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# Sensitivity analysis regression Sensitivity analysis in linear regression!Samprit Chatterjee, Ali S. Hadi. (Wiley series in probability and mathematical statistics, Applied probability and statistics.) p. cm. Bibliography: p. Includes index. 1. Regression analysis. 2. Perturbation (Mathematics) ISBN -171-82216-7. Regression analysis Regression analysis, in the context of sensitivity analysis, involves fitting a linear regression to the model response and using standardized regression coefficients as direct measures of sensitivity Sensitivity Analysis in Linear Regression | Wiley Treats linear regression diagnostics as a tool for application of linear regression models to real-life data. Presentation makes extensive use of examples to illustrate theory Sensitivity analysis in linear regression Jos e A. D az-Garc a Universidad Aut onoma Agraria Antonio Narro Department of Statistics and Computation 25315 Buenavista, Saltillo, Coahuila, M exic o. E-mail: jadiaz@uaaan.mx Graciela Gonz alez-F ar as Centro de Investigaci on en Matem aticas, A.C. Department of Probability and Statistic

Sensitivity analysis is a study of how changes in the inputs to a model influence the results of the model. Many techniques have recently been proposed for use when the model is probabilistic Sensitivity analysis is a financial model that determines how target variables are affected based on changes in other variables known as input variables. This model is also referred to as what-if..

regression - What do people mean by sensitivity analysis - Cross Validated 2 I have seen and heard people use sensitivity analysis to refer to both: How different values (e.g., just males or the whole cohort) of an independent variable affects the model, an Sensitivity Analysis is a tool used in financial modeling to analyze how the different values of a set of independent variables affect a specific dependent variable under certain specific conditions. In general, sensitivity analysis is used in a wide range of fields, ranging from biology and geography to economics and engineering Sensitivity analysis in logistic regression. Ask Question Asked 5 years, 6 months ago. Active 5 years, 6 months ago. Viewed 2k times 2 \$\begingroup\$ I would like to run a sensitivity analysis of two logistic regression model in order to compare them and make a judgment in for what model a specific IV had an higher impact on the probability.. Sensitivity analysis is used to identify how much variations in the input values for a given variable impact the results for a mathematical model. Sensitivity analysis can identify the best data to.. Usual (parametric) regression requires strong assumptions to be made about the form of the relationship between disease risk and each risk factor in the model. Claims of having controlled for confounders depend to some extent on the validity of such assumptions. Hence sensitivity analysis and regression diagnostic methods are recommended

### Sensitivity Analysis in Linear Regressio

Sensitivity analysis involves a series of methods to quantify how the uncertainty in the output of a model is related to the uncertainty in its inputs. In other words, sensitivity analysis assesses how sensitive the model is to fluctuations in the parameters and data on which it is built Maarten Buis Following your example in #8, it seems the two regression models are quite similar, and we could infer that a sensitivity analysis would perform just fine (in terms of corroborating the proposed model). Then, I typed afterwards The sensitivity analysis can also be used to identify areas of improvement that will have the greatest impact on the model output. This work aims at developing a framework to extend sensitivity analysis by using a regression analysis to create a simplified proxy model, which can be used to help disseminate LCA results A sensitivity analysis is a technique used to determine how different values of an independent variable impact a particular dependent variable under a given set of assumptions Sensitivity Analysis (SA) is defined as a method to determine the robustness of an assessment by examining the extent to which results are affected by changes in methods, models, values of unmeasured variables, or assumptions with the aim of identifying results that are most dependent on questionable or unsupported assumptions [ 2 ]

### Sensitivity analysis - Wikipedi

• A sensitivity analysis is a repeat of the primary analysis or meta-analysis, substituting alternative decisions or ranges of values for decisions that were arbitrary or unclear
• The formula for sensitivity analysis is basically a financial model in excel where the analyst is required to identify the key variables for the output formula and then assess the output based on different combinations of the independent variables. Mathematically, the dependent output formula is represented as, Z = X2 + Y
• Regression analysis is a comprehensive method used to get responses for complex models. Subjective sensitivity analysis: In this method the individual parameters are analyzed. This is a subjective method, simple, qualitative and an easy method to rule out input parameters. Using Sensitivity Analysis for decision makin
• Global sensitivity analysis (GSA) plays an important role in exploring the respective effects of input variables on response variables. In this paper, a new kernel function derived from orthogonal polynomials is proposed for support vector regression (SVR)
• Logistic Regression is a statistical analytical technique which has a wide application in business. It is one of the most commonly used techniques having wide applicability especially in building marketing strategies. Some business examples include identifying the best set of customers for engaging in a promotional activity. For example a telecom company wants to promote [
• Three very common measures are accuracy, sensitivity, and specificity. and proportional odds assumptions on your own. See the incredible usefulness of logistic regression and categorical data analysis in this one-hour training. Take Me to The Video! Tagged With: logistic regression, model accuracy, ROC Curve, sensitivity, specificity

