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

Weight Y

x1= 60

x3= 68

f(Y)

Height X

x2= 64 .

Conditional distribution of Y|X = 68

Marginal distribution of Y

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Regression line

Y 1 6 3Y 1 3 5Y 1 0 6

MY = 142

sY = 40

sY|X = 36

Under usual assumptions, the conditional distributions of Y at each level of Height, X, all have the same variance.

Predicting GPA from ACT

GPA Y

x1= 12

x3= 28

f(Y)

ACT X

x2= 20 .

Conditional distribution of Y|X = 28

Marginal distribution of Y

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Regression line

.Y 3 3 6 8 .Y 2 6 .Y 1832

MY = 2.6

sY = .8

sY|X = .64

Heteroscedastic pattern of errors.

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0The scattered points spread out quite unequally