Solutions to Tutorial 6 Problems
1.
The matrix plot of the Milk Production Data
88.25
38.75
CurrentMilk
82.25
Prev ious
38.75
6.0
Fat
3.2
7.0
Protein
3.2
231
Day s
91
6.25
Lactation
2.75
0.75
I79
0.25
. 75 8. 25
38
8
.75 2. 25
38
8
3. 2
6. 0
3. 2
7.0
91
1
23
5
5
2. 7 6. 2
5
0. 2
5
0. 7
The Residual Plot of the Milk Production Data
I Chart of Residuals
Residual
Residual
Normal Plot of Residuals
5
4
3
2
1
0
-1
-2
-3
-4
-3
-2
-1
0
1
2
5
4
3
2
1
0
-1
-2
-3
-4
-5
1
1
7
Mean=0.004375
2
5
Residual
Frequency
30
20
10
0
1
1.
2.
200
Residuals vs. Fits
40
0
100
Observation Number
Histogram of Residuals
Residual
LCL=-2.708
1
Normal Score
-5 -4 -3 -2 -1
6
0
3
UCL=2.717
5
5
2
3
4
5
5
4
3
2
1
0
-1
-2
-3
-4
20
30 40
50
60 70
80
90 100
Fit
The linearity assumption is ok.
The measurement error assumption:
a). Normality: seems ok
b). Mean zero: ok
c). Independence: seems ok
d). Homogeneity: slightly violated.
3. The predictor assumption:
a). Nonrandom: violated
b). No measurement errors: unknown
c). Linearly independence: not violated.
4. The observation assumption: violated. There are some outliers.
The matrix plot of the Right-to Walk Laws Data
0.75
RTWL
0.25
310.5
COL
169.5
5191.75
PD
1759.25
31.025
URate
14.675
7211393
Pop
2512000
5794.25
Taxes
4574.75
6489.5
Income
2684.5
0 .2
5
0 .7
5
9. 5 10. 5
16
3
.2 5
.7 5
5 9 191
17
5
5
5
.67 1. 02
14
3
0
3
00
39
12 211
25
7
. 75
. 25
74 7 94
45
5
.5
.5
84 4 89
26
6
The Residual Plot of the Right-to-Work Laws Data
Normal Plot of Residuals
I Chart of Residuals
3
Residual
Residual
2
1
0
-1
-2
-2
-1
0
1
4
3
2
1
0
-1
-2
-3
-4
UCL=3.084
Mean=-1.4E-03
LCL=-3.087
0
2
10
Normal Score
20
30
40
Observation Number
Histogram of Residuals
Residuals vs. Fits
3
10
Residual
Frequency
2
5
1
0
-1
0
-2
-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5
Residual
1.
2.
150
250
350
Fit
The linearity assumption is ok.
The measurement error assumption:
a). Normality: seems violated
b). Mean zero: ok
c). Independence: seems ok
d). Homogeneity: slightly violated.
3. The predictor assumption:
a). Nonrandom: violated
b). No measurement errors: unknown
c). Linearly independence: not violated.
4. The observation assumption: seems violated. There are 3 outliers.
The matrix plot of the Egyptian Skulls Data
-887.5
-2962.5
Year
140.75
MB
126.25
138.75
BH
126.25
105.75
BL
89.25
56
NH
48
.5
.5
62 -88 7
-29
5
5
6. 2 40. 7
12
1
5
5
6. 2 38 .7
12
1
.25
.75
89 1 05
48
56
The Residual Plot of the Egyptian Skulls Data
I Chart of Residuals
3
3
2
2
1
1
Residual
Residual
Normal Plot of Residuals
0
-1
0
-1
-2
-2
-3
-3
-3
-2
-1
0
1
2
1
2
2
22
5
LCL=-1.673
50
Normal Score
100
150
Observation Number
Histogram of Residuals
Residuals vs. Fits
3
2
Residual
Frequency
15
10
5
1
0
-1
-2
0
-3
-3
-2
-1
0
1
2
3
-4000
-3000
Residual
1.
2.
UCL=1.673
Mean=-4.0E-04
2
2
22
22 22
222
2
662 2 222
62 2
5 22
6 2
2 12
1
11
1 1
1
2
0
3
1
1
1
1
2
65
22 662 2
2
2 22
222
6 2 2 222 222
2
62 2
2
6
22
2 2
2
The linearity assumption seems violated.
All other assumptions can not be checked.
-2000
Fit
-1000
0
The matrix plot of the Domestic Immigration Data
The Residual Plot of the Domestic Immigration Data
Normal Plot of Residuals
I Chart of Residuals
4
Residual
Residual
3
2
1
0
-1
-2
-2
-1
0
1
5
4
3
2
1
0
-1
-2
-3
-4
1
UCL=2.888
Mean=-0.01214
LCL=-2.912
0
2
Normal Score
10
20
30
40
50
Observation Number
Histogram of Residuals
Residuals vs. Fits
4
10
Residual
Frequency
3
5
2
1
0
-1
0
-2
-2
-1
0
1
Residual
1.
2.
2
3
4
-50 -40 -30 -20 -10 0
10 20 30 40
Fit
The linearity assumption is ok.
The measurement error assumption:
a). Normality: seems ok
b). Mean zero: ok
c). Independence: seems ok
d). Homogeneity: seems ok.
3. The predictor assumption:
a). Nonrandom: violated
b). No measurement errors: unknown
c). Linearly independence: not violated.
4. The observation assumption: seems violated. There are outliers.
The matrix plot of the New York Rivers Data
1.695
1.005
Nitrogen
41
Agr
15
73.25
Forest
41.75
22.15
Rsdntial
7.65
2.355
ComIndl
0.845
05 .695
1. 0
1
15
41
.75 3.2 5
41
7
5
5
7. 6 22. 1
45 . 355
0.8
2
The Residual Plot of the New York Rivers Data
Normal Plot of Residuals
I Chart of Residuals
3
1
Residual
Residual
2
0
-1
-2
-3
-2
-1
0
1
4
3
2
1
0
-1
-2
-3
-4
UCL=3.048
Mean=-0.2295
5
0
2
Normal Score
LCL=-3.507
10
20
Observation Number
Histogram of Residuals
Residuals vs. Fits
3
10
Residual
Frequency
2
5
1
0
-1
-2
-3
0
-3
-2
-1
0
Residual
1.
2.
1
2
3
1.0
1.5
2.0
Fit
The linearity assumption is ok.
The measurement error assumption:
a). Normality: seems violated
b). Mean zero: ok
c). Independence: seems ok
d). Homogeneity: seems ok.
3. The predictor assumption:
a). Nonrandom: unknown
b). No measurement errors: unknown
c). Linearly independence: not violated.
4. The observation assumption: seems violated. There are some outliers.
Regression Plot
2. a) The SLR fit results in the following:
Minutes = 37.2127 + 9.96950 Units
S = 18.7534
R-Sq = 89.7 %
R-Sq(adj) = 89.2 %
200
Minutes
The regression equation is
Minutes = 37.2127 + 9.96950 Units
S = 18.7534
R-Sq = 89.7 %
100
R-Sq(adj) = 89.2 %
Analysis of Variance
0
0
Source
10
DF
SS
MS
F
P
1
67084.8
67084.8
190.749
0.000
Error
22
7737.2
351.7
Total
23
74822.0
Regression
Units
Assumptions Violated:
1). The Linearity Assumption
is violated
2). All other Assumptions can not be checked since linearity is violated.
20