### Video: Sensitivity Analysis in Linear Regression Wile

1. ed by the specified uncertainty distributions (hence probabilistic). Specifying method = src will perform a linear regression-based sensitivity analysis
2. He is the coauthor of Sensitivity Analysis in Linear Regression and A Casebook for a First Course in Statistics and Data Analysis, both published by Wiley. ALI S. HADI, PhD, is a Distinguished University Professor and former vice provost at the American University in Cairo (AUC). He is the founding Director of the Actuarial Science Program at AUC
3. ation, calibration, comparison, and model selection [ 1 ]
4. Traditionally we use linear regression to make an assessment between a variety of variables. On top of that assessment, what we are going to learn here is how you can adjust the inputs of various regression models to drive deeper understanding of the sensitivity or variability of the relationship between your explanatory & response variables
5. Sensitivity Analysis for Instrumental Variables Regression With Overidentifying Restrictions Dylan S. S MALL Instrumental variables regression (IV regression) is a method for making causal inferences about the effect of a treatment based on a
6. In this paper, we explore sensitivity analysis for quantile regression and confront it with diagnostic testing. Every model is misspecified (in the sense that no model coincides with the data-generating process), but a model is useful if the parameters of interest (the focus) are not sensitive to small perturbations of the underlying assumptions The paper is organized as follows. First, the objective of sensitivity analysis is defined. Then, the theoretical background of sensitivity analysis based on regression approach is presented. The extended tornado chart is developed, explained and compared to the conventional tornado chart. Second, the computational algorithm used in SABOR is. Using Regression-based Sensitivity Analysis in Exploratory Modeling of Complex Spatial Systems: An Example of Simulating the Impact of Agricultural Water Withdrawals on Fish Habitat Glenn O'Neil (Institute of Water Research - Michigan State University) Arika Ligmann-Zielinska, Ph.D. (Department of Geography - Michigan State University Three very common measures are accuracy, sensitivity, and specificity. and proportional odds assumptions on your own. See the incredible usefulness of logistic regression and categorical data analysis in this one-hour training. Take Me to The Video! Tagged With: logistic regression, model accuracy, ROC Curve, sensitivity, specificity

### (PDF) Sensitivity analysis in linear model

• Sensitivity Analysis Sensitivity analysis: is a series of analyses targeting the same estimand, with differing assumptions to explore the robustness of inferences from the main estimator to deviations from its underlying modelling assumptions and limitations in the data
• Sensitivity analysis in excel helps us study the uncertainty in the output of the model with the changes in the input variables. It primarily does stress testing of our modeled assumptions and leads to value-added insights. In the context of DCF valuation, Sensitivity Analysis in excel is especially useful in finance for modeling share price or.
• explains the empirical analysis and its interpretation, by providing the results of descriptive statistics, correlation analysis, regression analysis and sensitivity analysis. Section V gives the conclusion. II. LITERATURE REVIEW Smith  identified eight major approaches taken towards the management of the working capital

