Regression Analysis: y versus x1, x2, x3, x4
The regression equation is
y = - 123 + 0.757 x1 + 7.52 x2 + 2.48 x3 - 0.481 x4
Predictor
Constant
x1
x2
x3
x4
Coef
-123.1
0.7573
7.519
2.483
-0.4811
S = 11.7866
SE Coef
157.3
0.2791
4.010
1.809
0.5552
R-Sq = 85.2%
T
-0.78
2.71
1.87
1.37
-0.87
P
0.459
0.030
0.103
0.212
0.415
R-Sq(adj) = 76.8%
Analysis of Variance
Source
Regression
Residual Error
Total
DF
4
7
11
SS
5600.5
972.5
6572.9
MS
1400.1
138.9
F
10.08
P
0.005
Correlations: y, x1, x2, x3, x4
y
0.803
0.002
x1
x2
0.827
0.001
0.660
0.019
x3
0.093
0.774
-0.288
0.365
0.113
0.727
x4
-0.133
0.681
-0.024
0.942
-0.025
0.938
x1
x2
x3
0.079
0.807
Stepwise Regression: y versus x1, x2, x3, x4
Forward selection.
Alpha-to-Enter: 0.25
Response is y on 4 predictors, with N = 12
Step
Constant
1
-100.518
2
3.916
3
-162.135
x2
T-Value
P-Value
15.5
4.65
0.001
9.9
2.66
0.026
7.7
1.95
0.087
0.57
2.29
0.048
0.75
2.73
0.026
x1
T-Value
P-Value
x3
T-Value
P-Value
S
R-Sq
R-Sq(adj)
Mallows Cp
2.3
1.32
0.223
14.4
68.39
65.23
7.0
12.1
80.04
75.61
3.4
11.6
83.62
77.47
3.8
Stepwise Regression: y versus x1, x2, x3, x4
Backward elimination.
Alpha-to-Remove: 0.1
Response is y on 4 predictors, with N = 12
Step
Constant
1
-123.131
2
-162.135
3
3.916
x1
T-Value
P-Value
0.76
2.71
0.030
0.75
2.73
0.026
0.57
2.29
0.048
x2
T-Value
P-Value
7.5
1.87
0.103
7.7
1.95
0.087
9.9
2.66
0.026
x3
T-Value
P-Value
2.5
1.37
0.212
2.3
1.32
0.223
x4
T-Value
P-Value
-0.48
-0.87
0.415
S
R-Sq
R-Sq(adj)
Mallows Cp
11.8
85.20
76.75
5.0
11.6
83.62
77.47
3.8
12.1
80.04
75.61
3.4
Best Subsets Regression: y versus x1, x2, x3, x4
Response is y
Vars
1
1
2
2
3
3
4
R-Sq
68.4
64.4
80.0
75.8
83.6
81.2
85.2
R-Sq(adj)
65.2
60.8
75.6
70.5
77.5
74.2
76.8
Mallows
Cp
7.0
8.8
3.4
5.4
3.8
4.9
5.0
S
14.415
15.295
12.072
13.287
11.602
12.420
11.787
x x x x
1 2 3 4
X
X
X X
X
X
X X X
X X
X
X X X X