional on prices, and unidirectional causality from money to prices conditional on income.
So monetary policy should consider feedback effects between money and income
Bayesian and Non Bayesian Parameter Estimation for Bivariate Pareto Distribut...IJERA Editor
This document summarizes Bayesian and non-Bayesian methods for estimating parameters of the bivariate Pareto distribution based on censored samples. It introduces the bivariate Pareto distribution and describes how censoring can occur in medical studies with paired organs or engineering systems with two components. Maximum likelihood estimators are derived for the bivariate Pareto distribution parameters given censored data. Bayesian parameter estimation is also discussed, where posterior distributions for the parameters are obtained under different prior distribution assumptions. An extensive computer simulation is used to compare the performance of the proposed estimators.
SEMI-PARAMETRIC ESTIMATION OF Px,y({(x,y)/x >y}) FOR THE POWER FUNCTION DISTR...IJESM JOURNAL
The stress-strength model describes the life of a component which has a random strength X and is subjected to random stress Y, in the context of reliability. The component will function satisfactorily whenever X>Y and it fails at the instant the stress applied to it exceeds the strength. R=P(Y<X) is a measure of component reliability .In this paper, we obtain semi parametric estimators of the reliability under stress- strength model for the Power function distribution under complete and censored samples. We illustrate the performance of the estimators using a simulation study.
Investigations of certain estimators for modeling panel data under violations...Alexander Decker
This document investigates the efficiency of four methods for estimating panel data models (pooling, first differencing, between, and feasible generalized least squares) when the assumptions of homoscedasticity, no autocorrelation, and no collinearity are jointly violated. Monte Carlo simulations were conducted under varying conditions of heteroscedasticity, autocorrelation, collinearity, sample size, and time periods. The results showed that in small samples, the feasible generalized least squares estimator is most efficient when heteroscedasticity is severe, regardless of autocorrelation and collinearity levels. However, when heteroscedasticity is low to moderate with moderate autocorrelation, first differencing and feasible generalized least squares
Parametric sensitivity analysis of a mathematical model of facultative mutualismIOSR Journals
The complex dynamics of facultative mutualism is best described by a system of continuous non-linear first order ordinary differential equations. The methods of 1-norm, 2-norm, and infinity-norm will be used to quantify and differentiate the different forms of the sensitivity of model parameters. These contributions will be presented and discussed.
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
This document presents an exponential-Lindley additive failure rate model (ELAFRM) by combining the hazard functions of an exponential distribution and a Lindley distribution. The key properties of the ELAFRM are derived, including the probability density function, cumulative distribution function, hazard function, moments, and graphical representations. Estimation of the model parameters is also discussed. The document proposes this new ELAFRM distribution and analyzes its mathematical properties.
Stability of Individuals in a Fingerprint System across Force LevelsITIIIndustries
This research studied the question: “Are all
individual’s performance stable in a fingerprint recognition
system?” The fingerprints of 154 individuals, provided at
different force levels, were examined using the biometric
menagerie tool, first coined by Doddington et al. in 1998. The
Biometric Menagerie illustrates how each person in a given
dataset performs in a biometric system, by using their genuine
and impostor scores, and providing them a classification based
upon those scores. This research examined the biometric
menagerie classifications across different force levels in a
fingerprint recognition study to uncover if individuals performed
the same over five force levels. The study concluded that they did
not, and a new metric has been created to quantify this
phenomenon. As a result of this discovery, the new metric,
Stability Score Index is described to showcase the movement of
individuals in the menagerie.
Simulation modeling of the sensitivity analysis of differential effects of th...IJAEMSJORNAL
The vulnerability of the differential effects of the intrinsic growth rates of the fish population on the uncertainty analysis can only be controlled by using the mathematical technique of a sensitivity analysis that is called a local minimum selection method based on a Matlab numerical scheme of ordinary differential equations of order 45 (ODE 45). The quantification of the p-norms sensitivity analysis depends on the application of the 1-norm, 2-norm, 3-norm, 4-norm, 5-norm, 6-norm and infinity-norm. In the context of this study, the best-fit intrinsic growth rate of fish population with a small error has occurred when its value is 0.303 which minimizes the bigger sensitivity values previously obtained irrespective of the p-norm sensitivity values. The novel results which we have obtained have not been seen elsewhere. These results are fully presented and discussed in this study.