### Sensitivity Analysis Definitio

• Sensitivity analysis can help in identifying critical control points, prioritizing additional data collection or research, and verifying and validating a model. Ten sensitivity analysis methods, including four mathematical methods, five statistical methods, and one graphical method, are identified
• Log-Weibull extended regression model: Estimation, sensitivity and residual analysis. Statistical Methodology, 2010. G. Oliveira Silva. 37 Full PDFs related to this paper. READ PAPER. Log-Weibull extended regression model: Estimation, sensitivity and residual analysis. Download. Log-Weibull extended regression model: Estimation, sensitivity.
• Sensitivity Analysis; Regression Analysis; View all Topics. Download as PDF. Set alert. About this page. Meta-regression analysis uses the individual study as the unit of observation in assessing the relationship between the magnitude of the treatment effect and different predictors. Predictors may be study-specific (e.g., the dose or route.
• regression sensitivity analysis. IV regression with more than one proposed IV is called IV regression with overidentifying restrictions because only one valid IV is needed to identify the causal e ect of treatment so more than one IV \overidenti es the causal e ect. IV regression with overidentifying restrictions is often used in economics. A
• Regression Diagnostics and Sensitivity Analysis Regression Diagnostics and Sensitivity Analysis Chapter: (p.206) 6 Regression Diagnostics and Sensitivity Analysis Source: Using R for Data Analysis in Social Sciences Author(s): Quan Li Publisher: Oxford University Pres
• A sensitivity analysis is a repeat of the primary analysis or meta-analysis, substituting alternative decisions or ranges of values for decisions that were arbitrary or unclear. For example, if the eligibility of some studies in the meta-analysis is dubious because they do not contain full details, sensitivity analysis may involve undertaking.
• using logistic regression to evaluate the sensitivity of sto-chastic PVA models, the approach of McCarthy et al. (1995, 1996) has received little attention, and logistic regression re-mains a relatively unused method of analyzing sensitivity. We evaluated logistic regression as a method of sensi-tivity analysis for stochastic PVA using a well-know

Sensitivity Analysis of an OLS Multiple Regression Inference with Respect to Possible Linear Endogeneity in the Explanatory Variables, for Both Modest and for Extremely Large Samples Richard A. Ashley 1 and Christopher F. Parmeter 2,* 1 Department of Economics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24060, USA. regression . Once we have trained our regression, we perform a sensitivity analysis and propagate the uncertainty from the drug-induced channel block recordings into the QT interval. illustrates the work flow of our method: Our input are drug-induced channel block recordings from single cell patch clamp electrophysiology 

Sensitivity analysis gives you insight in how the optimal solution changes when you change the coefficients of the model. After the solver found a solution, you can create a sensitivity report. 1. Before you click OK, select Sensitivity from the Reports section After last week's post, I thought it might be useful to have some practical examples of how to do sensitivity analysis (SA) of complex models (like climate models) with an emulator.SA is one of those things that everyone wants to do at some point, and I'll be able to point people here for code examples The least angle sensitivity (LARS) algorithm is used to realize the global sensitivity analysis of slope stability, while simultaneously considering the effects of several geotechnical parameters on slope stability. In addition, the Sobol sequence is applied in the sample simulation to generate the geotechnical parameters, thereby increasing the accuracy of the results Assesses the effect of measurement errors on the estimated coefficients, which is not accounted for in a standard least squares estimate but is important where regression coefficients are used to apportion effects due to different variables. Also assesses qualitatively and numerically the robustness of the regression fit

### regression - What do people mean by sensitivity analysis

• A sensitivity analysis consists of repeating the estimation of µ at different plausible values of α so as to assess the sensitivity of inferences about µ to assumptions about the missing data mechanism as encoded by α and model (6)
• We describe a fast nonparametric regression-based method for estimating per-patient EVSI that requires only the probabilistic sensitivity analysis sample (i.e., the set of samples drawn from the joint distribution of the parameters and the corresponding net benefits)
• Sensitivity Analysis Of Independent Variables On Traffic Crash Prediction Models By Using Stata Deo Chimba Negative binomial regression Prob >chi2 =0 Log likelihood=-5571.5611 PseudoR2 =0.0673 crashes Coef. IRR Std. Err. z P>|z| [95% Conf.Interval] length 2.39931 11.01560.11006921.80.000 2.1835772.615038.
• g that the initial analysis found a significant effect of the treatment). Liu, Kuramoto, and Stuart describe seven commonly used techniques for sensitivity analysis. Based on the study objectives, these.
• In sensitivity: Global Sensitivity Analysis of Model Outputs. Description Usage Arguments Details Value Author(s) References See Also Examples. View source: R/src.R. Description. src computes the Standardized Regression Coefficients (SRC), or the Standardized Rank Regression Coefficients (SRRC), which are sensitivity indices based on linear or monotonic assumptions in the case of independent.
• Estimation of sensitivity and specificity at fixed specificity and sensitivity: compile a table with estimation of sensitivity and specificity, with a BC a bootstrapped 95% confidence interval (Efron, 1987; Efron & Tibshirani, 1993), for a fixed and prespecified specificity and sensitivity of 80%, 90%, 95% and 97.5% (Zhou et al., 2002)

