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Basic Econometrics Chapter 2 :

Basic Econometrics Chapter 2 :. THE NATURE OF REGRESSION ANALYSIS. . Historical origin of the term “Regression”. The term REGRESSION was introduced by Francis Galton

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Basic Econometrics Chapter 2 :

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  1. Basic EconometricsChapter 2: THE NATURE OF REGRESSION ANALYSIS

  2. . Historical origin of the term “Regression” • The term REGRESSION was introduced by Francis Galton • Tendency for tall parents to have tall children and for short parents to have short children, but the average height of children born from parents of a given height tended to move (or regress) toward the average height in the population as a whole (F. Galton, “Family Likeness in Stature”) • Galton’s Law was confirmed by Karl Pearson: The average height of sons of a group of tall fathers < their fathers’ height. And the average height of sons of a group of shortfathers > their fathers’ height. Thus “regressing” tall and short sons alike toward the average height of all men. (K. Pearson and A. Lee, “On the law of Inheritance”) • By the words of Galton, this was “Regression to mediocrity”

  3. Statistical vs.Deterministic Relationships • In regression analysis we are concerned with STATISTICAL DEPENDENCEamong variables (not Functional or Deterministic), we essentially deal with RANDOM or STOCHASTIC variables (with the probability distributions

  4. Regression vs. Causation • Regression does not necessarily imply causation. A statistical relationship cannot logically imply causation. “A statistical relationship, however strong and however suggestive, can never establish causal connection: our ideas of causation must come from outside statistics, ultimately from some theory or other” (M.G. Kendal and A. Stuart, “The Advanced Theory of Statistics”)

  5. Regression vs Correlation • Correlation Analysis: the primary objective is to measure the strength or degree of linear association between two variables (both are assumed to be random) • Regression Analysis: we try to estimate or predict the average value of one variable (dependent, and assumed to be stochastic) on the basis of the fixed values of other variables (independent, and non-stochastic)

  6. 1-6. Terminology and Notation Dependent Variable  Explained Variable  Predictand  Regressand  Response  Endogenous Explanatory Variable(s)  Independent Variable(s)  Predictor(s)  Regressor(s)  Stimulus or control variable(s)  Exogenous(es) Prof.VuThieu

  7. The Nature and Sources of Data for Econometric Analysis Types of Data : • Time series data; • Cross-sectional data; • Pooled data 2) The Sources of Data 3) The Accuracy of Data

  8. The method of ordinary least square (OLS) • OLS estimators are expressed solely in terms of observable quantities. They are point estimators • The sample regression line passes through sample means of X and Y

  9. The assumptions underlying the method of least squares • Ass 1: Linear regression model • (in parameters) • Ass 2: X values are fixed in repeated • sampling • Ass 3: Zero mean value of ui: E(uiXi)=0 • Ass 4: Homoscedasticity or equal • variance of ui: Var (uiXi) = 2 • [VS. Heteroscedasticity] • Ass 5: No autocorrelation between the • disturbances:Cov(ui,ujXi,Xj ) = 0 • with i # j [VS. Correlation, + or - ] • Ass 6: Zero covariance between ui and Xi • Cov(ui,Xi) = E(ui, Xi) = 0 • Ass 7: The number of observations n must be greater than the number of parameters to be estimated • Ass 8: Variability in X values. They must not all be the same • Ass 9: The regression model is correctly specified • Ass 10: There is no perfect multicollinearity between Xs

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