Formulation of M.L.R Model for Correlating the Factors Responsible for Indust...IJERA Editor
Industrial accidents proves to be more costly and thus efforts are made to lower them and enhance safety.Safety Management system is a proactive and systematic approach for identification, evaluation, mitigation, prevention and control of hazards that could occur as a result of failures in process, procedures, or equipment. Increasing industrial accidents, loss of life & property, public scrutiny, statutory requirements, aging facilities and intense industrial processes, all contribute to a growing need for Safety Management Program to ensure safety and risk management. The proposed paper work envisages to minimize industrial accidents by identifying the various factors responsible for industrial accidents and developing the approximate model to correlate the causes of accidents with the severity and the man days lost
Interoperability and the Stability Score IndexITIIIndustries
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Multivariate regression techniques for analyzing auto crash variables in nigeria
1. Journal of Natural Sciences Research www.iiste.org
ISSN 2224-3186 (Paper) ISSN 2225-0921 (Online)
Vol.1, No.1, 2011
Multivariate Regression Techniques for Analyzing Auto-
Crash Variables in Nigeria
Olushina Olawale Awe1* Mumini Idowu Adarabioyo2
1. Department of Mathematics, Obafemi Awolowo University Ile-Ife, Nigeria.
2. Department of Mathematical Sciences, Afe Babalola University, Ado Ekiti,
Nigeria.
*E-mail of the corresponding author: olawaleawe@yahoo.co.uk
Abstract
It is unequivocally indisputable that motor vehicle accidents have increasingly become a
major cause of concern for highway safety engineers and transportation agencies in
Nigeria over the last few decades. This great concern has led to so many research
activities, in which multivariate statistical analysis is inevitable. In this paper, we explore
some regression models to capture the interconnectedness among accident related
variables in Nigeria. We find that all the five variables considered are highly interrelated
over the past decade, resulting in a high risk of mortality due to auto-crash rate. The
result of our analysis, using an appropriate statistical software, also reveals that the
simple regression models capture the relationships among the variables more than the
multiple regression model considered.
Key Words: Multivariate Model, Analyzing, Regression, Data, Accident, Rate.
1. Introduction
Multivariate techniques and statistical tests are needed to analyze data in many areas of human
endeavor in order to provide descriptive and inferential procedures which we can use to detect
behavioral patterns or test hypotheses about parameters of interest. Controversy has continued to trail
the exact number of deaths recorded yearly through road accident in Nigeria with World Health
Organization(WHO), the National Union of Road Transport Workers(NURTW) and the Federal road
Safety Commission of Nigeria(FRSCN) giving conflicting reports. While the international agency claimed
that 32,000 died yearly through road accidents in Nigeria, the FRSCN insisted that the country had only
recorded between 4000 and 5000 deaths from road accidents in the last three years. The president of
the National Union of Road Transport Workers of Nigeria(NURTW) once claimed that, “despite the fact
19 | P a g e
www.iiste.org
2. Journal of Natural Sciences Research www.iiste.org
ISSN 2224-3186 (Paper) ISSN 2225-0921 (Online)
Vol.1, No.1, 2011
that not all deaths and accidents on our roads are officially reported, 8, 672 people were said to have
lost their lives to road accidents in Nigeria in 2003, while another 28,215 people sustained different
degrees of injuries within the period. The number of people dying as a result of road accident in
Nigeria has reached an alarming proportion as accident rates increases towards the end of the
year especially as from the month of September (Ojo, 2008). Analysis of the traffic crashes
recorded over a five year period of 2000- 2006 showed that 98,494 cases of traffic crashes were
recorded out of which 28,366 were fatal and resulted into deaths(FRSCN Report,2009).This
revealing statistics shows that Nigeria is placed among the fore front nations experiencing the
highest rate of road tragedies in the world. This paper focuses on determining the degree of
association between those who are killed in road crashes and variables like the number of
vehicles involved, number of accidents recorded, number injured and the particular month the
accident occurred. The rest of the paper is organized as follows: section two considers the data
and methodology used in the study, section three enumerates the main results, section four is on
the discussion and findings from the study, while section five concludes the study. The various
analysis performed are presented and labeled as exhibits below the conclusion.
