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

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 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

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

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

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

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

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

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

Generic statistical model CORRELATION AND REGRESSION IN R

Generic linear model CORRELATION AND REGRESSION IN R

Regression model CORRELATION AND REGRESSION IN R

Fitted v al u es CORRELATION AND REGRESSION IN R

Resid u als CORRELATION AND REGRESSION IN R

Fitting proced u re CORRELATION AND REGRESSION IN R

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

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

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

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

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

Galton ' s data CORRELATION AND REGRESSION IN R

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

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