Stat 764, HW 12
In an experiment with Factor A of 4 levels and Factor B of 2 levels, 3 responses
were obtained from each of 8 treatments which produced SSTO = 23733, the
mean responses to the 4 levels of Factor A: 110, 118, 80, 85 and the mean responses t
Stat 764 HW11
1. Determine if two factors A and B in 19.4 on p864 interact.
ij
34
40
3
j
23
29
-8
i
-3
ij = + i + j for all i, j
3
= 34
36
42
5
Thus Factors A and B do not interact.
2. Determine if two factors A and B in 19.5 on p865 interact.
ij
j
250
Stat 764 HW10
p890 20.8
(1) Test the hypothesis that the rst two levels of temperature have the same
eects and the last two levels of temperature have the same eects.
Let j , j = 1, 2, 3, 4, be the eects of the four levels of temperature.
H0 : 1 = 2 and 3
Stat 764 HW09
p890 20.8 (b)
(i) Present ANOVA table (You may use SAS as your tool, but do not hand
in SAS program or output le)
Source
Model
Hum
Tem
Error
C.Total
DF
5
2
3
6
11
SS
204.3217
2.1217
202.2000
6.5850
210.9067
MS
40.8643
1.0608
67.4000
1.0975
F
Stat 764 HW08
For dada in 19.20 on page 871 and model yijk N ( + i + j , 2 ), i = 1, 2,
j = 1, 2, 3 and k = 1, 2, 3, 4 with 1 + 2 = 0 and 1 + 2 + 3 = 0,
1. Fill out ANOVA table with the columns: Source, DF, SS, MS, F, p-value;
and rows: Model, Factor A, F
Stat 764 HW07
1. Suppose the responses to 4 treatments form 4 samples with sizes, means
and standard deviations below
n1
n2
n3
n4
= 5,
= 6,
= 6,
= 5,
y 1.
y 2.
y 3.
y 4.
= 6.3645, S1. = 3.0012
= 10.3054, S2. = 2.3891
= 5.9085, S3. = 1.9383
= 10.8782, S4.
Stat 764 HW06
1. In an experiment with one factor of 4 levels, the responses from 4 samples
that produced the following statistics. Let i be the mean response to the
ith treatment (ith level of the factor).
i
ni
Xi
2
Si
1
8
7.875
4.125
2
6
7.6667
2.6667
3
Stat 764, HW 05
p771 17.18 (a)
(1) Your SAS program
data a;
infile "C:\Fall10\Work764\Week05\CH16PR12.txt";
input time agent;
proc print;
run;
proc means n mean;
var time;
by agent;
run;
proc anova;
class agent;
model time=agent;
run;
(2) List values of n
Stat 764 HW04
For p723 16.7
(1) Write H0 : i = j for all i, j = 1, 2, 3 as H0 : C = 0
1
Let C = 1
0
1
0
1 and = 2 . Then H0 : C = 0
1
3
(2) Convert H0 : C = 0 to H0 : D = 0 where the columns
of D are orthogonal with respect to the inner product x, y =
i
x
Stat 764 HW03
p723 16.7
(d) Obtain ANOVA table with the entry for p-value
Source
Treatment
Error
C.Total
DF
2
24
26
SS
20.1252
15.3622
35.4874
MS
10.0626
0.6401
F
15.72
p-value
0
(e) (f) and (g) Perform the test using p-value and interpret the conclusion
Stat764 HW01
1. Let M Rnr be the model specication matrix dened in class. Show
(a) = M + Y
(b) (n r)S 2 = Y (I M M + )Y
Proof Let B = (M M )1 M . Then M B = M (M M )1 M is symmetric.
BM = (M M )1 M M = Ir is symmetric. M BM = M Ir = M and
BM B = Ir B = B