2. Data and Methodology
2.1 Data
Accidents Statistics covering s period of five years were collected (2003-2007) from
Lagos State Command of the Federal Road Safety Corps. The data were then summed up
according to the particular month the accident occurred, thereby giving us a sample size
of twelve. The essence of this is to determine the effect of a particular month in the year
on accident situation in Lagos State as the month increases to December.
2.2 Methodology
A simple linear regression equation of the dependent variable on each of the other factors
and a multiple regression equation was fitted on all the independent variables. The simple
linear regression is a special case of the multiple linear regression(Rencher,2002),so we
consider first simple linear regressions of the dependent variable on each of the
independent variables.The dependent variable for the analysis is the number of people
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killed and the independent variables are x1 , x2 , x3 and x4 (what each variable represents
is given below).
Y = f(X1+ X2+ X3+ X4)----------------------------(1)
The hypothesis tested in the study is that: there is no significant relationship between
Number of people killed and the variables x1 , x2 , x3 and x4 which could not be
explained on the basis of chance alone.
The Multiple linear regressions is defined by:
Y =α + X β + X β
i i i i 2 2
+ X β
3 3
+ X β +ε
4 4 i
-------------------(2)
Where Y i _ killed
= the number people killed in the accident
X 1i _ accident
= the number of accidents
X 2 injured
_ = the number of injured persons
X 3i _ vehicle
=Number of vehicles involved
X 4i _ month
= the particular month the accident occurred.
ἑi is the random error term of the model
After identifying the hypothesis for testing, statistical analysis was performed on all the
variables (Y, X1, X2, X3 and X4). The results of the analyses are presented in exhibits 1,
2, 3, 4 and 5.
The simple linear regression is carried out between Y i _ killed
and each of the independent
variables X 1i _ accident
, X 2i _ injured , X 3i _ vehicle and X 4i _ month
and the results are displayed in Tables 1, 2, 3 and 4.
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2.3 Classical Assumptions of the Linear Regression Model
The assumptions of the linear regression model are stated as follows:
• The model has a linear functional form.
• The independent variables are fixed.
• Independent observations.
• Normality of the residuals.
• Homogeneity of residuals variance.
• No Multicollinearity.
• No autocorrelation of the errors.
• No outlier distortion.
3. Main Results
This section discusses the results of the various regression models fitted to the accident
data.
3.1 Linear regression of Y i _ killed
on X 1i _ accident
.
In the analysis the coefficient of correlation(r) between the two variables is 0.326 and the
coefficient of determination (r2) is 0.1063. r2 is small that is the amount of variation in the
number killed accounted for by the number of accident is 10.63% with probability value
of 0.151 greater than alpha (0.05) so the association is not so statistically significant.
The regression equation is
Y i _ killed
=1786.116 + 0.559 X 1i _ accident ------------------------------(3)
that is for every unit change in the number of accident, there is a positive 0.559 change in
the number of those killed. This is a direct relationship. The model is not significant at
P(0.05) as the P-value is 0.301 greater than alpha. See exhibit 1.
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3.2 Linear regression of Y i _ killed on X 2 i _ injured
.
In the analysis, the coefficient of correlation(r) between the two variables is 0.702 and the
coefficient of determination (r2) is 0.493. r2 is large that is the amount of variation in the
number killed accounted for by the number injured is 49.3% with probability value of
0.011 less than alpha (0.05) so the association is statistically significant.
