ࡱ> {` RbjbjFF 4,,{J1   499989:4Zl; D(EEEE,!HHXYYYYYYY$Zh9]Y JEEJJYEEYRRRJ8E EYRJYRR:X, NXE`; 9Kj:X YY0ZDX ]\L]NX] NXL%I>cI,RI$I!%I%I%IYY0R^%I%I%IZJJJJ444494449444  Introductory Econometrics: Using Monte Carlo Simulation with Microsoft Excel by Humberto Barreto and Frank Howland Cambridge University Press  HYPERLINK "http://www.cambridge.org/9780521843195" www.cambridge.org/9780521843195  HYPERLINK "http://www.wabash.edu/econometrics" www.wabash.edu/econometrics Preface User Guide Conventions and Organization Preparing and Working with Microsoft Excel Chapter 1: Introduction Definition of Econometrics Regression Analysis  HYPERLINK "Ch01Introduction/ExcelFiles/Cig.xls" Cig.xls Conclusion Exercises References Part 1: Description Chapter 2: Correlation 2.1 Introduction 2.2 Correlation Basics  HYPERLINK "Ch02Correlation/ExcelFiles/Correlation.xls" Correlation.xls 2.3 Correlation Dangers  HYPERLINK "Ch02Correlation/ExcelFiles/Correlation.xls" Correlation.xls  HYPERLINK "Ch02Correlation/ExcelFiles/IMRGDP.xls" IMRGDP.xls 2.4 Ecological Correlation  HYPERLINK "Ch02Correlation/ExcelFiles/EcolCorr.xls" EcolCorr.xls  HYPERLINK "Ch02Correlation/ExcelFiles/EcolCorrCPS.xls" EcolCorrCPS.xls 2.5 Conclusion 2.6 Exercises References Chapter 3: Pivot Tables 3.1 Introduction 3.2 The Basic Pivot Table  HYPERLINK "../Basic%20Tools/InternetData/CPS/IndianaFTWorkers.xls" IndianaFTWorkers.xls  HYPERLINK "../Basic%20Tools/ExcelAddIns/Histogram/Histogram.doc" Histogram.xla (Excel add-in) 3.3 The Crosstab and Conditional Average  HYPERLINK "../Basic%20Tools/InternetData/CPS/IndianaFTWorkers.xls" IndianaFTWorkers.xls 3.4 PivotTables and the Conditional Mean Function  HYPERLINK "Ch03PivotTables/ExcelFiles/EastNorthCentralFTWorkers.xls" EastNorthCentralFTWorkers.xls 3.5 Conclusion 3.6 Exercises References Chapter 4: Computing the OLS Regression Line 4.1 Introduction 4.2 Fitting the Ordinary Least Squares Regression Line  HYPERLINK "Ch04ComputingRegression/ExcelFiles/Reg.xls" Reg.xls 4.3 Least Squares Formulas  HYPERLINK "Ch04ComputingRegression/ExcelFiles/Reg.xls" Reg.xls 4.4 Fitting the Regression Line in Practice  HYPERLINK "Ch04ComputingRegression/ExcelFiles/Reg.xls" Reg.xls 4.5 Conclusion 4.6 Exercises References Appendix: Deriving the Least Squares Formulas Chapter 5: Interpreting OLS Regression 5.1 Introduction 5.2 Regression as Double Compression  HYPERLINK "Ch05InterpretingRegression/ExcelFiles/DoubleCompression.xls" DoubleCompression.xls  HYPERLINK "Ch03PivotTables/ExcelFiles/EastNorthCentralFTWorkers.xls" EastNorthCentralFTWorkers.xls 5.3 Galton and Two Regression Lines  HYPERLINK "Ch05InterpretingRegression/ExcelFiles/TwoRegressionLines.xls" TwoRegressionLines.xls 5.4 Properties of the Sample Average and Regression