### Overview of Sensitivity Analysis - What is Sensitivity

in that OLS estimation of multiple regression models with explanatory variables of suspect exogeneity is very common in applied economic work. The present paper proposes a sensitivity analysis for OLS estimation/inference in the pres-ence of unmodeled endogeneity in the explanatory variables of multiple regression models Repeat the sensitivity analysis with new settings until you are satisfied with the results. You could also repeat the parameter optimization. For more information, go to Perform a parameter optimization. Switch the view. Each simulation has two parts: the model and the results. Use the ribbon buttons to toggle between the two views The logistic regression model is then. Ideally we would obtain a sample of data on , and fit the logistic regression model to estimate and . But let us assume that rather than , our dataset contains a misclassified version . The misclassification mechanism can be characterised by the sensitivity and specificity Although other methods exist that take spatial correlations into account when performing inference (Douglas et al. 2000; Elmore et al. 2006; Wilks 1997), the MMR approach is more natural in the present application because the sensitivity analysis is done within a regression framework already

### Sensitivity analysis in logistic regression - Cross Validate

Regression coefficients and regression mapped values are just scaled versions of each other.Correlation coefficients are rank-order correlation, which works well for linear or non-linear correlations.In the Sensitivity Analysis window, when you select Display Significant Inputs Using: Regression (Coefficients), @RISK will display R² (RSqr) in each column Sensitivity analysis of a (scikit-learn) machine learning model - sensitivity_analysis_example.py. Sensitivity analysis of a (scikit-learn) machine learning model - sensitivity_analysis_example.py from sklearn. datasets import make_regression: import pandas as pd: from xgboost import XGBRegressor: import matplotlib. pyplot as plt: import. What is Sensitivity Analysis? Sensitivity Analysis is a tool used in financial modeling What is Financial Modeling Financial modeling is performed in Excel to forecast a company's financial performance. Overview of what is financial modeling, how & why to build a model. to analyze how the different values of a set of independent variables affect a specific dependent variable under certain. Large-scale sensitivity analysis using regression. Leave a reply. In this markdown (source here), we work through an example where we have a lot of variables, but only a few are significant. It demonstrates how different regularized regression techniques, namely ridge and lasso, can be used to tackle this problem with fewer data points than.

Data with missing covariate values but fully observed binary outcomes are an important subset of the missing data challenge. Common approaches are complete case analysis (CCA) and multiple imputation (MI). While CCA relies on missing completely at random (MCAR), MI usually relies on a missing at ran 1. Sensivity Analysis in Python Codehttps://drive.google.com/open?id=1-WwbgV_YeS_ZcZEfj8WbPrucAoTO9PsA2. Linear Programming in Python Lecture Videohttps://ww.. Meta-regression provides a framework for replication and offers a sensitivity analysis for model specification. There are a number of strategies for identifying and coding empirical observational data. Meta-regression models can be extended for modeling within-study dependence, excess heterogeneity and publication selection practitioners to conduct sensitivity analysis of the robustness of conclusions on the quantile regression coe¢ cient to the independent censoring mechanism. Bootstrap con-dence sets are also constructed. In-terpreting the dependent variable and the censoring variable in our censored quantile regression model a

Sensitivity and specificity are statistical terms but would not apply to a linear regression with the standard model. Logistic regression would include a sensitivity analysis. A more detailed description of your problem is required The methodology we develop in this paper allows practitioners to conduct sensitivity analysis of the robustness of conclusions on the quantile regression coefficient to the independent censoring mechanism. Bootstrap confidence sets are also constructed Implements a suite of sensitivity analysis tools that extends the traditional omitted variable bias framework and makes it easier to understand the impact of omitted variables in regression models, as discussed in Cinelli, C. and Hazlett, C. (2020), Making Sense of Sensitivity: Extending Omitted Variable Bias. Journal of the Royal Statistical Society, Series B (Statistical Methodology) <doi.