The regression equation is Y i _ killed
=1005.283 +1.674 X 2i _ injured --------------(4)
that is for every unit change in the number injured; there is a positive 1.674 change in the
number of those killed. This is a direct relationship. The model is significant at P(0.05) as
the P-value is 0.011less than alpha. See Exhibit 2.
3.3. Linear regression of Y i _ killed
on X 3i _ vehicle
.
In the analysis the coefficient of correlation(r) between the two variables is 0.705 and the
coefficient of determination (r2) is 0.443. r2 is large that is the amount of variation in the
number killed accounted for by the number of vehicle involved is 44.3% with probability
value of 0.011 less than alpha (0.05) so the association is statistically significant.
The regression equation is
Y i _ killed
=845.674 +0.688 X 3i _ vehicle
--------------------------(5)
that is for every unit change in the number of vehicle, there is a positive 0.688 change in
the number of those killed. This is a direct relationship. The model is significant at
P(0.05) as the P-value is 0.011 less than alpha. See exhibit 3.
3.4 Linear regression of Y i _ killed
on X 4i _ month
.
In the analysis the coefficient of correlation(r) between the two variables is 0.675 and the
coefficient of determination (r2) is 0.455. r2 is large that is the amount of variation in the
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number killed accounted for by the particular month is 45.5% with probability value of
0.016 less than alpha (0.05) so the association is statistically significant.
The regression equation is
Y i _ killed
= 2445.132 +69.318 X 3i _ vehicle -----------------------------(6)
that is for every unit change in the number of vehicle, there is a positive 69.318 change in
the number of those killed. This is a direct relationship. The model is significant at
P(0.05) as the P-value is 0.016 less than alpha. See exhibit 4.
3.5 Multiple Linear Regression Analysis of Y i _ killed
on all the explanatory variables.
In the analysis, the coefficient of correlation(r) between the two variables is 0.0.79 and
the coefficient of determination (r2) is 0.591. r2 is large, that is the amount of variation in
the number killed accounted for by all the independent variables is 59.1% with
probability value of 0.135 greater than alpha (0.05) so the association is not statistically
significant.
The multiple regression equation is
Y i _ killed
=739.489 +0.075 X 1i _ accident +0.657 X 2i _ injured
+0.39 X 3i _ vehicle +15.576 X 4i _ month (6)
There is positive correlation between Y i _ killed
and all other independent variables. The P-
value of all variables except X 1i _ accident
are less than alpha and so shows statistically
significant relationship. The p-value of X 1i _ accident
is 0.151 greater than alpha and shows
that there is no statistically significant relationship between the number of people who
were killed and the number of vehicles involved.
4. Discussion of Findings
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Our findings reveal that the Multiple Linear Regression Model fitted is not statistically
significant. However, the relationship between each variable and the Y i _ killed
separately
are statistically significant in except for the variable X 1i _ accident . The variance accounted
for by the variable Y i _ killed
was low in all the variables. The correlation matrix (Exhibit
5) more accurately justifies the hypothesis of positive correlation between all the
independent variables and the dependent variable. The correlation of those who were
killed with the injured, the number of vehicles and the month the accidents occurred were
strongly positive (Exhibits 2, 3 and 4). The implications of these findings is that the more
vehicles involved in an accident the more people are killed and as the months approaches
December the more people are killed in road accident in Nigeria. The overall probability
value of the model is 0.135 which is greater than the alpha value of 0.05, so the model is
not relevant. However, there may be many more variables affecting number of people
killed in an accident Y i _ killed
that needs to be explored in further studies.
5.0 Conclusion.
From our analysis, we have seen that the overall model (Multiple Linear Regression
Model) fitted for the accident data is not significant, though there is positive and strong
correlation between the dependent variable and each of the independent variables. This
suggests that there are other variables that actually account for deaths resulting from
auto-crash in Lagos State, Nigeria, which if included in the model will make it more
relevant. These variables need to be explored to form a more robust model for predicting
factors affecting number of people killed as a result of auto-crash in Lagos State, Nigeria.
