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

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

-- 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) "nanobarn"

"Observed cross section per bin"

alpha = 7.2973525693 10^(-3)
c = 299792458.0 meter / second
h = 6.62607015 10^(-34) joule second
hbar = h / float(2 pi)
eV = 1.602176634 10^(-19) joule

s = (14.0 10^9 eV)^2

C1 = alpha^2 / (4 s)
C2 = (hbar c)^2
C3 = 10^37 "nanobarn" / meter^2

C = C1 C2 C3

yhat = C ((x^2 + 3) / (x - 1))^2

"Predicted cross section"

yhat

"Coefficient of determination (R squared)"

ybar = sum(y) / dim(y)

RSS = sum((y - yhat)^2) -- residual sum of squares
TSS = sum((y - ybar)^2) -- total sum of squares

1 - RSS / TSS