f(Y) sY = 40 Marginal distribution of Y MY = 142 Weight Y sY|X = 36 . Conditional distribution of Y|X = 68 . . . . . . . . . . . . . . . . . . . . . . . x1= 60 . . . . . . . . . . . . . . . . x2= 64 . . . . . x3= 68 Regression line Under usual assumptions, the conditional distributions of Y at each level of Height, X, all have the same variance. Weight & Height for Female UL Students Height X

f(Y) sY = .8 Marginal distribution of Y MY = 2.6 GPA Y sY|X = .64 . Conditional distribution of Y|X = 28 . . . . . . . . . . . . . . . . . . . . . . . x1= 12 . . . . . . . . . . . . . . . . x2= 20 . . . . . x3= 28 Regression line Under usual assumptions, the conditional distributions of Y at each level of Height, X, all have the same variance. Predicting GPA from ACT ACT X

The scattered points spread out quite unequally Heteroscedastic pattern of errors . xt yt The scattered points spread out quite unequally