References
Anyata, B. U.et al (1986); A Case for Increased Investment on Road Usage Education
in
Nigeria, Proceedings of the First International Conference Held in University of
Benin, Nigeria.
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Alvin.C. Rencher (2002):Methods of Multivariate Analysis.2nd Edition.Bringham
Young University. A John Wiley Publications.
Brussels, (2006); Commission of the European Communities Proposal for a Directive
of the
European Parliament and of the Council on Road Infrastructures Safety. Management.
[SEC(2006) 1231/1232]
Hohnsheid, K. J, (2003): Road Saftey Impact Assessment. Bergisch Gladbach,
Bundesanstalt
Strassenwesen. (Internet report)
Reurings M, (2006): Modelling the Number of Road Accidents using Generalized
Linear
Models. SWOV, Leidschendan
Rob E. (2005): Accident Prediction Models and Road Safety Assessment (Internet
Report)
Slefan. C. (2006): Predictive Model of Injury Accidents on Austrian Motorways.
KFV. Vienna.
Vikas Singh, (2006); Statistical Analysis of the Variables Affecting Infant Mortality
Rate in
United States. Journal of the Department of Health Services Administration,
University of Arkansas Medical Services
Wichert S, (226): Accident Prediction Models For Portuguese Motorways. LNEC,
Lisbon
www.makeroadsafe.org
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Exhibit 1
Model Summaryb
Change Statistics
Adjusted Std. Error of R Square
Model R R Square R Square the Estimate Change F Change df1 df2 Sig. F Change
1 .326a .106 .017 367.27931 .106 1.187 1 10 .301
a. Predictors: (Constant), X1_ACCDT
b. Dependent Variable: Y_KILLED
Coefficientsa
Unstandardized Standardized
Coefficients Coefficients Correlations Collinearity Statistics
Model B Std. Error Beta t Sig. Zero-order Partial Part Tolerance VIF
1 (Constant) 1786.116 1023.944 1.744 .112
X1_ACCDT .559 .513 .326 1.090 .301 .326 .326 .326 1.000 1.000
a. Dependent Variable: Y_KILLED
ANOVAb
Sum of
Model Squares df Mean Square F Sig.
1 Regression 160133.4 1 160133.360 1.187 .301a
Residual 1348941 10 134894.089
Total 1509074 11
a. Predictors: (Constant), X1_ACCDT
b. Dependent Variable: Y_KILLED
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Residuals Statisticsa
Minimum Maximum Mean Std. Deviation N
Predicted Value 2664.2156 3065.2813 2895.7500 120.65479 12
Std. Predicted Value -1.919 1.405 .000 1.000 12
Standard Error of
106.032 237.487 143.759 44.506 12
Predicted Value
Adjusted Predicted Value 2177.2100 3041.1980 2870.2766 226.39478 12
Residual -564.965 677.78455 .00000 350.18708 12
Std. Residual -1.538 1.845 .000 .953 12
Stud. Residual -1.869 2.419 .029 1.143 12
Deleted Residual -834.152 1164.790 25.47340 509.89718 12
Stud. Deleted Residual -2.198 3.564 .089 1.438 12
Mahal. Distance .000 3.682 .917 1.210 12
Cook's Distance .000 2.103 .286 .618 12
Centered Leverage Value .000 .335 .083 .110 12
a. Dependent Variable: Y_KILLED
EXHIBIT 2
Model Summaryb
Change Statistics
Adjusted Std. Error of R Square
Model R R Square R Square the Estimate Change F Change df1 df2 Sig. F Change
1 .702a .493 .443 276.47418 .493 9.742 1 10 .011
a. Predictors: (Constant), X2_INJURED
b. Dependent Variable: Y_KILLED
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Coefficientsa
Unstandardized Standardized
Coefficients Coefficients Correlations Collinearity Statistics
Model B Std. Error Beta t Sig. Zero-order Partial Part Tolerance VIF
1 (Constant) 1005.283 610.904 1.646 .131
X2_INJURED 1.674 .536 .702 3.121 .011 .702 .702 .702 1.000 1.000
a. Dependent Variable: Y_KILLED
ANOVAb
Sum of
Model Squares df Mean Square F Sig.
