lecture4 - Economics 10: Introduction to Statistical...

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Economics 10: Introduction to Statistical Methods Class #4 More on Bivariate Statistics Data Transformations
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Correlation vs. Causation From The Elusive Quest for Growth : There are many stories about going astray mistaking correlation for causality. The most common story involves nineteenth- century Russian peasants. Supposedly the peasants noticed that the villages with a lot of smallpox also had more doctors’ visits than villages without smallpox. They drew the natural conclusion and started shooting the doctors.
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Correlation vs. Causation History of malaria: In nineteenth century doctors did not understand what caused malaria. Based on observation they developed an “empirical theory”- they observed that people who lived or traveled close to swamps caught malaria. Hence they turned the association between the incidence of malaria and the presence of swamps into a causal relationship that the incidence of malaria was CAUSED by swamps- and elaborated the theory by arguing that malaria was transmitted by mists, bad airs, and miasmas emitted by swaps and bogs.
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Last Class Bivariate statistics: relationship between variables Graphical Scatter plot, “best fit” (least squares) line, smooth fit (local linear regression) In STATA: scatter yvar xvar lfit yvar xvar lowess yvar xvar Numerical Covariance, correlation, least-squares regression slope In STATA…
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Sample covariance in STATA Correlate, cov command in STATA calculate this correlate educ lnwage, covariance For short: correl educ lnwage, cov (or more generally : correl xvar yvar, cov ) Reports the “variance-covariance matrix”… ( 29 ( 29 = - - - = n i i i xy y y x x n s 1 1 1 X Y X S x 2 Y S xy S y 2 Var(X) Var(Y) Cov(X,Y)
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Sample covariance in STATA s xy s y 2 s x 2 n
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Correlation Could use numbers in the variance-covariance matrix to calculate the correlation by hand… …But STATA can also give it to you directly: correl lnwage educ Reports the “correlation matrix” 3395 . 0 6519 . 0 158 . 5 6225 . 0 2 2 = = = = y x xy y x xy s s s s s s r
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Sample correlation coefficient r
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R 2 in “regress” output R 2
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R-squared… R-squared is the fraction of variation in y “explained by” variation in x R 2 =1: a perfect fit; all points on regression line R 2 =0: no fit 0< R 2 <1: usual case; higher → better fit Related to sample correlation coefficient In bivariate linear regression, it is the square of the sample correlation coefficient: Size of R 2 says nothing about causality!! 2 2 r R =
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Data Transformations
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Sometimes we want to create new variables in our data that are functions of old variables: Conversion – e.g., we want to convert data on height in inches into height in feet Standardization – convert fraction of questions answered correctly on the SAT into a score from 400 to 800 Other, nonlinear transformations – e.g. squared, logs, etc., more examples below. In STATA you create a new variable with the “gen”
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This note was uploaded on 05/05/2010 for the course ECON 010 taught by Professor Giummo during the Spring '08 term at Dartmouth.

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lecture4 - Economics 10: Introduction to Statistical...

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