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The Nature of Regression Analysis: Historical Origins and Interpretations

Explore the historical origin of "Regression" by Francis Galton, the modern interpretation, statistical vs. deterministic relationships, regression vs. causation, and correlation analysis. Understand terminology, notation, data types, and sources for econometric analysis. Learn how regression estimates and predicts variable dependence. Ensure success by using accurate and appropriate data sources with clear definitions and collection methods.

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The Nature of Regression Analysis: Historical Origins and Interpretations

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  1. Basic Econometrics Chapter 1: THE NATURE OF REGRESSION ANALYSIS Prof. Himayatullah

  2. 1-1. 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”) Prof. Himayatullah

  3. 1-1. Historical origin of the term “Regression” • 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” Prof. Himayatullah

  4. 1-2. Modern Interpretation of Regression Analysis • The modern way in interpretation of Regression: Regression Analysis is concerned with the study of the dependence of one variable (The Dependent Variable), on one or more other variable(s) (The Explanatory Variable), with a view to estimating and/or predicting the (population) mean or average value of the former in term of the known or fixed (in repeated sampling) values of the latter. • Examples: (pages 16-19) Prof. Himayatullah

  5. Dependent Variable Y; Explanatory Variable Xs 1. Y = Son’s Height; X = Father’s Height 2. Y = Height of boys; X = Age of boys 3. Y = Personal Consumption Expenditure X = Personal Disposable Income 4. Y = Demand; X = Price 5. Y = Rate of Change of Wages X = Unemployment Rate 6. Y = Money/Income; X = Inflation Rate 7. Y = % Change in Demand; X = % Change in the advertising budget 8. Y = Crop yield; Xs = temperature, rainfall, sunshine, fertilizer Prof. Himayatullah

  6. 1-3. 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) Prof. Himayatullah

  7. 1-4. 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”) Prof. Himayatullah

  8. 1-5. 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) Prof. Himayatullah

  9. 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) 1-6. Terminology and Notation Prof. Himayatullah

  10. 1-7. The Nature and Sources of Data for Econometric Analysis 1) Types of Data : • Time series data; • Cross-sectional data; • Pooled data 2) The Sources of Data 3) The Accuracy of Data Prof. Himayatullah

  11. 1-8. Summary and Conclusions 1) The key idea behind regression analysis is the statistic dependence of one variable on one or more other variable(s) 2) The objective of regression analysis is to estimate and/or predict the mean or average value of the dependent variable on basis of known (or fixed) values of explanatory variable(s) Prof. Himayatullah

  12. 1-8. Summary and Conclusions 3) The success of regression depends on the available and appropriate data 4) The researcher should clearly state the sources of the data used in the analysis, their definitions, their methods of collection, any gaps or omissions and any revisions in the data Prof. Himayatullah

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