(defun source () (format t " These data are from Ezekiel, M. (1941). Methods of Correlation Analysis, 2nd ed, New York: Wiley, p. 378-380. The data are haystack measurements taken in Nebraska in 1927 and 1928. At that time, farmers sold hay unbailed and in the stack, requiring estimation of the volume of a stack. Two measurements that could be made easily with a rope were usually employed: the circumference around the base of the stack and the OVER, the distance from the ground on one side of a stack to the ground on the other side of the stack. Stacks vary in height and shape so using a simple computation like the volume of a hemisphere, while perhaps a useful first approximation, might not be sufficiently accurate. In the data Vol = True volume in cubic feet of a stack as obtained by using many different measurement of a haystack. Circum = Stack circumference in feet Over = Stack over measurement in feet. ~%")) (let* ((names '("Vol" "Circum" "Over")) (data (transpose (split-list '( 285300 690 3700 270200 650 3650 309900 730 3850 130600 625 2650 229400 700 3500 272500 680 3650 330900 710 3925 279000 640 3675 275600 620 3850 523792 800 4300 314982 670 3760 549846 790 4460 339783 660 3800 300756 620 3680 457429 790 4110 622859 730 4800 231864 630 3020 317671 680 3775 235231 700 3250 217444 690 3162 269472 730 3450 333353 700 3725 432892 785 4000 211504 670 3125 248908 665 3375 229665 645 3238 311721 655 3758 408836 740 4033 418088 720 4050 231819 630 3300 194690 580 3100 247989 610 3650 317480 730 3700 215154 640 3300 347568 730 3950 439308 710 4200 281950 690 3500 370349 700 3850 274281 725 3450 300240 660 3550 185419 690 3050 198207 620 3100 247086 650 3350 120315 601 2625 284384 710 3600 263625 660 3600 199839 650 3200 200503 640 3200 256876 660 3500 216118 650 3250 211220 670 3200 300933 650 3800 199224 630 3100 274698 700 3400 223827 640 3500 174747 670 3000 286391 670 3600 359347 720 3900 243548 620 3500 243018 630 3400 259007 670 3500 357768 700 4100 329924 730 4000 198614 640 3250 310904 680 3800 282156 710 3700 293224 670 3800 330463 680 3800 256546 720 3500 450993 740 4133 480401 810 4200 424180 750 4075 451610 692 4325 501162 775 4310 211073 650 3150 277570 760 3460 392790 720 3900 421277 800 4150 356264 785 3850 285396 750 3550 329438 690 3800 168954 630 3050 222884 620 3300 236261 640 3400 308828 680 3850 382079 700 4000 312664 630 3690 362475 710 3845 302397 730 3650 604542 790 4700 310011 640 3700 337807 700 3800 304029 770 3500 225216 650 3250 355261 760 3700 263590 660 3450 320141 710 3550 259021 690 3500 374355 760 3825 385803 730 3950 382944 740 3975 255644 660 3300 311907 690 3600 212238 655 3200 292192 690 3600 293635 725 3450 242766 760 3300 206938 650 3150 189954 720 3000 428928 785 4050 240739 675 3250 309799 660 3550 389367 755 3925 223866 680 3175 231479 640 3310 266707 660 3470 258207 680 3350 342650 750 3700 230734 600 3340 396041 760 3930 ) 3)))) (source) (rcode :data (/ data (list 100 10 100)) :data-names names :menu "Haystacks")) (def b (/ circum (* 2 pi))) (def ta (* .9 b)) (def ha (sqrt (- (^ (- (/ over 2) ta) 2) (^ (- b ta) 2)))) (def fa (* (/ 1 3) pi ha (+ (^ b 2) (* b ta) (* ta ta)))) (send haystacks :add-data ha "height") (send haystacks :add-data fa "VolBCS") (send haystacks :add-data b "base-radius") (send haystacks :add-data (- (log vol 2) (+ (log fa 2) .092)) "rBCS")