Line  HYPERLINK "Ch05InterpretingRegression/ExcelFiles/OLSFormula.xls" OLSFormula.xls 5.5 Residuals and Root Mean Square Error  HYPERLINK "Ch05InterpretingRegression/ExcelFiles/ResidualPlot.xls" ResidualPlot.xls  HYPERLINK "Ch05InterpretingRegression/ExcelFiles/RMSE.XLS" RMSE.xls 5.6 R-squared (R2)  HYPERLINK "Ch05InterpretingRegression/ExcelFiles/RSquared.xls" RSquared.xls 5.7 Limitations of Data Description with Regression  HYPERLINK "Ch05InterpretingRegression/ExcelFiles/Anscombe.xls" Anscombe.xls  HYPERLINK "Ch05InterpretingRegression/ExcelFiles/IMRGDPReg.XLS" IMRGDPReg.xls  HYPERLINK "Ch05InterpretingRegression/ExcelFiles/SameRegLineDifferentData.xls" SameRegLineDifferentData.xls  HYPERLINK "Ch05InterpretingRegression/ExcelFiles/HourlyEarnings.xls" HourlyEarnings.xls 5.8 Conclusion 5.9 Exercises References Appendix: Proof that the Sample Average is a Least Squares Estimator Chapter 6: Functional Form of the Regression 6.1 Introduction 6.2 Understanding Functional Form via an Econometric Fable  HYPERLINK "Ch06FunctionalForm/Excel%20Files/Galileo.xls" Galileo.xls 6.3 Exploring Two Other Functional Forms  HYPERLINK "Ch06FunctionalForm/Excel%20Files/IMRGDPFunForm.xls" IMRGDPFunForm.xls 6.4 The Earnings Function  HYPERLINK "Ch06FunctionalForm/Excel%20Files/SemiLogEarningsFn.xls" SemiLogEarningsFn.xls 6.5 Elasticity 6.6 Conclusion 6.7 Exercises References Appendix: A Catalog of Functional Forms  HYPERLINK "Ch06FunctionalForm/Excel%20Files/FuncFormCatalog.xls" FuncFormCatalog.xls Chapter 7: Multiple Regression 7.1 Introduction 7.2 Introducing Multiple Regression  HYPERLINK "Ch07MultipleRegression/ExcelFiles/MultiReg.xls" MultiReg.xls 7.3 Improving Description via Multiple Regression  HYPERLINK "Ch07MultipleRegression/ExcelFiles/MultiReg.xls" MultiReg.xls 7.4 Multicollinearity  HYPERLINK "Ch07MultipleRegression/ExcelFiles/Multicollinearity.xls" Multicollinearity.xls 7.5 Conclusion 7.6 Exercises References Appendix: The Multivariate Least Squares Formula and the Omitted Variable Rule Chapter 8: Dummy Variables 8.1 Introduction 8.2 Defining and Using Dummy Variables  HYPERLINK "Ch08DummyVariables/ExcelFiles/Female.xls" Female.xls 8.3 Properties of Dummy Variables 8.4 Dummy Variables as Intercept Shifters  HYPERLINK "Ch08DummyVariables/ExcelFiles/Female.xls" Female.xls 8.5 Dummy Variable Interaction Terms 8.6 Conclusion 8.7 Exercises References Part 2: Inference Chapter 9: Monte Carlo Simulation 9.1 Introduction 9.2 Random Number Generation Theory  HYPERLINK "Ch09MonteCarloSimulation/ExcelFiles/RNGTheory.xls" RNGTheory.xls 9.3 Random Number Generation in Practice  HYPERLINK "Ch09MonteCarloSimulation/ExcelFiles/RNGPractice.xls" RNGPractice.xls 9.4 Monte Carlo Simulation: An Example  HYPERLINK "Ch09MonteCarloSimulation/ExcelFiles/MonteCarlo.xls" MonteCarlo.xls 9.5 The Monte Carlo Simulation Add-In  HYPERLINK "Ch09MonteCarloSimulation/ExcelFiles/MonteCarlo.xls" MonteCarlo.xls  HYPERLINK "../Basic%20Tools/ExcelAddIns/MCSim/MCSim.doc" MCSim.xla (Excel add-in)  HYPERLINK "../Basic%20Tools/ExcelAddIns/MCSimSolver/MCSimSolver.doc" MCSimSolver.xla (Excel add-in) 9.6 Conclusion 9.7 Exercises References Chapter 10: Review of Statistical Inference 10.1 Introduction 10.2 Introducing Box Models for Chance Processes 10.3 The Coin Flip Box Model  HYPERLINK "Ch10InferentialStatsReview/Excel%20Files/BoxModel.xls" BoxModel.xls 10.4 The Polling Box Model  HYPERLINK "Ch10InferentialStatsReview/Excel%20Files/PresidentialHeights.xls" PresidentialHeights.xls 10.5 Hypothesis Testing  HYPERLINK "../Basic%20Tools/ExcelAddIns/PValueCalculator/PValue.doc" PValue.xla (Excel add-in) 10.6 Consistent Estimators  HYPERLINK "Ch10InferentialStatsReview/Excel%20Files/Consistency.xls" Consistency.xls 10.7 The Algebra of Expectations  HYPERLINK "Ch10InferentialStatsReview/Excel%20Files/AlgebraofExpectations.xls" AlegbraofExpectations.xls 10.8 Conclusion 10.9 Exercises References Appendix: The Normal Approximation Chapter 11: The Measurement Box Model 11.1 Introduction 11.2 Introducing the Problem 11.3 The Measurement Box Model 11.4 Monte Carlo Simulation  HYPERLINK "Ch11MeasurementBoxModel/ExcelFiles/Measure.xls" Measure.xls 11.5 Applying the Box Model  HYPERLINK "Ch11MeasurementBoxModel/ExcelFiles/Measure.xls" Measure.xls 11.6 Hookes Law  HYPERLINK "Ch11MeasurementBoxModel/ExcelFiles/HookesLaw.xls" HookesLaw.xls 11.7 Conclusion 11.8 Exercises References Chapter 12: Comparing Two Populations 12.1 Introduction 12.2 Two Boxes 12.3 Monte Carlo Simulation of a Two Box Model  HYPERLINK "Ch12ComparingTwoPop/ExcelFiles/TwoBoxModel.xls" TwoBoxModel.xls 12.4 A Real Example: Education and Wages  HYPERLINK "Ch12ComparingTwoPop/ExcelFiles/CPS90Workers.xls" CPS90Workers.xls 12.5 Conclusion 12.6 Exercises  HYPERLINK "Ch12ComparingTwoPop/ExcelFiles/CPS90ExpWorkers.xls" CPS90ExpWorkers.xls References Chapter 13: The Classical Econometric Model 13.1 Introduction 13.2 Introducing the CEM via a Skiing Example  HYPERLINK "Ch13ClassicalEconometricModel/ExcelFiles/Skiing.xls" Skiing.xls 13.3 Implementing the CEM via a Skiing Example  HYPERLINK "Ch13ClassicalEconometricModel/ExcelFiles/Skiing.xls" Skiing.xls 13.4 CEM Requirements 13.5 Conclusion 13.6 Exercises References Chapter 14: The GaussMarkov Theorem 14.1 Introduction 14.2 Linear Estimators  HYPERLINK "Ch14GaussMarkov/ExcelFiles/GaussMarkovUnivariate.xls" GaussMarkovUnivariate.xls 14.3 Choosing an Estimator  HYPERLINK "Ch14GaussMarkov/ExcelFiles/GaussMarkovUnivariate.xls" GaussMarkovUnivariate.xls 14.4 