Author: Dr.Y.Funatsu, Professor of Meisei university, Tokyo Email@Contents of forms@Top page
... 


x and y are variables that take
known values. z is the random
variable. Column of "Sample" 
should be 1 or 0.

Sample size=„3
Mean of x=
Mean of y=
Mean of z=
Total variation of x=
Total variation of y=
Total variation of z=
Variance of x=
Variance of y=
Variance of z=
Total covariation of z and x
  =
Total covariation of x and y
  =
Total covariation of y and z
  =
Covariance of z and x=
Covariance of x and y=
Covariance of y and z=
Simple correlation coefficient
  of z and x =
Simple correlation coefficient
  of x and y =
Simple correlation coefficient
  of y and z =

Value of covariance determinant
 (order of zxy)=
Cofactor of ƒÐ2z=
Cofactor of ƒÐ2x=
Cofactor of ƒÐ2y=
Cofactor of ƒÐzx=
Cofactor of ƒÐxy=
Cofactor of ƒÐyz=
Partial correlation coefficient
  of z and x =
Partial correlation coefficient
  of x and y =
Partial correlation coefficient
  of y and z =


For least squares regression
plane z=a+bx+cy

ƒ¿(unbiased for a)=
ƒÀ(unbiased for b)=
ƒÁ(unbiased for c)=
Sum of residual squares of
  z=
Residual variance of z=
s2(unbiased for ƒÐ2)=
s=
Sample variance of ƒ¿(unbiased
  for V(ƒ¿))=
Sample variance of ƒÀ(unbiased
  for V(ƒÀ))=
Sample variance of ƒÁ(unbiased
  for V(ƒÁ))=
Sample standard deviation of
  ƒ¿=
Sample standard deviation of
  ƒÀ=
Sample standard deviation of
  ƒÁ=
Sample covariance of ƒ¿ and ƒÀ
 (unbiased for Cov(ƒ¿,ƒÀ))
  =
Sample covariance of ƒÀ and ƒÁ
 (unbiased for Cov(ƒÀ,ƒÁ))
  =
Sample covariance of ƒÁ and ƒ¿
 (unbiased for Cov(ƒÁ,ƒ¿))
  =
Sample correlation coefficient
  of ƒ¿ and ƒÀ =
Sample correlation coefficient
  of ƒÀ and ƒÁ =
Sample correlation coefficient
  of ƒÁ and ƒ¿ =
Coefficient of determination of
  z by x and y =
Multiple correlation coefficient
  of z and x,y =

For a time series(input order of
timejDurbin-Watson's statistic
@ DW=
Least squares regression plane z=a+bx+cy

......Variable.....Variable.....Variable
.......x.....................y.....................z..................Sample
. 1
. 2
. 3
. 4
. 5
. 6
. 7
. 8
. 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25 		Least squares regression plane z=a+bx+cy

......Variable.....Variable.....Variable
.......x.....................y.....................z..................Sample
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50