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What does covariance tell you? What it is a function of? What coefficient tells you the strength of the relationship? Wh

What does covariance tell you? What it is a function of? What coefficient tells you the strength of the relationship? What is confidence a function of?. Review. What is the central limit theorem? What is a normal distribution? What inference does the central limit theorem help us with?.

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What does covariance tell you? What it is a function of? What coefficient tells you the strength of the relationship? Wh

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  1. What does covariance tell you?What it is a function of?What coefficient tells you the strength of the relationship?What is confidence a function of? Review

  2. What is the central limit theorem?What is a normal distribution?What inference does the central limit theorem help us with? Review of central limit theorem

  3. yi = a + bxi + eiyhat = a + bx Two formulas • What is yhat? • What is yi? • What is xi? • What is ei? • What is b? • What is a?

  4. Interpreting results What is the difference between b and Beta? What is the standard error How do you compute t? What is the significance level?

  5. Residual review What is a residual? What is the mean of residuals? What assumption do we make about residuals?

  6. What is a z score?How is it computed?What is the beta coefficient?How is it different from the b in terms of interpreting the effect? Z score review

  7. T statistic review • What is the formula for the t statistic? • If the t = 2, how confident are we? • (what are we confident about?)

  8. The intercept? • If the intercept is 3, and the dependent variable ranges from 1-4 and the independent variable is 1-4, what other information do we need to know the value of the DV when the IV is at its lowest value? • The slope is 2. • What is the value of the DV when the IV is at its lowest value?

  9. If you multiply the dependent variable by 100, what numbers change? How do they change? * • What numbers do not change? * *Potential answers: B, Beta, standard error, t, significance

  10. Where does our estimate of the error come from? • The residuals. If the points are far from the slope, then we are less confident. • If the points are close to the slope, then we are more confident.

  11. Can we be wrong about rejecting a null hypothesis?There are two kinds of errors: • (Type 1) a true null hypothesis can be incorrectly rejected • (Type 2) a false null hypothesis can fail to be rejected.

  12. Type 2 error is more serious • We you fail to reject the hypothesis, you do not prove the hypothesis is wrong. (remember, we don’t ever prove anything). • It could be measurement error and all kinds of statistical problems that lead to rejecting a null hypothesis.

  13. Null Hypothesis Rejected • If you reject it, then you have tried to prove your theory wrong and you could not. • Don’t forget that you haven’t proven anything (we never prove anything) • You still have other ways of trying to prove it wrong

  14. What is the question that we ask in statistical analysis? • How much better have we done than the mean in predicting values of y from x?

  15. How do we know we have done better than the mean? • Distance between the slope and the mean is great • What is the confidence of “doing better than the mean” likely determined by? • Ratio of explained to unexplained variance

  16. Wouldn’t it be great to have a coefficient that told us the ratio of explained to unexplained variance? • Total Variance • = • Explained Variance • + • Unexplained variance

  17. R square • R square = Explained Variance Unexplained + Explained Variance Unexplained Variance + Explained Variance = what? (total variance)

  18. For each observation, you calculate the distance from the mean to the slope squared to get explained variance. • Then divide by the total sum of squares, which is total variance

  19. Pearson r and R square • Pearson r squared is the same as R square • (in the bivariate case – one independent variable) (Pearson r)2 = R square R square is standardized and symmetric Symmetric means that it doesn’t matter which is the independent variable and which is the dependent variable

  20. Formula for the slope(in the bivariate case)

  21. Formula for r and beta* * Beta is the same as r in the case of bivariate

  22. Theory: Severity of grievance makes a person more likely to participate • One measure of political participation is a count of the number of activities – • Ranging from 0-31

  23. Guttman Scale measure of political participation: How “hard” the participation is: . tab part_category part_category | Freq. Percent Cum. ----------------------------------------+----------------------------------- Did not participate | 555 50.55 50.55 Contacted official in writing or in per | 124 11.29 61.84 Participated in rally | 274 24.95 86.79 Participated in illegal activity or hun | 145 13.21 100.00 ----------------------------------------+----------------------------------- Total | 1,098 100.00