Proving the Gauss Markov Theorem in the Univariate Case 14.5 Linear Estimators in Regression Analysis  HYPERLINK "Ch14GaussMarkov/ExcelFiles/GaussMarkovBivariate.xls" GaussMarkovBivariate.xls 14.6 OLS is BLUE: The Gauss Markov Theorem for the Bivariate Case  HYPERLINK "Ch14GaussMarkov/ExcelFiles/GaussMarkovBivariate.xls" GaussMarkovBivariate.xls 14.7 Using the Algebra of Expectations  HYPERLINK "Ch14GaussMarkov/ExcelFiles/GaussMarkovUnivariate.xls" GaussMarkovUnivariate.xls  HYPERLINK "Ch14GaussMarkov/ExcelFiles/GaussMarkovBivariate.xls" GaussMarkovBivariate.xls 14.8 Conclusion 14.9 Exercises References Chapter 15: Understanding the Standard Error 15.1 Introduction 15.2 SE Intuition  HYPERLINK "Ch15UnderstandingSE/ExcelFiles/SEb1OLS.xls" SEb1OLS.xls 15.3 The Estimated SE  HYPERLINK "Ch15UnderstandingSE/ExcelFiles/SEb1OLS.xls" SEb1OLS.xls 15.4 The Determinants of the SE of the OLS Sample Slope  HYPERLINK "Ch15UnderstandingSE/ExcelFiles/SEb1OLS.xls" SEb1OLS.xls 15.5 Estimating the SD of the Errors  HYPERLINK "Ch15UnderstandingSE/ExcelFiles/EstimatingSDErrors.xls" EstimatingSDErrors.xls 15.6 The Standard Error of the Forecast and the Standard Error of the Forecast Error  HYPERLINK "Ch15UnderstandingSE/ExcelFiles/SEForecast.xls" SEForecast.xls 15.7 Conclusion 15.8 Exercises References Chapter 16: Confidence Intervals and Hypothesis Testing 16.1 Introduction 16.2 Distributions of OLS Regression Statistics  HYPERLINK "Ch16ConfIntervalsHypoTest/ExcelFiles/LinestRandomVariables.xls" LinestRandomVariables.xls 16.3 Understanding Confidence Intervals HYPERLINK "Ch16ConfIntervalsHypoTest/ExcelFiles/ConfidenceIntervals.xls"ConfidenceIntervals.xls 16.4 The Logic of Hypothesis Testing  HYPERLINK "Ch16ConfIntervalsHypoTest/ExcelFiles/HypothesisTest.xls" HypothesisTest.xls 16.5 Z and t Tests HYPERLINK "Ch16ConfIntervalsHypoTest/ExcelFiles/ConfidenceIntervals.xls"ConfidenceIntervals.xls  HYPERLINK "Ch16ConfIntervalsHypoTest/ExcelFiles/ZandTTests.xls" ZandTTests.xls 16.6 A Practical Example  HYPERLINK "Ch16ConfIntervalsHypoTest/ExcelFiles/CigDataInference.xls" CigDataInference.xls 16.7 Conclusion 16.8 Exercises  HYPERLINK "Ch06FunctionalForm/Excel%20Files/SemiLogEarningsFn.xls" SemiLogEarningsFn.xls References Chapter 17: Joint Hypothesis Testing 17.1 Introduction 17.2 Restricted Regression  HYPERLINK "Ch17JointHypothesisTesting/ExcelFiles/NoInterceptBug.xls" NoInterceptBug.xls 17.3 The Chi-Square Distribution  HYPERLINK "Ch17JointHypothesisTesting/ExcelFiles/ChiSquareDist.xls" ChiSquareDist.xls 17.4 The F-Distribution  HYPERLINK "Ch17JointHypothesisTesting/ExcelFiles/FDist.xls" FDist.xls 17.5 An F-test: The Galileo Example  HYPERLINK "Ch17JointHypothesisTesting/ExcelFiles/FDistGalileo.xls" FDistGalileo.xls 17.6 