-- 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"
s = (14.0 "GeV")^2

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

yhat = zero(N)

for(k,1,N, yhat[k] = C (x[k]^2 + 3)^2 / (x[k] - 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