Author: Dr.Y.Funatsu, Professor of Meisei university, Tokyo Email@Contents of forms@Top page
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Total frequency=
Total of x(weighted)=
Total of y(weighted)=
Total of z(weighted)=
Mean of x=
Mean of y=
Mean of z=
Total variation of x=
Total variation of y=
Total variation of z=
Unbiased variance of
  x=
Unbiased variance of
  y=
Unbiased variance of
  z=

(Descriptive statistics)
Variance of x=
Variance of y=
Variance of z=
Standard deviation
  of x=
Standard dediation 
  of y=
Standard deviation
  of z=
Coefficient of variation
  of x=
Coefficient of variation
  of y=
Coefficient of variation
  of z=


Value of covariance determinant
  (order of zxy)=
Cofactor of z2=
Cofactor of x2=
Cofactor of y2=
Cofactor of zx=
Cofactor of xy=
Cofactor of yz=
Covariation of z and x=
Covariance of z and x=
Simple correlation coefficient
  of z and x=
Partial correlation coefficient
  of z and x=
Covariation of x and y=
Covariance of x and y=
Simple correlation coefficient
  of x and y=
Partial correlation coefficient
  of x and y=
Covariation of y and z=
Covariance of y and z=
Simple correlation coefficient
  of y and z=
Partial correlation coefficient
  of y and z=

For least squares regression plane
 z=a+bx+cy
  a=
  b=
  c=
  Sum of Residual squares
   of z=
  Residual variance of z=
  Coefficient of determination
   of z by x and y =
  Multiple correlation coefficient
   of z and x,y =
Least squares regression plane z=a+bx+cy

.....Variable.......Variable.........Variable..........Frequency
.......x.....................y......................z.....................f
. 1
. 2
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. 7
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25 		Least squares regression plane z=a+bx+cy

.....Variable.......Variable.........Variable..........Frequency
.......x.....................y......................z.....................f
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