"Alpha decay 3" years = 365.25 24 60 60 days = 24 60 60 mins = 60 -- observed half-life in seconds tau = ( 9.1 mins, -- U228 20.23 days, -- U230 68.9 years, -- U232 2.455 10^5 years, -- U234 2.342 10^7 years, -- U236 4.463 10^9 years, -- U238 30.70 mins, -- Th226 1.9125 years, -- Th228 7.54 10^4 years, -- Th230 1.40 10^10 years) -- Th232 Y = log(tau) Y -- atomic number of daughter nucleus Z = (90,90,90,90,90,90,88,88,88,88) Z = float(Z) -- parent mass M1 = ( 228.031369, -- U228 230.0339401, -- U230 232.0371548, -- U232 234.0409503, -- U234 236.0455661, -- U236 238.0507876, -- U238 226.0249037, -- Th226 228.0287397, -- Th228 230.0331323, -- Th230 232.0380536) -- Th232 -- daughter mass M2 = ( 224.021466, -- Th224 226.0249037, -- Th226 228.0287397, -- Th228 230.0331323, -- Th230 232.0380536, -- Th232 234.0435998, -- Th234 222.0153734, -- 222Ra 224.0202104, -- 224Ra 226.0254082, -- 226Ra 228.0310686) -- 228Ra -- helium mass M3 = 4.00260325413 E = M1 - M2 - M3 E = 931.49410372 E -- convert to MeV E -- design matrix X = zero(3,10) X[1] = Z / sqrt(E) X[2] = Z^(2/3) X[3] = X[3] + 1 -- ordinary least squares beta = dot(inv(dot(X,transpose(X))),X,Y) beta Yhat = dot(beta,X) 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 Run