theta_r = alpha theta_i

chisq =  134.647058824 ,     ndof =  7
pval =  6.71100320296e-26

Fitted parameters and standard deviations:
thetaHat[ 0 ] =  0.666176470588   +-   0.00350070020424

i, j, cov[i,j], rho[i,j]:
0    0    1.225490192e-05    1.0

------------------------------------------

theta_r = alpha theta_i - beta theta_i^2

chisq =  0.0 ,     ndof =  6
pval =  1.0

Fitted parameters and standard deviations:
thetaHat[ 0 ] =  0.825   +-   0.0141278410737
thetaHat[ 1 ] =  0.0025   +-   0.000215447556375

i, j, cov[i,j], rho[i,j]:
0    0    0.000199595893404    1.0
0    1    2.94888597385e-06    0.968814446819
1    0    2.94888597385e-06    0.968814446819
1    1    4.64176495481e-08    1.0

------------------------------------------

theta_r = sin^{-1} ((sin theta_i)/r)

chisq =  14.002173916 ,     ndof =  7
pval =  0.0511427017175

Fitted parameters and standard deviations:
thetaHat[ 0 ] =  1.31161185048   +-   0.0055754665537

i, j, cov[i,j], rho[i,j]:
0    0    3.10858272915e-05    1.0