1 Regression 744694.5 1 744694.535 9.742 .011a
Residual 764379.7 10 76437.971
Total 1509074 11
a. Predictors: (Constant), X2_INJURED
b. Dependent Variable: Y_KILLED
Residuals Statisticsa
Minimum Maximum Mean Std. Deviation N
Predicted Value 2403.0457 3288.5745 2895.7500 260.19128 12
Std. Predicted Value -1.894 1.510 .000 1.000 12
Standard Error of
79.831 176.882 109.159 29.982 12
Predicted Value
Adjusted Predicted Value 2588.7886 3266.6946 2907.2408 243.34302 12
Residual -420.170 396.56958 .00000 263.60779 12
Std. Residual -1.520 1.434 .000 .953 12
Stud. Residual -1.587 1.499 -.017 1.039 12
Deleted Residual -458.388 432.93729 -11.49076 316.14455 12
Stud. Deleted Residual -1.741 1.615 -.029 1.086 12
Mahal. Distance .000 3.586 .917 1.074 12
Cook's Distance .001 .551 .105 .153 12
Centered Leverage Value .000 .326 .083 .098 12
a. Dependent Variable: Y_KILLED
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EXHIBIT 3
Model Summaryb
Change Statistics
Adjusted Std. Error of R Square
Model R R Square R Square the Estimate Change F Change df1 df2 Sig. F Change
1 .703a .494 .443 276.32907 .494 9.763 1 10 .011
a. Predictors: (Constant), X3_VEHICLE
b. Dependent Variable: Y_KILLED
Coefficientsa
Unstandardized Standardized
Coefficients Coefficients Correlations Collinearity Statistics
Model B Std. Error Beta t Sig. Zero-order Partial Part Tolerance VIF
1 (Constant) 845.674 660.937 1.280 .230
X3_VEHICLE .688 .220 .703 3.125 .011 .703 .703 .703 1.000 1.000
a. Dependent Variable: Y_KILLED
ANOVAb
Sum of
Model Squares df Mean Square F Sig.
1 Regression 745496.7 1 745496.714 9.763 .011a
Residual 763577.5 10 76357.754
Total 1509074 11
a. Predictors: (Constant), X3_VEHICLE
b. Dependent Variable: Y_KILLED
Residuals Statisticsa
Minimum Maximum Mean Std. Deviation N
Predicted Value 2314.8884 3233.5776 2895.7500 260.33138 12
Std. Predicted Value -2.231 1.298 .000 1.000 12
Standard Error of
79.858 202.291 107.818 34.666 12
Predicted Value
Adjusted Predicted Value 2522.6218 3470.0000 2919.4845 251.47191 12
Residual -763.578 220.83029 .00000 263.46943 12
Std. Residual -2.763 .799 .000 .953 12
Stud. Residual -3.162 .897 -.036 1.096 12
Deleted Residual -1000.00 278.41348 -23.73454 350.88265 12
Stud. Deleted Residual -.951 .888 .239 .498 11
Mahal. Distance .002 4.978 .917 1.389 12
Cook's Distance .000 1.548 .192 .452 12
Centered Leverage Value .000 .453 .083 .126 12
a. Dependent Variable: Y_KILLED
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EXHIBIT 4
Model Summaryb
Change Statistics
Adjusted Std. Error of R Square
Model R R Square R Square the Estimate Change F Change df1 df2 Sig. F Change
1 .675a .455 .401 286.69806 .455 8.360 1 10 .016
a. Predictors: (Constant), X4_MONTH
b. Dependent Variable: Y_KILLED
Coefficientsa
Unstandardized Standardized
Coefficients Coefficients Correlations Collinearity Statistics
