Eigenmath Demo

-- Compute R-squared for Bhabha scattering data from DESY PETRA

-- Data from www.hepdata.net/record/ins191231 (Table 3, 14.0 GeV)

N = 16 -- number of observations

-- x is cos(theta)

x = (
-0.73,
-0.6495,
-0.5495,
-0.4494,
-0.3493,
-0.2491,
-0.149,
-0.0488,
0.0514,
0.1516,
0.252,
0.3524,
0.4529,
0.5537,
0.6548,
0.7323)

-- y is differential cross section

y = (
0.10115,
0.12235,
0.11258,
0.09968,
0.14749,
0.14017,
0.1819,
0.22964,
0.25312,
0.30998,
0.40898,
0.62695,
0.91803,
1.51743,
2.56714,
4.30279)

y = y "nanobarn"

"Observed cross section per bin"

alpha = 0.0072973525693
hbar = 6.582119569 10^(-25) GeV second
c = 299792458 meter / second
E = 7.0 GeV
s = 4 E^2

yhat = zero(N)

for(k,1,N,
  t = -2 E^2 (1 - x[k]),
  u = -2 E^2 (1 + x[k]),
  f = (s^2 + u^2) / t^2 + 2 u^2 / (s t) + (t^2 + u^2) / s^2,
  yhat[k] = 1/2 alpha^2 f / s (hbar c)^2 10^37 "nanobarn" / meter^2
)

"Predicted cross section"

yhat

"Coefficient of determination (R-squared)"

ybar = 1/N sum(k,1,N,y[k])

SSE = sum(k,1,N,(y[k] - yhat[k])^2)
SST = sum(k,1,N,(y[k] - ybar)^2)

1 - SSE/SST