比如，有下面一套数据
=============================
x1
x2
x3
x4
y
7
26
6
60
78.5
1
29
15
52
74.3
11
56
8
20
104.3
11
31
8
47
87.6
7
52
6
33
95.9
11
55
9
22
109.2
3
71
17
6
102.7
1
31
22
44
72.5
2
54
18
22
93.1
21
47
4
26
115.9
1
40
23
34
83.8
11
66
9
12
113.3
10
68
8
12
109.4
=================================
若采用带常数的非标准化回归（不对原始数据标准化），有

Coefficient
---------------------------
X1
1.551103
X2
0.510168
X3
0.101909
X4
-0.144061
C
62.40537
----------------------------
R-squared
0.982376
Adjusted R-squared
0.973563
S.E. of regression2.446008
Sum squared resid
47.86364
Log likelihood
-26.91834
F-statistic
111.4792
Prob(F-statistic)
0
Mean dependent var
95.42308
S.D. dependent var
15.04372
Akaike info criterion
4.910515
Schwarz criterion
5.127803
Hannan-Quinn criter.
4.865852
Durbin-Watson stat
2.052597
===================================
而对x和y都进行标准化后，再回归得到不带常数的方程，结果为

Coefficient
----------------------------
X11
0.606512
X22
0.527706
X33
0.04339
X44
-0.160287
-----------------------------------
Adjusted R-squared
0.976501
S.E. of regression        0.153294
Sum squared resid
0.211493
Log likelihood
8.324146
Durbin-Watson stat
2.052597
S.D. dependent var
1
Akaike info criterion
-0.665253
Schwarz criterion
-0.491423
Hannan-Quinn criter.
-0.700983
===================================
现在我想知道，这两种情况下，得到的残差“S.E. of regression”之间有什么样的数学关系？
即，可以用什么数学公式来将它们联系起来？


谢谢各位帮我解答一下。