522 Introduction to Robust Estimation and Hypothesis Testing · · 2 Standardized residuals 1 0 -1 -2 -3 · · 0.0 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 0.5 1.0 1.5 Robust distances 2.0 2.5 3.0 Figure 10.6: The plot created by the function reglev based on the reading data. Points to the right of the vertical line located at 2.24 on the x-axis are declared leverage points. Points outside the two horizontal lines are declared regression outliers. These three points are not agged as regression outliers, so they are deemed to be good leverage points. I 10.16 Logistic Regression and the General Linear Model A common situation is where the outcome variable y is binary. In the context of regression, a general approach is to assume that P(y = 1|X = x) = F(x ), (10.14) where F is some strictly increasing cumulative distribution function and is a vector of unknown parameters. The best-known choice for F is F(t) = exp(t) , 1 + exp(t) which yields what is generally known as the logistic regression model. That is, assume that P(y = 1|X = x) = exp( 0 + 1 x 1 + · · · + p x p ) . 1 + exp( 0 + 1 x 1 + · · · + p x p ) (10.15) www.elsevierdirect.com