### How Is Sensitivity Analysis Used? - investopedia

Probabilistic Sensitivity Analysis with R. Posted on February 9, 2018 by Health Economics with R in R bloggers | 0 Comments parameters from regression models due to the multivariate central limit theorem. Decision-analytic models rely heavily on estimates from regression models. For example, time to treatment discontinuation and patient. The sensemakr package implements a suite of sensitivity analysis tools that makes it easier to understand the impact of omitted variables in linear regression models, as discussed in Cinelli and Hazlett (2020). Details. The main function of the package is sensemakr, which computes the mos There are several reasons to perform a sensitivity analysis by entering multiple values for a particular input variable. First, you might not know the exact value of a variable. By specifying a range of values, you can determine how important that variable is, and how the solution changes depending on its value ### Regression modelling and other methods to control

Regression Sensitivity Analysis and Bounded-Influence Estimation* ROYE. WELSCH SLOAN SCHOOL OF MANAGEMENT MASSACHUSETTS INSTITUTE OF TECHNOLOGY CAMBRIDGE, MASSACHUSETTS 1. Introduction Economists and others have been building and using econometric models for many years. A subset of these builders and users hasalways bee In a regression analysis setting, the consequences of falsely assuming independent censoring on parameter estimates are not clear. Neither the direction nor the magnitude of the potential bias can be easily predicted. We provide an approach to do sensitivity analysis for the widely used Cox proportional hazards models Sensitivity Analysis for Instrumental Variables Regression With Overidentifying Restrictions Dylan S. Small Instrumental variables regression (IV regression) is a method for making causal inferences about the effect of a treatment based on a View Sensitivity Analysis and Regression.docx from LAW 100 at St. John's University. One of the significant strengths of the forecasting models displayed in chapter 6 is that it gives out a bette I'm trying to run a one-way sensitivity analysis on a regression model to show what the results would be in a larger model which incorporates its outputs if values are varied over their confidence intervals. I get relatively constrained variation over almost all of the other parameters in the model, however for this regression model, I'm seeing.

### Sensitivity Analysis and Model Validation SpringerLin

Sensitivity is the probability that a test will indicate 'disease' among those with the disease: Sensitivity: A/(A+C) × 100 . Specificity is the fraction of those without disease who will have a negative test result: Specificity: D/(D+B) × 100 . Sensitivity and specificity are characteristics of the test. The population does not affect the. Regression discontinuity (RD) analysis is a rigorous nonexperimental1approach that can be used to estimate program impacts in situations in which candidates are selected for treatment based on whether their value for a numeric rating exceeds a designated threshold or cut-point In summary, sensitivity analysis is a prediction of how a specific percentage increase in price will lead to a subsequent percentage decrease in the quantity of products sold. On the other hand, scenario analysis entails making several premises about different independent variables and then examining how the outcome changes

### How to conduct sensitivity analysis in multiple linear

The regression coefficients are calculated by a process called stepwise multiple regression. The main idea is that the longer the bar or the larger the coefficient, the greater the impact that particular input has on the output that you are analyzing The following section describes sensitivity analysis for the MAR assumption, followed by two examples: one to specify sets of observations for imputation models and the other to adjust imputed values for a subset of observations. SENSITIVITY ANALYSIS FOR THE MAR ASSUMPTION Multiple imputation usually assumes that the data are missing at random. Estimate marginal quantile regression coefficients instead of conditional on random effects. Allows for sensitivity analysis which is essential for the analysis of missing data (NAS 2010). Allows the missingness to be non-ignorable. Recursive integration simplifies computation and can be implemented in high dimensions

### Extending sensitivity analysis using regression to

In addition, a sensitivity analysis was done of a 100 MW CC-OTEC plant to estimate net power and efficiency regarding variations of water velocity, water temperature, and water pipe diameter, and a direct relationship was found between water mass flow and working fluid mass flow, which means that decreasing water mass flow will lower the. Therefore, regression diagnostics help us to recognize those schools that are of interest to study by themselves. The last type of diagnostic statistics is related to coefficient sensitivity. It concerns how much impact each observation has on each parameter estimate. Similar to OLS regression, we also have dfbeta's for logistic regression ### How can I do a sensitivity analysis for a binary logistic

Sensitivity analysis can be used to investigate the model response to these uncertain input variables. Such studies are particularly usefhl to identify the most influential The regression coefficient, which is the partial derivative of the dependent variable with respect to each of the independent variables, is a measur Single-Variable Sensitivity Analysis Excel Data Tables. The first step in creating a data table that predicts force as a result of changing temperature is to create column of varying temperature somewhere on the worksheet. In the cell immediately above and to the right, calculate the result or link to the cell that already contains the result

