lecture 4 introduction to regression-p-1.pptx

# lecture 4 introduction to regression-p-1.pptx - Business...

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Randomization and causation Meet the bivariate regression model Properties of simple regression Outline for Today Business Econometrics
Review: Selection Bias What we want: Treatment effect What we get: Comparison of means Relationship S = selection bias (or selection effect) What do we learn from comparing means? Business Econometrics

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Selection bias = - Total pre-existing (prior to treatment) differences between treated and untreated groups One case when selection bias is zero: random assignment of No systematic difference in any pre-treatment characteristics btwn and If randomized, comparison of means tells us treatment effect When is selection bias zero? Business Econometrics
What to do without randomization? Business Econometrics Randomization often infeasible… Data already collected Too expensive to run an experiment Not technically possible to randomize Regression Analysis to the rescue! First tool when randomization unavailable Useful both for measuring correlation and, possibly causation

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On to regression – start with data Business Econometrics Price Quantity 1.49 441 1.29 493 1.19 502 1.09 536 0.99 615 0.89 643 0.79 740 0.69 757 0.49 810 Downloads and price for i-Tunes
Is there a relationship? How would you describe it? Plot the data points (scatterplot) Business Econometrics 0.4 0.6 0.8 1 1.2 1.4 1.6 0 100 200 300 400 500 600 700 800 900 Price Quantity

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Regression equation Regression line Business Econometrics
Slope coefficient Each one-unit increase in x is associated with a

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