Linear Least-Square Regression Example 1
Dependent Variable, Y: Oxygen Purity (%)
Independent Variable, X: Hydrocarbon Level (%)
Obs Purity H_Carbon
1 90.01 0.99
2 89.05 1.02
3 91.43 1.15
4 93.74 1.29
5 96.73 1.46
6 94.45 1.36
7 87.59 0.87
8 91.77 1.23
9 99.42 1.55
10 93.65 1.40
11 93.54 1.19
12 92.52 1.15
13 90.56 0.98
14 89.54 1.01
15 89.85 1.11
16 90.39 1.20
17 93.25 1.26
18 93.41 1.32
19 94.98 1.43
20 87.33 0.95
Linear Least-Square Regression Example 2
Dependent Variable, Y: Oxygen Purity (%)
Independent Variable, X: Hydrocarbon Level (%)
The REG Procedure
Model: MODEL1
Dependent Variable: Purity
Analysis of Variance
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 1 152.12708 152.12708 128.86 <.0001
Error 18 21.24982 1.18055
Corrected Total 19 173.37689
Root MSE 1.08653 R-Square 0.8774
Dependent Mean 92.16050 Adj R-Sq 0.8706
Coeff Var 1.17895
Parameter Estimates
Parameter Standard
Variable DF Estimate Error t Value Pr > |t|
Intercept 1 74.28331 1.59347 46.62 <.0001
H_Carbon 1 14.94748 1.31676 11.35 <.0001
Linear Least-Square Regression Example 3
Dependent Variable, Y: Oxygen Purity (%)
Independent Variable, X: Hydrocarbon Level (%)
The REG Procedure
Model: MODEL1
Dependent Variable: Purity
Output Statistics
Dep Var Predicted Std Error Std Error Student
Obs Purity Value Mean Predict Residual Residual Residual
1 90.0100 89.0813 0.3641 0.9287 1.024 0.907
2 89.0500 89.5297 0.3358 -0.4797 1.033 -0.464
3 91.4300 91.4729 0.2504 -0.0429 1.057 -0.0406
4 93.7400 93.5656 0.2727 0.1744 1.052 0.166
5 96.7300 96.1066 0.4241 0.6234 1.000 0.623
6 94.4500 94.6119 0.3251 -0.1619 1.037 -0.156
7 87.5900 87.2876 0.4932 0.3024 0.968 0.312
8 91.7700 92.6687 0.2470 -0.8987 1.058 -0.849
9 99.4200 97.4519 0.5256 1.9681 0.951 2.070
10 93.6500 95.2098 0.3622 -1.5598 1.024 -1.523
11 93.5400 92.0708 0.2431 1.4692 1.059 1.387
12 92.5200 91.4729 0.2504 1.0471 1.057 0.990
13 90.5600 88.9318 0.3741 1.6282 1.020 1.596
14 89.5400 89.3803 0.3450 0.1597 1.030 0.155
15 89.8500 90.8750 0.2681 -1.0250 1.053 -0.973
16 90.3900 92.2203 0.2430 -1.8303 1.059 -1.728
17 93.2500 93.1171 0.2572 0.1329 1.056 0.126
18 93.4100 94.0140 0.2927 -0.6040 1.046 -0.577
19 94.9800 95.6582 0.3924 -0.6782 1.013 -0.669
20 87.3300 88.4834 0.4049 -1.1534 1.008 -1.144
Output Statistics
Cook's
Obs -2-1 0 1 2 D
1 | |* | 0.052
2 | | | 0.011
3 | | | 0.000
4 | | | 0.001
5 | |* | 0.035
6 | | | 0.001
7 | | | 0.013
8 | *| | 0.020
9 | |**** | 0.654
10 | ***| | 0.145
11 | |** | 0.051
12 | |* | 0.028
13 | |*** | 0.171
14 | | | 0.001
15 | *| | 0.031
16 | ***| | 0.079
17 | | | 0.000
18 | *| | 0.013
19 | *| | 0.034
20 | **| | 0.106
Linear Least-Square Regression Example 4
Dependent Variable, Y: Oxygen Purity (%)
Independent Variable, X: Hydrocarbon Level (%)
The REG Procedure
Model: MODEL1
Dependent Variable: Purity
Sum of Residuals 0
Sum of Squared Residuals 21.24982
Predicted Residual SS (PRESS) 27.51735
Linear Least-Square Regression Example 5
Dependent Variable, Y: Oxygen Purity (%)
Independent Variable, X: Hydrocarbon Level (%)
Plot of RESID*YHAT. Legend: A = 1 obs, B = 2 obs, etc.
|
|
2.0 + A
|
|
|
| A
1.5 + A
|
|
|
|
1.0 + A
| A
|
|
| A
0.5 +
R |
e | A
s | A A
i | A
d 0.0 + A
u |
a | A
l |
|
-0.5 + A
| A
| A
|
| A
-1.0 + A
|
| A
|
|
-1.5 +
| A
|
| A
|
-2.0 +
|
---+----------+----------+----------+----------+----------+----------+--
86 88 90 92 94 96 98
Predicted Value of Purity
Linear Least-Square Regression Example 6
Dependent Variable, Y: Oxygen Purity (%)
Independent Variable, X: Hydrocarbon Level (%)
Plot of STDR*YHAT. Legend: A = 1 obs, B = 2 obs, etc.
|
2.5 +
|
|
|
| A
2.0 +
|
|
|
| A
1.5 +
| A
|
S |
t |
u 1.0 + A
d | A
e |
n |
t | A
i 0.5 +
z |
e | A
d | A A
| A
R 0.0 + A
e |
s | A
i |
d |
u -0.5 + A
a | A
l | A
| A
|
-1.0 + A
| A
|
|
|
-1.5 + A
|
| A
|
|
-2.0 +
|
---+----------+----------+----------+----------+----------+----------+--
86 88 90 92 94 96 98
Predicted Value of Purity
Linear Least-Square Regression Example 7
Dependent Variable, Y: Oxygen Purity (%)
Independent Variable, X: Hydrocarbon Level (%)
Plot of NSCORE*RESID. Legend: A = 1 obs, B = 2 obs, etc.
|
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2.0 +
| A
|
|
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1.5 +
| A
|
R |
a | A
n 1.0 +
k | A
|
f | A
o | A
r 0.5 +
| A
V | A
a | A
r | A
i 0.0 +
a | A
b | A
l | A
e | A
-0.5 +
R | A
E | A
S |
I | A
D -1.0 +
| A
|
|
| A
-1.5 +
|
|
|
| A
-2.0 +
|
---+-------------+-------------+-------------+-------------+--
-2 -1 0 1 2
Residual
Linear Least-Square Regression Example 8
Dependent Variable, Y: Oxygen Purity (%)
Independent Variable, X: Hydrocarbon Level (%)
Plot of NTSCORE*STDR. Legend: A = 1 obs, B = 2 obs, etc.
|
|
2.0 +
| A
|
|
|
1.5 +
| A
|
|
R | A
a 1.0 +
n | A
k |
| A
f | A
o 0.5 +
r | A
| A
V | A
a | A
r 0.0 +
i | A
a | A
b | A
l | A
e -0.5 +
| A
S | A
T |
D | A
R -1.0 +
| A
|
|
| A
-1.5 +
|
|
|
| A
-2.0 +
|
-+-------------+-------------+-------------+-------------+-------------+-
-2 -1 0 1 2 3
Studentized Residual