Ch 8. Quantitative and Qualitative
Predictors
8.1
Polynomial Models
1. Fitting the model Center X:
X and X 2 highly correlated =
computational diculty for (X X)1
xi = Xi X =
multicollinearity.
Yi = 0 + 1xi + 2x2 + i
i
.
0: intercept when Xi = X, averag

Ch 18. ANOVA Diagnostics
Yij = i + ij
ij i.i.d. N (0, 2)
Model Assumption:
Normality
Equal/constant error variance
Independency (within and between Trs)
Need to check for outliers
1. Residual Analysis:
eij = Yij Y i
(a) Plot eij vs Y i
Unequal var (

ANOVA Models: All predictors are Qualitative.
Regression
ANOVA
Purpose
Statistical relations between
Y and 1 or more X
Same
Goal
Describe Y = f (X)
Compare E(Y )s at di. Tx level
Focus
Reg Coecient:
Factor E = Di in factor level means
Data Type
Obsl and

Ch 17. Analysis of Factor Level Means
Recall:
Yij = i + ij
ij i.i.d. N (0, 2 )
Yij ind. N (i, 2)
F test for equal factor level means:
H0 : 1 = 2 = = r
Ha : not all i are equal
Test statistic from 1-way ANOVA table:
M ST R
F =
F1 (r 1, N r)
M SE
Suppo

Ch 19. 2-Way ANOVA:
Equal Sample Size
Example: Diet and exercise.
Y = Cholbefore Cholafter.
No D
D
No Ex
1
3
Ex
2
4
Could do 1-Way ANOVA: H0 : 1 = = 4.
Questions of interests:
1 +2
= 3 +4
Is diet eective?
2
2
1 +3
2+4
exercise ?
= 2
2
Given diet, doe

Ch 20. 2-Factor, 1 Case per Tr
Replication:
Estimate experimental error.
Recall:
Yijk Y = Y ij Y + Yijk Y ij
Total
between Tr
within Tr
= Y i Y + Y j Y
A
B
+ Y ij Y i Y j + Y + Yijk Y ij
AB interaction
eijk
SST = SSA + SSB + SSAB + SSE
SSE =
(Yijk Y