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Vis u ali z ation of Linear Models C OR R E L ATION AN D R E G R - PowerPoint PPT Presentation

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Vis u ali z ation of Linear Models C OR R E L ATION AN D R E G R E SSION IN R Ben Ba u mer Assistant Professor at Smith College Poss u ms ggplot(data = possum, aes(y = totalL, x = tailL)) + geom_point() CORRELATION AND REGRESSION IN R Thro

  1. Vis u ali z ation of Linear Models C OR R E L ATION AN D R E G R E SSION IN R Ben Ba u mer Assistant Professor at Smith College

  2. Poss u ms ggplot(data = possum, aes(y = totalL, x = tailL)) + geom_point() CORRELATION AND REGRESSION IN R

  3. Thro u gh the origin ggplot(data = possum, aes(y = totalL, x = tailL)) + geom_point() + geom_abline(intercept = 0, slope = 2.5) CORRELATION AND REGRESSION IN R

  4. Thro u gh the origin , better fit ggplot(data = possum, aes(y = totalL, x = tailL)) + geom_point() + geom_abline(intercept = 0, slope = 1.7) CORRELATION AND REGRESSION IN R

  5. Not thro u gh the origin ggplot(data = possum, aes(y = totalL, x = tailL)) + geom_point() + geom_abline(intercept = 40, slope = 1.3) CORRELATION AND REGRESSION IN R

  6. The " best " fit line ggplot(data = possum, aes(y = totalL, x = tailL)) + geom_point() + geom_smooth(method = "lm") CORRELATION AND REGRESSION IN R

  7. Ignore standard errors ggplot(data = possum, aes(y = totalL, x = tailL)) + geom_point() + geom_smooth(method = "lm", se = FALSE) CORRELATION AND REGRESSION IN R

  8. Let ' s practice ! C OR R E L ATION AN D R E G R E SSION IN R

  9. Understanding Linear Models C OR R E L ATION AN D R E G R E SSION IN R Ben Ba u mer Assistant Professor at Smith College

  10. Generic statistical model CORRELATION AND REGRESSION IN R

  11. Generic linear model CORRELATION AND REGRESSION IN R

  12. Regression model CORRELATION AND REGRESSION IN R

  13. Fitted v al u es CORRELATION AND REGRESSION IN R

  14. Resid u als CORRELATION AND REGRESSION IN R

  15. Fitting proced u re CORRELATION AND REGRESSION IN R

  16. Least sq u ares Eas y, deterministic , u niq u e sol u tion Resid u als s u m to z ero Line m u st pass thro u gh ( , ) ¯ y ¯ x Other criteria e x ist — j u st not in this co u rse CORRELATION AND REGRESSION IN R

  17. Ke y concepts Y - hat is e x pected v al u e gi v en corresponding X Beta - hats are estimates of tr u e , u nkno w n betas Resid u als ( e ' s ) are estimates of tr u e , u nkno w n epsilons " Error " ma y be misleading term — be � er : noise CORRELATION AND REGRESSION IN R

  18. Let ' s practice ! C OR R E L ATION AN D R E G R E SSION IN R

  19. Regression v s . regression to the mean C OR R E L ATION AN D R E G R E SSION IN R Ben Ba u mer Assistant Professor at Smith College

  20. Heredit y Galton ' s " regression to the mean " Tho u ght e x periment : consider the heights of the children of NBA pla y ers CORRELATION AND REGRESSION IN R

  21. Galton ' s data CORRELATION AND REGRESSION IN R

  22. Regression modeling " Regression ": techniq u es for modeling a q u antitati v e response T y pes of regression models : Least sq u ares Weighted Generali z ed Nonparametric Ridge Ba y esian . . . CORRELATION AND REGRESSION IN R

  23. Let ' s practice ! C OR R E L ATION AN D R E G R E SSION IN R

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