  24. The effect on the number of family members that were victims on count . regr polpartbes2 relatives_victims Source | SS df MS Number of obs = 1098 -------------+------------------------------ F( 1, 1096) = 23.19 Model | 510.137776 1 510.137776 Prob > F = 0.0000 Residual | 24106.0854 1096 21.9946034 R-squared = 0.0207 -------------+------------------------------ Adj R-squared = 0.0198 Total | 24616.2231 1097 22.4395835 Root MSE = 4.6898 ------------------------------------------------------------------------------ polpartbes2 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- relatives_~s | -.5865734 .121797 -4.82 0.000 -.8255551 -.3475917 _cons | 3.486299 .2412254 14.45 0.000 3.012983 3.959614 ------------------------------------------------------------------------------

  25. The effect on the number of family members that were victims on Guttman scale . regr part_category relatives_victims Source | SS df MS Number of obs = 1098 -------------+------------------------------ F( 1, 1096) = 5.42 Model | 6.93949761 1 6.93949761 Prob > F = 0.0200 Residual | 1401.98673 1096 1.27918497 R-squared = 0.0049 -------------+------------------------------ Adj R-squared = 0.0040 Total | 1408.92623 1097 1.28434479 Root MSE = 1.131 ------------------------------------------------------------------------------ part_categ~y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- relatives_~s | -.0684136 .0293728 -2.33 0.020 -.1260469 -.0107804 _cons | 1.11792 .0581744 19.22 0.000 1.003775 1.232066 ------------------------------------------------------------------------------

  26. The effect on the number of family members that died on count . regr polpartbes2 relatives_died Source | SS df MS Number of obs = 1098 -------------+------------------------------ F( 1, 1096) = 9.00 Model | 200.387171 1 200.387171 Prob > F = 0.0028 Residual | 24415.836 1096 22.2772226 R-squared = 0.0081 -------------+------------------------------ Adj R-squared = 0.0072 Total | 24616.2231 1097 22.4395835 Root MSE = 4.7199 ------------------------------------------------------------------------------ polpartbes2 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- relatives_~d | .4331152 .1444106 3.00 0.003 .1497628 .7164676 _cons | 2.248116 .1735599 12.95 0.000 1.907569 2.588663 ------------------------------------------------------------------------------

  27. The effect on the number of family members that died on Guttman scale . regr part_category relatives_died Source | SS df MS Number of obs = 1098 -------------+------------------------------ F( 1, 1096) = 1.96 Model | 2.51377401 1 2.51377401 Prob > F = 0.1619 Residual | 1406.41246 1096 1.28322304 R-squared = 0.0018 -------------+------------------------------ Adj R-squared = 0.0009 Total | 1408.92623 1097 1.28434479 Root MSE = 1.1328 ------------------------------------------------------------------------------ part_categ~y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- relatives_~d | .04851 .0346593 1.40 0.162 -.019496 .1165161 _cons | .9748847 .0416553 23.40 0.000 .8931516 1.056618 ------------------------------------------------------------------------------

  28. The effect on the severity of psychological damage on respondent on count . regr polpartbes2 sevpsych Source | SS df MS Number of obs = 316 -------------+------------------------------ F( 1, 314) = 9.47 Model | 210.190105 1 210.190105 Prob > F = 0.0023 Residual | 6967.51876 314 22.1895502 R-squared = 0.0293 -------------+------------------------------ Adj R-squared = 0.0262 Total | 7177.70886 315 22.7863773 Root MSE = 4.7106 ------------------------------------------------------------------------------ polpartbes2 | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- sevpsych | .9232447 .2999749 3.08 0.002 .3330298 1.51346 _cons | -.7109326 1.124305 -0.63 0.528 -2.923056 1.50119 ------------------------------------------------------------------------------

  29. The effect on the severity of psychological damage on respondent on Guttman scale . regr part_category sevpsych Source | SS df MS Number of obs = 316 -------------+------------------------------ F( 1, 314) = 4.29 Model | 5.28062712 1 5.28062712 Prob > F = 0.0392 Residual | 386.678234 314 1.23145934 R-squared = 0.0135 -------------+------------------------------ Adj R-squared = 0.0103 Total | 391.958861 315 1.24431384 Root MSE = 1.1097 ------------------------------------------------------------------------------ part_categ~y | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- sevpsych | .1463368 .0706677 2.07 0.039 .0072948 .2853788 _cons | .5650835 .2648621 2.13 0.034 .0439547 1.086212 ------------------------------------------------------------------------------

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