# Comparing predictions from different regression equations

I have some regression equations, take from various published studies, that predict an individual's mass from its length. Typically only an equation's parameter values, R-squared, standard error of the estimate, and sample size are reported in a manuscript. I'm then using those equations to predict the masses of individuals from a new set of length observations. I'm mainly interested in total mass per unit area, so I'm summing the masses of all individuals and dividing by the area they occupy. Here's a brief example using R code:

# regression equation 1 information
eq1 <- list(b0= 0.9, b1= 3.2, n= 10, r2= 0.984, see= 1.28)

# regression equation 2 information
eq2 <- list(b0= 1.1, b1= 2.8, n= 16, r2= 0.971, see= 1.65)

# new observations
length <- rgamma(100, 4)
area <- 1000

# equation 1 prediction
mass.eq1 <- eq1$b0 + eq1$b1 * length
massPerArea.eq1 <- sum(mass.eq1) / area

# equation 2 prediction
mass.eq2 <- eq2$b0 + eq2$b1 * length
massPerArea.eq2 <- sum(mass.eq2) / area

# compare the two massPerArea predictions...?


Each regression equation of course results in a different final estimate, but how can I determine the uncertainty in those estimates and to what degree they differ statistically? Since I'm summing up individuals, is propagation of error part of that uncertainty? If a direct computation of that uncertainty is possible, that'd would be great, but if there's a solution that requires numerical simulations, that'd be fine also (and actually, I've tried some simulating, but I thought I'd ask first if a direct approach exists). Thanks!

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You could calculate the prediction error for each observation with each model error = Yfitted - Yobserved. Then you can bootstrap the confidence interval for each models' accuracy and compare them.