F- and t-Tests for Equality of Two Parameters  HYPERLINK "Ch17JointHypothesisTesting/ExcelFiles/FDistFoodStamps.xls" FDistFoodStamps.xls 17.7 F-Test for Multiple Parameters  HYPERLINK "Ch17JointHypothesisTesting/ExcelFiles/FDistEarningsFn.xls" FDistEarningsFn.xls 17.8 The Consequences of Multicollinearity  HYPERLINK "Ch17JointHypothesisTesting/ExcelFiles/CorrelatedEstimates.xls" CorrelatedEstimates.xls 17.9 Conclusion 17.10 Exercises  HYPERLINK "Ch17JointHypothesisTesting/ExcelFiles/MyMonteCarlo.xls" MyMonteCarlo.xls References Chapter 18: Omitted Variable Bias 18.1 Introduction 18.2 Why Omitted Variable Bias is Important 18.3 Omitted Variable Bias Defined and Demonstrated  HYPERLINK "Ch18OmittedVarBias/ExcelFiles/SkiingOVB.xls" SkiingOVB.xls 18.4 A Real Example of Omitted Variable Bias  HYPERLINK "Ch18OmittedVarBias/ExcelFiles/ComputerUse1997.xls" ComputerUse1997.xls 18.5 Random Xs: A More Realistic Data Generation Process  HYPERLINK "Ch18OmittedVarBias/ExcelFiles/ComputerUse1997.xls" ComputerUse1997.xls 18.6 Conclusion 18.7 Exercises References Chapter 19: Heteroskedasticity 19.1 Introduction 19.2 A Univariate Example of Heteroskedasticity  HYPERLINK "Ch19Heteroscedasticity/ExcelFiles/Het.xls" Het.xls 19.3 A Bivariate Example of Heteroskedasticity  HYPERLINK "Ch19Heteroscedasticity/ExcelFiles/Het.xls" Het.xls 19.4 Diagnosing Heteroskedasticity with the B-P Test  HYPERLINK "Ch19Heteroscedasticity/ExcelFiles/Het.xls" Het.xls  HYPERLINK "Ch19Heteroscedasticity/ExcelFiles/BPSampDist.xls" BPSampDist.xls 19.5 Dealing with Heteroskedasticity: Robust Standard Errors  HYPERLINK "Ch19Heteroscedasticity/ExcelFiles/HetRobustSE.xls" HetRobusSE.xls  HYPERLINK "../Basic%20Tools/ExcelAddIns/OLSRegression/OLSRegression.doc" OLSRegression.xla (Excel add-in) 19.6 Correcting for Heteroskedasticity: Generalized Least Squares  HYPERLINK "Ch19Heteroscedasticity/ExcelFiles/HetGLS.xls" HetGLS.xls 19.7 A Real Example of Heteroskedasticity: The Earnings Function  HYPERLINK "Ch19Heteroscedasticity/ExcelFiles/WagesOct97.xls" WagesOct97.xls 19.8 Conclusion 19.9 Exercises References Chapter 20: Autocorrelation 20.1 Introduction 20.2 Understanding Autocorrelation  HYPERLINK "Ch20Autocorrelation/ExcelFiles/AutoCorr.xls" AutoCorr.xls 20.3 Consequences of Autocorrelation  HYPERLINK "Ch20Autocorrelation/ExcelFiles/AutoCorr.xls" AutoCorr.xls 20.4 Diagnosing Autocorrelation  HYPERLINK "Ch20Autocorrelation/ExcelFiles/AutoCorr.xls" AutoCorr.xls 20.5 Correcting Autocorrelation  HYPERLINK "Ch20Autocorrelation/ExcelFiles/AutoCorr.xls" AutoCorr.xls 20.6 Conclusion  HYPERLINK "Ch20Autocorrelation/ExcelFiles/CPIMZM.xls" CPIMZM.xls  HYPERLINK "Ch20Autocorrelation/ExcelFiles/Luteinizing.xls" Luteinizing.xls 20.7 Exercises  HYPERLINK "Ch20Autocorrelation/ExcelFiles/Misspecification.xls" Misspecification.xls  HYPERLINK "Ch20Autocorrelation/ExcelFiles/FreeThrowAutoCorr.xls" FreeThrowAutoCorr.xls References Chapter 21: Topics in Time Series 21.1 Introduction 21.2 Trends in Time Series Models  HYPERLINK "Ch21TimeSeriesTopics/ExcelFiles/IndiaPopulation.xls" IndiaPopulation.xls  HYPERLINK "Ch21TimeSeriesTopics/ExcelFiles/ExpGrowthModel.xls" ExpGrowthModel.xls  HYPERLINK "Ch21TimeSeriesTopics/ExcelFiles/AnnualGDP.xls" AnnualGDP.xls  HYPERLINK "Ch21TimeSeriesTopics/ExcelFiles/Spurious.xls" Spurious.xls 21.3 Dummy Variables in Time Series Models  HYPERLINK "Ch21TimeSeriesTopics/ExcelFiles/TimeSeriesDummyVariables.xls" TimeSeriesDummyVariables.xls  HYPERLINK "Ch21TimeSeriesTopics/ExcelFiles/CoalMining.xls" CoalMining.xls 21.4 Seasonal Adjustment  HYPERLINK "Ch21TimeSeriesTopics/ExcelFiles/SeasonalTheory.xls" SeasonalTheory.xls  HYPERLINK "Ch21TimeSeriesTopics/ExcelFiles/SeasonalPractice.xls" SeasonalPractice.xls 21.5 Stationarity  HYPERLINK "Ch21TimeSeriesTopics/ExcelFiles/Stationarity.xls" Stationarity.xls 21.6 Weak Dependence  HYPERLINK "Ch21TimeSeriesTopics/ExcelFiles/Stationarity.xls" Stationarity.xls  HYPERLINK "Ch21TimeSeriesTopics/ExcelFiles/Spurious.xls" Spurious.xls 21.7 Lagged Dependent Variables  HYPERLINK "Ch21TimeSeriesTopics/ExcelFiles/PartialAdjustment.xls" PartialAdjustment.xls 21.8 Money Demand  HYPERLINK "Ch21TimeSeriesTopics/ExcelFiles/MoneyDemand.xls" MoneyDemand.xls  HYPERLINK "Ch21TimeSeriesTopics/ExcelFiles/LaggedDepVar.xls" LaggedDepVar.xls 21.9 Comparing Forecasts using Different Models of the DGP  HYPERLINK "Ch21TimeSeriesTopics/ExcelFiles/AnnualGDP.xls" AnnualGDP.xls  HYPERLINK "Ch21TimeSeriesTopics/ExcelFiles/ForecastingGDP.xls" ForecastingGDP.xls 21.10 Conclusion 21.11 Exercises References Chapter 22: Dummy Dependent Variable Models 22.1 Introduction 22.2 Developing Intuition about Dummy Dependent Variable Models  HYPERLINK "Ch22DummyDepVar/ExcelFiles/Raid.xls" Raid.xls 22.3 The Campaign Contributions Example  HYPERLINK "Ch22DummyDepVar/ExcelFiles/CampCont.xls" CampCont.xls 22.4 A DDV Box Model  HYPERLINK "Ch22DummyDepVar/ExcelFiles/Raid.xls" Raid.xls  HYPERLINK "Ch22DummyDepVar/ExcelFiles/CampCont.xls" CampCont.xls 22.5 The Linear Probability Model (OLS with a Dummy Dependent Variable)  HYPERLINK "Ch22DummyDepVar/ExcelFiles/CampCont.xls" CampCont.xls  HYPERLINK "Ch22DummyDepVar/ExcelFiles/LPMMonteCarlo.xls" LPMMonteCarlo.xls 22.6 Non-Linear Least Squares Applied to Dummy Dependent Variable Models  HYPERLINK "Ch22DummyDepVar/ExcelFiles/NLLSFit.xls" NLLSFit.xls  HYPERLINK "Ch22DummyDepVar/ExcelFiles/NLLSMCSim.xls" NLLSMCSim.xls 22.7 Interpreting NLLS Estimates  HYPERLINK "Ch22DummyDepVar/ExcelFiles/NLLSFit.xls" NLLSFit.xls 22.8 Is there Mortgage Discrimination?  