Model B Std. Error Beta t Sig. Zero-order Partial Part Tolerance VIF
1 (Constant) 2445.182 176.450 13.858 .000
X4_MONTH 69.318 23.975 .675 2.891 .016 .675 .675 .675 1.000 1.000
a. Dependent Variable: Y_KILLED
Residuals Statisticsa
Minimum Maximum Mean Std. Deviation N
Predicted Value 2514.5000 3277.0000 2895.7500 249.93026 12
Std. Predicted Value -1.525 1.525 .000 1.000 12
Standard Error of
83.626 155.683 114.262 26.497 12
Predicted Value
Adjusted Predicted Value 2474.0601 3249.8181 2896.0913 246.51793 12
Residual -391.091 378.18182 .00000 273.35587 12
Std. Residual -1.364 1.319 .000 .953 12
Stud. Residual -1.576 1.498 .000 1.050 12
Deleted Residual -538.200 487.93985 -.34125 333.19846 12
Stud. Deleted Residual -1.725 1.614 -.015 1.100 12
Mahal. Distance .019 2.327 .917 .847 12
Cook's Distance .002 .520 .114 .156 12
Centered Leverage Value .002 .212 .083 .077 12
a. Dependent Variable: Y_KILLED
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ANOVAb
Sum of
Model Squares df Mean Square F Sig.
1 Regression 687116.5 1 687116.477 8.360 .016a
Residual 821957.8 10 82195.777
Total 1509074 11
a. Predictors: (Constant), X4_MONTH
b. Dependent Variable: Y_KILLED
EXHIBIT 5
Model Summaryb
Change Statistics
Adjusted Std. Error of R Square
Model R R Square R Square the Estimate Change F Change df1 df2 Sig. F Change
1 .769a .591 .357 297.07324 .591 2.525 4 7 .135
a. Predictors: (Constant), X4_MONTH, X1_ACCDT, X3_VEHICLE, X2_INJURED
b. Dependent Variable: Y_KILLED
Coefficientsa
Unstandardized Standardized
Coefficients Coefficients Correlations Collinearity Statistics
Model B Std. Error Beta t Sig. Zero-order Partial Part Tolerance VIF
1 (Constant) 739.489 1850.432 .400 .701
X1_ACCDT .075 .478 .044 .158 .879 .326 .059 .038 .752 1.330
X2_INJURED .657 2.108 .276 .312 .764 .702 .117 .075 .075 13.384
X3_VEHICLE .390 .367 .399 1.064 .323 .703 .373 .257 .417 2.401
X4_MONTH 15.576 84.752 .152 .184 .859 .675 .069 .044 .086 11.639
a. Dependent Variable: Y_KILLED
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ANOVAb
Sum of
Model Squares df Mean Square F Sig.
1 Regression 891306.7 4 222826.671 2.525 .135a
Residual 617767.6 7 88252.509
Total 1509074 11
a. Predictors: (Constant), X4_MONTH, X1_ACCDT, X3_VEHICLE, X2_INJURED
b. Dependent Variable: Y_KILLED
Correlations
Y_KILLED X1_ACCDT X2_INJURED X3_VEHICLE X4_MONTH
Pearson Correlation Y_KILLED 1.000 .326 .702 .703 .675
X1_ACCDT .326 1.000 .220 .472 .218
X2_INJURED .702 .220 1.000 .683 .955
X3_VEHICLE .703 .472 .683 1.000 .627
X4_MONTH .675 .218 .955 .627 1.000
Sig. (1-tailed) Y_KILLED . .151 .005 .005 .008
X1_ACCDT .151 . .246 .061 .248
X2_INJURED .005 .246 . .007 .000
X3_VEHICLE .005 .061 .007 . .014
X4_MONTH .008 .248 .000 .014 .
N Y_KILLED 12 12 12 12 12
X1_ACCDT 12 12 12 12 12
X2_INJURED 12 12 12 12 12
X3_VEHICLE 12 12 12 12 12
X4_MONTH 12 12 12 12 12
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