How to remove outliers from nonlinear regression curve? with 3-sigma limits? - r

Question

I tried to remove outliers from nonlinear regression curve, and get the updated formula and error criteria. Someone suggested me to use 3-sigma limits, a statistical calculation where the data are within three standard deviations from a mean. But I don't know how to realize it in my case.
Here is the original data.
ISIDOR <- structure(list(Pos_heliaphen = c("W30", "X41", "Y27", "Z24",
"Y27", "W30", "W30", "X41", "Y27", "W30", "X41", "Z40", "Z99"
), traitement = c("WW", "WW", "WW", "WW", "WW", "WW", "WW", "WW",
"WW", "WW", "WW", "WW", "WW"), Variete = c("Isidor", "Isidor",
"Isidor", "Isidor", "Isidor", "Isidor", "Isidor", "Isidor", "Isidor",
"Isidor", "Isidor", "Isidor", "Cali"), FTSW_apres_arros = c(0.462837958498518,
0.400045032939416, 0.352560790392534, 0.377856799586057, 0.170933345859364,
0.315689846065931, 0.116825600914318, 0.0332444780173884, 0.00966070114456602,
0.0871102539376406, 0.0107280083093036, 0.195548432729584, 1),
NLE = c(0.903498791068124, 0.954670066942938, 0.970762905436272,
0.873838605282389, 0.647875257025359, 0.53056603773585, 0.0384548155916796,
0.0470924009989314, 0.00403163281128882, 0.193696514297641,
0.0718450645564359, 0.295346695941639, 1)), class = c("tbl_df",
"tbl", "data.frame"), row.names = c(NA, -13L))
Here is my original code.
pred_df <- data.frame(FTSW_apres_arros = seq(min(ISIDOR$FTSW_apres_arros),
max(ISIDOR$FTSW_apres_arros),
length.out = 100))
pred_df$NLE <- predict(mod, newdata = pred_df)
mod = nls(NLE ~ 2/(1+exp(a*FTSW_apres_arros))-1,start = list(a=1),data = ISIDOR)
ISIDOR$pred = predict(mod,ISIDOR)
a = coef(mod)
RMSE = rmse(ISIDOR$NLE, ISIDOR$pred)
MSE = mse(ISIDOR$NLE, ISIDOR$pred)
Rsquared = summary(lm(ISIDOR$NLE~ ISIDOR$pred))$r.squared
ggplot(ISIDOR, aes(FTSW_apres_arros, NLE)) +
geom_point(aes(color = Variete), pch = 19, cex = 3) +
geom_line(data = pred_df) +
scale_color_manual(values = c("red3","blue3"))+
scale_y_continuous(limits = c(0, 1.0)) +
scale_x_continuous(limits = c(0, 1)) +
labs(title = "Isidor",
y = "Expansion folliaire totale relative",
x = "FTSW",
subtitle = paste0("y = 2/(1 + exp(", round(a, 3), "* x)) -1)","\n",
"R^2 = ", round(Rsquared, 3)," RMSE = ",
round(RMSE, 3), " MSE = ", round(MSE, 3)))+
theme(plot.title = element_text(hjust = 0, size = 14, face = "bold",
colour = "black"),
plot.subtitle = element_text(hjust = 0,size=10, face = "italic",
colour = "black"),
legend.position = "none")
Here is the picture I got. I also want to get the updated formula and error criteria (circled in red).
If 3-sigma limits doesn't work for my case, could anyone recommend me other ways to deal with outliers?