HYPERLINK "Ch22DummyDepVar/ExcelFiles/MortDisc.xls" MortDisc.xls  HYPERLINK "Ch22DummyDepVar/ExcelFiles/MortDiscMCSim.xls" MortDiscMCSim.xls  HYPERLINK "../Basic%20Tools/ExcelAddIns/DummyDepVar/DDV.doc" DDV.xla (Excel add-in)  HYPERLINK "../Basic%20Tools/ExcelAddIns/DDVGaussNewton/DDVGaussNewton.doc" DDVGN.xla (Excel add-in) 22.9 Conclusion 22.10 Exercises References Chapter 23: Bootstrap 23.1 Introduction 23.2 Bootstrapping the Sample Percentage  HYPERLINK "Ch23Bootstrap/ExcelFiles/PercentageBootstrap.xls" PercentageBootstrap.xls 23.3 Paired XY Bootstrap  HYPERLINK "Ch23Bootstrap/ExcelFiles/PairedXYBootstrap.xls" PairedXYBootstrap.xls 23.4 The Bootstrap Add-In  HYPERLINK "Ch23Bootstrap/ExcelFiles/PairedXYBootstrap.xls" PairedXYBootstrap.xls  HYPERLINK "../Basic%20Tools/ExcelAddIns/Bootstrap/Bootstrap.doc" Bootstrap.xla (Excel add-in) 23.5 Bootstrapping R2  HYPERLINK "Ch23Bootstrap/ExcelFiles/BootstrapR2.xls" BootstrapR2.xls 23.6 Conclusion 23.7 Exercises References Chapter 24: Simultaneous Equations 24.1 Introduction 24.2 Simultaneous Equations Model Example 24.3 Simultaneity Bias with OLS  HYPERLINK "Ch24SimultaneousEquations/ExcelFiles/SimEq.xls" SimEq.xls 24.4 Two Stage Least Squares  HYPERLINK "Ch24SimultaneousEquations/ExcelFiles/SimEq.xls" SimEq.xls 24.5 Conclusion 24.6 Exercises References     Page  PAGE 1 of  NUMPAGES 11 "MNPTVyz   ! < = > ? @ G H I M T Ⱦ}yuqjfh C hhyahyahLhZhA`7 huuhf5Mhf5Mjhk>Uh4yhk>0Jjhk>U hk>hk>jhk>Uhk>h  hf5MCJ hf5M5CJh0Jh0J6CJ$H*aJ$h0Jhf5M6CJ$aJ$h0Jh0J6CJ$aJ$h0Jhf5MCJ$aJ$(PQTVyz> ? @ H I T q = gd  & Fgdya & Fgdya`$a$gdk>$a$$a${RRR  2 3 4 ; < = G H R \ ] ^ s t    # $ \ ] ^ m n o r s ̷̾hydhG0Jj=h7UhGjvh7Ujh7Uhf5M huuhf5M hhf5M hh Ch Ch-hydh 0Jjh7UhydjhydUh hLhya4= H R ] ^ r t  o  i { C gdpO`gd C ^`gd & Fgdya     V W X g h i y z * + , @ A B C F G ɾܷܙ陝hydhB0Jj]h7UhBhFjh7Uhf5M huuhf5M hhf5M hh-hh-h Cjh7Uh hydh 0JjhydUjh7Uhyd03456jmn &056"#$+,-[^_׷װϏτ׀xjh;|6Uh;|6j h7Uj h7Uhf5Mh2{ huuhf5M hhf5M hh ChhydhpO0Jj h7UhydhpOh Ch hGhydhyd0JjhydUj4h7U/ 6j6I-[)<c4Z p@ ugdG()cfg234Z]^CDESؾؾ{ؾpjh7Ujh7Uhydh0Jj0 h7UhhydhpO0JjG h7UhydjhydUhpOhf5Mh2{ huuhf5M hhf5Mh C hh;|6hydh;|60Jjh;|6Uj h/u[U,U(=rFWgt; (STU&'(9:;<@A   abcpquv﷯jh7Uj5h7Uj^h7Ujh7Uh Ch CH*h;|6h C6jh7UhydhpO0JhydhG0Jjh7UhydhGh ChpOjhydU3012DEFLVW;>?yz{  +,pqrĽ󭩞󭩊jh7Ujh7UhLhpO0Jjh7UhLjhLUhf5Mh2{ hhf5M hhf5Mhch;|6h h ChydhpO0Jjh7UhydhpOjhydU189:=>MNOPQ\dop,-ijkwxlȶvrhshLhs0Jjh7UhLhL0Jjh7UhLhpO0Jj4h7Uh MhpO hh M hhf5M hhf5M hhpO h;|60JhLhG0Jj]h7UhLjhLUhG,OPp*ykl /[p^pgds^gd:Q`gdL`  ^_  %/0BClm-./>?ilm~zhfjh7UhLhkl[0Jj9h7Uhkl[ hRhf5M hhR hh hhf5MhLhL0Jjvh7UhLhs0Jjh7UhLjhLUhf5Mhs hhf5M-  0Ci@i=  $ 1 2 ` t !:!!!("gdR+,-;<=@A{|}  2 3 ? 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