How to find the intersecting point in the regression line

Question

In the above graph two vertical and horizontal line segments are drawn which will intersect the regression line. How to write code to draw those lines to find the intersecting point?

Answer 1

To find the intersecting point use the following code:

data <- data.frame(load = rep(c(0,4.4,10.7,17,21.4), each = 4), 
                 Gradient = c(0,5,10,15), 
                 VO2max= c(28.0,41.0,56.3,71.3,28.2,41.1,57.0,
                           75.0,31.0,45.4,63.6,82.1, 32.0,48.8,
                           66.8,85.5,34.6,50.5,69.9,89.3))

data$Gradient <- as.factor(data$Gradient)

You can use ggplot2 to plot the intersecting points.

ibrary(ggplot2)

ggplot(data, aes(load, VO2max, group = Gradient)) + 
  geom_point(aes(shape = Gradient), size = 3) + 
  geom_abline(aes(slope = 0.31, intercept = 27.46)) +
  geom_abline(aes(slope = 0.49, intercept = 40.18)) +
  geom_abline(aes(slope = 0.67, intercept = 55.54)) +
  geom_abline(aes(slope = 0.84, intercept = 71.63)) +
  geom_segment(df = data.frame(x = c(x5, x10, x15),
                                 y = c(50, 60, 75),
                                 Gradient = factor(c(50, 60, 75))),
               aes(x, y, xend = x, yend = 0, colour = Gradient),
               linetype = 2) +
  geom_point(df = data.frame(load = c(x5, x10, x15), 
                               VO2max = c(50, 60, 75),
                               Gradient = 1)) +
  coord_cartesian(ylim = c(0, 105), xlim = c(0, 25),
                  expand = 0) +
  geom_hline(df = data.frame(y = c(50, 60, 75), 
                               Gradient = factor(c(50, 60, 75))),
             aes(yintercept = y, colour = Gradient), linetype = 2) +
  theme_minimal() +
  theme(axis.line = element_line()) +
  guides(colour = "none")