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Bivariate Relationships

Bivariate Relationships. Plotting a Line. Review: Covariance. When it tends to be the case that x is greater than the mean when y is greater than the mean AND x is lower than the mean when y is lower than the mean, then there is a positive covariation. Plot showing positive covariance.

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Bivariate Relationships

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  1. Bivariate Relationships Plotting a Line

  2. Review: Covariance • When it tends to be the case that x is greater than the mean when y is greater than the mean AND x is lower than the mean when y is lower than the mean, then there is a positive covariation

  3. Plot showing positive covariance Mean urban % Mean female literacy

  4. Expected value • But we may want to know more specific knowledge than that – we may want to know the expected value of y for each increased value of x • I may know the mean of everyone’s height in class • But if I know gender, then I can generate two expected values • If you remember, we are always trying to do better than the mean

  5. Substantive effect • For every 10K dollars given in humanitarian aid, there is an increase in 3K spent on weapons • For every 10K dollars given in humanitarian aid, there is a .5K increase spent on weapons • For every 10K dollars given in humanitarian aid, there is a 8K increase spent on weapons • Unit of analysis?

  6. Regression equation • y = a + bx + e • ŷ = a + bx • ŷ is also known as yhat • y is the dependent variable value • yhat is the predicted value • a is the intercept

  7. X and Y • Y X • 2 1 • 2 • 4 3 • 3 4 • 6 5 • 5 6

  8. X and Y • Y X • 2 1 • 2 • 4 3 • 3 4 • 6 5 • 5 6

  9. ŷ= a + bx ŷ = .6 + .83x

  10. Theory Interest in politics causes a person to vote.

  11. Syntax • regr vars = vote_usually intpol/depe = vote_usually/enter.

  12. Output

  13. ŷ= a + bx • b is slope – rise over run • a is the y intercept; constant • Standard error is the average error from the actual points to the slope • T is the ratio of the slope divided by the standard error • Beta = Pearson r in bivariate analysis

  14. Another example

  15. Life Happiness and Occupational Prestige

  16. 3.5 3 2.5 2 Are you happy? (mean = 1.9) 1.5 1 0.5 0 0 10 20 30 40 50 60 Occupational Prestige: (mean = 37) Life happiness = 3.33 - .038 Occupational Prestige

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