R loop until condition is met

You could do a while loop that stores the sum of squared errors in a vector for each iteration. The loop stops when the sum of squares stops falling, at which point we should have an accurate a and b, and the number of iterations is given by the length of the sse vector.

df <- data.frame(x=c(1.0,2.1,2.2,3.5,5.3,5.4,6.5,7.4),
                 y=c(4,4,4,5,5,6,8,8))

r <- 0.001
a <- 0.386
b <- 0.799

yp  <- b * df$x + a
sse <- sum(((df$y - yp)^2))

while(TRUE)
{
  a <- a - r * sum(-(df$y - yp))
  b <- b - r * sum(-(df$y - yp) * df$x)
  yp <- b * df$x + a
  sse <- c(sse, sum((df$y - yp)^2))
  if(tail(sse, 1) >= sse[length(sse) - 1]) break
}

To see the results, we can do:

cat('iterations: ', length(sse), '\n Intercept = ', a, '\n Slope = ', b, '\n')
#> iterations:  9152 
#>  Intercept =  2.691678 
#>  Slope =  0.6726519

And we can see that our results are correct (to the first six decimal places) by running an lm:

coef(lm(y~x, df))
#> (Intercept)           x 
#>   2.6916789   0.6726517

^{Created on 2022-03-15 by the reprex package (v2.0.1)}