Finding points of intersection between error bars and a line

Question

I have a data frame with raw data split into 2 columns corresponding to the x and y-axis. I added error bars through arrows() function (only vertical ones) based on standard deviation, and I also used abline() function to plot a 45° line.

df1 <- data.frame(col1= c(5.37, 2.86, 2.72, 4.62, 5.76, 3.07, 1.35, 6.12),
                  col2= c(4.06, 4.50, 3.90, 5.62, 4.65, 6.18, -0.31, 8.42))

plot(df1$col1, df1$col2,
     xlab="x",
     ylab="y",
     pch=19,
     xlim=c(-2,10),
     ylim=c(-2,10),
     col="blue")

abline(0,1,lty=1,lwd=2,col="black") # 45° line

df1_sd <- apply(df1, 2, sd)

# Adding vertical arrows (error bars)
arrows(x0=df1$col1, y0=(df1$col2-df1_sd[[1]]), 
       x1=df1$col1, y1=(df1$col2+df1_sd[[1]]), 
       code=3, col="blue", angle=90, length=0.1)

I aim to select the points (from the data frame) which are intersecting the 45° line, taking into account the error bar.

As an exemplification, I would like to remove the two points marked in yellow from my output (since they're out of my tolerance).

Can you please guide me on how to achieve this?

Answer 1

subset(df1, col1 >col2 - df1_sd[1] & col1< col2 + df1_sd[2])
  col1  col2
1 5.37  4.06
2 2.86  4.50
3 2.72  3.90
4 4.62  5.62
5 5.76  4.65
7 1.35 -0.31

Note that the 6th and 8th points have been removed