UNITED STATES NATIONAL MUSEUM BULLETIN 285 



9. Construct bivariate scatter diagrams of ratios and 

 compute regression lines or lines of best lit. 



The programs described here, for use on the IBM 7094, 



perform all of these operations. In addition, they punch out 

 the final measurements and ratios and print out the statistics 

 listed in Table 1 . 



Table 1. — Symbols and Formulae for Statistics Computed by Data Assembly and Analysis (DASAN) 

 (x or y = any variate; *see section on statistics) 



Statistics 



Univariate Statistics 



Number of non-zero values or pairs of values 



Maximum value 



Minimum value 



Observed range 



Arithmetic mean 

 Standard deviation 

 Standard error of the mean 



Coefficient of variation 



Bivariate Statistics (Routine #1) 

 Correlation coefficient 



Slope of reduced major axis 



Standard error of A 



(/-intercept of reduced major axis 



Coefficient of relative dispersion from reduced major axis 



Arithmetic mean of y 

 Arithmetic mean of ,v 

 Ordinate of point at which reduced major axis crosses 



maximum value of .v on scale of a plot printed by 



VPLOT 

 Ordinate of YMAX 1 in scale-units of a plot printed by 



VPLOT 

 Ordinate of y-intercept in scale-units of a plot printed 



by VPLOT 



Bivariate Statistics (Routine #2) 

 Correlation coefficient 

 Slope of regression of y on x 

 Y-intercept of regression of )' on .v 

 Slope of regression of x on y 



X-intercept of regression of .v on y 

 Standard error of estimate in y direction 

 Standard error or estimate in .v direction 



Coefficient of relative dispersion from regression of v on x 

 Standard error of D(Y.X) 



R 



A(YX) 



B(Y) 



A(XY) 



B(X) 



S(Y.X) 

 S(X.Y) 



D(Y.X) 

 S(DYX) 



V 



R 



BYX 

 AY 

 BXY 



AX 



STESTY 

 STESTX 



DYX 

 ERRDYX 



6 

 D 



y 



X 



T 



b vx 



Ctr 



s vx 



Formula 



OR x =x x - 



2.v 



x = 



N 



VX(x — x 



V-- 



100 s, 



a 



_X(x-x)(y-y\_ 



slz(x-Wz(y-W 



Sy 



N~ 

 b = y — xa 



V x 2 +y 2 





b vx = 



Same as above. 



X(x-x)(y-y) 

 i(x~W 

 Oy=y—b„ x x 



, z(s— 5)(y— v) 



a x = x — b zu y 

 s„i = s„Vl — r 2 

 s I „=s I VT— r 2 

 100 g»x 