Sensitivity Analysis: Standard Regression Coefficients. UQ with UQLab. Community Q&A and How To. sensitivity. AHz. July 10, 2020, 8:34pm #1. Dear All, I am trying to run SRC from sample-based sensitivity analysis. I've got 1000 inputs and 200 outputs, and the sample size is 10000. I intend to measure how much the dependant variable varies to. A study of the performance of sensitivity analysis techniques on different test models was performed by Iman and Helton [14,15]. These studies pointed out the effectiveness of the regression based non-para- metric techniques such as the Standardised Rank Regression Coefficient (SRRC

A sensitivity analysis is a technique used to determine how different values of an independent variable impact a particular dependent variable under a given set of assumptions. This technique is used within specific boundaries that depend on one or more input variables, such as the effect that changes in interest rates have on bond prices Example of how to build a sensitivity analysis table in Excel to evaluate how changing two inputs simultaneously will affect an output (profit). This is one. What is Sensitivity Analysis? Sensitivity analysis is defined as the study of how uncertainty in the output of a model can be attributed to different sources of uncertainty in the model input.In the context of using Simulink ® Design Optimization™ software, sensitivity analysis refers to understanding how the parameters and states (optimization design variables) of a Simulink model. Abstract A vast literature uses cross-country regressions to search for empirical linkages between long-run growth rates and a variety of economic policy, political, and institutional indicators. This paper examines whether the conclusions from existing studies are robust or fragile to small changes in the conditioning information set

Sensitivity analysis is widely used in capital budgeting decisions to assess how the change in such inputs as sales, variable costs, fixed costs, cost of capital, and marginal tax rate will affect such outputs as net present value (NPV) of a project, internal rate of return (IRR), and discounted payback period This example illustrates sensitivity analysis in multiple imputation under the MNAR assumption in which you search for a tipping point that reverses the study conclusion. Suppose that a pharmaceutical company is conducting a clinical trial to test the efficacy of a new drug Robust regression offers an alternative to OLS regression that is less sensitive to outliers and still defines a linear relationship between the outcome and the predictors. Note that robust regression does not address leverage. This page shows an example of robust regression analysis in Stata with footnotes explaining the output How to do a sensitivity analysis in Excel with two input variables

The interest on the analysis of the zero-one augmented beta regression (ZOABR) model has been increasing over the last few years. In this work, we developed a Bayesian inference for the ZOABR model, providing some contributions, namely: we explored the use of Jeffreys-rule and independence Jeffreys prior for some of the parameters, performing a sensitivity study of prior choice, comparing. Sensitivity analysis of the influence of solar wind parameters on high-latitude current patterns: A multiple linear regression model of solar wind-magnetosphere coupling correlations using Godhavn magnetometer dat 3/17/2020 Advanced Regression Analysis.ipynb - Colaboratory 2/18 The First Equation describes the Random Component, here it is the Gaussian Distribution The second equation is the systematic component which has the covariates and the coe±cients.This is the Linear Predictor The third equation links the random component to the Link Function The above set of equations are a generic. Power analysis is an important aspect of experimental design. It allows us to determine the sample size required to detect an effect of a given size with a given degree of confidence. Conversely, it allows us to determine the probability of detecting an effect of a given size with a given level of confidence, under sample size constraints

Differential Sensitivity Analysis (PD). Differential analyses, also referred to as the direct method, are structured on the behavior of the model for a base-case scenario, e.g., all parameters set equal to their mean value. Differential sensitivity analysis is based on partial differentiation of the aggregated model. When an explicit algebraic. A sensitivity analysis excluding diabetic individuals from the models is presented in Additional file 1: Table S4b, showing borderline association between the MCAi and ischemic changes (adjusted OR = 1.6, 95% CI 0.9-2.7, p = 0.09) for Q 1 vs Q 2-4. All-cause and cause specific mortalit The estimates using the spatial regression test were evaluated against the measurements for stations within the four states (California, Nevada, Utah, and Nebraska) for the year 2000. The settings used for the sensitivity analysis of the spatial regression test are shown in Table 1. For example, in the radius analysis, the length of the time.

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