《计量经济学》ch-02-wooldridg.ppt
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1、Chapter 2,The Simple Regression Model,Wooldridge:Introductory Econometrics:A Modern Approach,5eInstructed by professor Yuan,Huiping,Chapter 2 The Simple Regression Model,2.1 Definition of the Simple Regression Model,2.2 Deriving the Ordinary Least Squares Estimates,2.3 Algebraic Properties of OLS on
2、 Any Sample of Data,2.4 Units of Measurement and Functional Form,The End,2.5 Expected Values and Variances of the OLS Estimators,2.6 Regression through the Origin and Regression on a Constant,Introduction to Eviews,Assignments:Problems 6-10,Computer Exercises C2,C4,C6,Dependent variable,explained va
3、riable,response variable,Independent variable,explanatory variable,regressor,Error term,disturbance,unobservables,Intercept,Slope parameter,Explains variable in terms of variable“,Chapter 2 The Simple Regression Model,Chapter,End,2.1 Definition of the Simple Regression Model(1/6),Interpretation of t
4、he simple linear regression modelThe simple linear regression model is rarely applicable in prac-tice but its discussion is useful for pedagogical reasons,Studies how varies with changes in:“,as long as,By how much does the dependent variable change if the independent variable is increased by one un
5、it?,Interpretation only correct if all otherthings remain equal when the indepen-dent variable is increased by one unit,Chapter 2 The Simple Regression Model,Chapter,End,2.1 Definition of the Simple Regression Model(2/6),Example:Soybean yield and fertilizerExample:A simple wage equation,Measures the
6、 effect of fertilizer on yield,holding all other factors fixed,Rainfall,land quality,presence of parasites,Measures the change in hourly wagegiven another year of education,holding all other factors fixed,Labor force experience,tenure with current employer,work ethic,intelligence,Chapter 2 The Simpl
7、e Regression Model,Chapter,End,2.1 Definition of the Simple Regression Model(3/6),When is there a causal interpretation?Conditional mean independence assumptionExample:wage equation,e.g.intelligence,The explanatory variable must notcontain information about the meanof the unobserved factors,The cond
8、itional mean independence assumption is unlikely to hold becauseindividuals with more education will also be more intelligent on average.,Chapter 2 The Simple Regression Model,Chapter,End,2.1 Definition of the Simple Regression Model(4/6),Population regression function(PFR)The conditional mean indep
9、endence assumption implies thatThis means that the average value of the dependent variable can be expressed as a linear function of the explanatory variable,Chapter 2 The Simple Regression Model,Chapter,End,2.1 Definition of the Simple Regression Model(5/6),Chapter 2 The Simple Regression Model,Chap
10、ter,End,2.1 Definition of the Simple Regression Model(6/6),In order to estimate the regression model one needs dataA random sample of observations,First observation,Second observation,Third observation,n-th observation,Value of the expla-natory variable of the i-th observation,Value of the dependent
11、variable of the i-th ob-servation,Chapter 2 The Simple Regression Model,Chapter,End,2.2 Deriving the Ordinary Least Squares Estimates(1/10),Fit as good as possible a regression line through the data points:,Fitted regression line,For example,the i-th data point,Chapter 2 The Simple Regression Model,
12、Chapter,End,2.2 Deriving the Ordinary Least Squares Estimates(2/10),What does as good as possible“mean?Regression residualsMinimize sum of squared regression residualsOrdinary Least Squares(OLS)estimates,Chapter 2 The Simple Regression Model,Chapter,End,2.2 Deriving the Ordinary Least Squares Estima
13、tes(3/10),Supplementary materials,Chapter 2 The Simple Regression Model,Chapter,End,2.2 Deriving the Ordinary Least Squares Estimates(4/10),The summation operator:,See A.1 The Summation Operator and Descriptive Statistics at p703-705.,Sample:,Population:,CEO Salary and return on equityFitted regress
14、ionCausal interpretation?,Salary in thousands of dollars,Return on equity of the CEOs firm,Intercept,If the return on equity increases by 1 percent,then salary is predicted to change by 18,501$,Chapter 2 The Simple Regression Model,Chapter,End,2.2 Deriving the Ordinary Least Squares Estimates(5/10),
15、Fitted regression line(depends on sample),Unknown population regression line,Chapter 2 The Simple Regression Model,Chapter,End,2.2 Deriving the Ordinary Least Squares Estimates(6/10),Wage and educationFitted regressionCausal interpretation?,Hourly wage in dollars,Years of education,Intercept,In the
16、sample,one more year of education wasassociated with an increase in hourly wage by 0.54$,Chapter 2 The Simple Regression Model,Chapter,End,2.2 Deriving the Ordinary Least Squares Estimates(7/10),Voting outcomes and campaign expenditures(two parties)Fitted regressionCausal interpretation?,Percentage
17、of vote for candidate A,Percentage of campaign expenditures candidate A,Intercept,If candidate As share of spending increases by onepercentage point,he or she receives 0.464 percen-tage points more of the total vote,Chapter 2 The Simple Regression Model,Chapter,End,2.2 Deriving the Ordinary Least Sq
18、uares Estimates(8/10),Chapter 2 The Simple Regression Model,Chapter,End,2.2 Deriving the Ordinary Least Squares Estimates(9/10),Chapter 2 The Simple Regression Model,Chapter,End,2.2 Deriving the Ordinary Least Squares Estimates(10/10),Fitted values and residualsAlgebraic properties of OLS regression
19、,Fitted or predicted values,Deviations from regression line(=residuals),Chapter 2 The Simple Regression Model,Chapter,End,2.3 Algebraic Properties of OLS on Any Sample of Data(1/6),Deviations from regression line sum up to zero,Correlation between deviations and regressors is zero,Sample averages of
20、 y and x lie on regression line,For example,CEO number 12s salary was526,023$lower than predicted using thethe information on his firms return on equity,Chapter 2 The Simple Regression Model,Chapter,End,2.3 Algebraic Properties of OLS on Any Sample of Data(2/6),Goodness-of-FitMeasures of Variation,H
21、ow well does the explanatory variable explain the dependent variable?“,Total sum of squares,represents total variation in dependent variable,Explained sum of squares,represents variation explained by regression,Residual sum of squares,represents variation notexplained by regression,Chapter 2 The Sim
22、ple Regression Model,Chapter,End,2.3 Algebraic Properties of OLS on Any Sample of Data(3/6),Decomposition of total variationGoodness-of-fit measure(R-squared),Total variation,Explained part,Unexplained part,R-squared measures the fraction of the total variation that is explained by the regression,Ch
23、apter 2 The Simple Regression Model,Chapter,End,2.3 Algebraic Properties of OLS on Any Sample of Data(4/6),Chapter 2 The Simple Regression Model,Chapter,End,2.3 Algebraic Properties of OLS on Any Sample of Data(5/6),CEO Salary and return on equityVoting outcomes and campaign expendituresCaution:A hi
24、gh R-squared does not necessarily mean that the regression has a causal interpretation!,The regression explains 85.6%of the total variation in election outcomes,Chapter 2 The Simple Regression Model,Chapter,End,The regression explains only 1.3%of the total variation in salaries,ceosal1.wf1ls salary
25、c roe,2.3 Algebraic Properties of OLS on Any Sample of Data(6/6),Chapter 2 The Simple Regression Model,Chapter,End,2.4 Units of Measurement and Functional Form(1/6),The Effects of Changing Units of Measurement on OLS Statistics,Incorporating nonlinearities:Semi-logarithmic formRegression of log wage
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