/* "Experiments to Determine the force of Fired Gunpowder"
by Benjamin Count of Rumford. Philosophical Transactions of the
Royal Society of London. Vol. 87 (1797) pp222-292.

Theory: X=charge of gunpowder   Y=elasticity of generated fluid

  Y = X**(1+0.0004X)  ==>  ln(Y) = (1+0.0004X)*ln(X)

*/

options nodate nonumber ps=54 ls=76;

data gunpwder;
input charge elasticity;
elasticity=elasticity/1.841;    /* Converts atmospheres back to =parts  */
lnelas=log(elasticity);
lnchar=log(charge);
charlnchar=charge*lnchar;
theory=lnchar+(0.0004*charlnchar);
cards;
39 77.86
78 182.30
117 228.2
156 382.4
195 561.2
234 685.6
273 811.7
312 1164.8
351 1551.3
390 1884.3
429 2219.0
468 2573.7
507 3283.3
546 4008.0
585 4722.5
624 7090.0
702 10977.0
;
run;

proc reg;
model lnelas = lnchar charlnchar;
output out=gunout p=yhat r=e;
run;

data gunout;
set gunout;
etheory=lnelas-theory;
run;

proc means uss;
var etheory e;
run;

quit;