Your data must be in Matrix form and use Matrix Multiplications. Suppose a data frame of 2 predictors/regressors and the parameters 'a' as a constant and coefficients B [b1 and b2] since we have 2 regressors. Then, you go smoothly as follows;
predic <- data.frame( 'Model_01' = rnorm(50, mean = 4.5, sd = 1.5 ),
'Model_02' = rnorm(50, mean = 3.5, sd = 1.2 ) )
predic2Mat <- as.matrix(predic, byrow = F)
predic2Mat <- cbind(rep(1, nrow(predic2Mat)), predic2Mat) # We add 1 for mutrix multiplications
pars <- c('a' = 2, 'b1' = 3.5, 'b2' = 1.8) # a = constant, b1 & b2 are coefficients from your model
new_pred <- predic2Mat %*% pars # Get the new predictions
Created on 2022-05-24 by the reprex package (v2.0.1)