Here's some sample data that is obviously quadratic, and code to calculate cumsum in linear and quadratic cases. I'm not sure what to do next with K-S.

df <- data.frame(x=c(6, 9, 12, 14, 30, 35, 40, 47, 51, 55, 60),

y=c(14, 28, 50, 70, 89, 94, 90, 75, 59, 44, 27))

linear <- lm(df$y ~ df$x)

summary(linear)

df$fit_linear <- fitted(linear)

df$ab_linear <- ifelse(df$fit_linear >= df$y, 1, -1)

df$csum_linear <- cumsum(df$ab_linear)

plot(df$x, df$y, pch=16, cex = 1.3, col = "blue", main = "Linear")

abline(lm(df$y ~ df$x), col="firebrick1")

quad <- lm(df$y ~ df$x + I(df$x^2))

summary(quad)

df$fit_quad <- fitted(quad)

df$ab_quad <- ifelse(df$fit_quad >= df$y, 1, -1)

df$csum_quad <- cumsum(df$ab_quad)

df

bo <- quad$coefficient[1]

b1 <- quad$coefficient[2]

b2 <- quad$coefficient[3]

equation = function(x){bo+b1*x+b2*x^2}

plot(df$x, df$y, pch=16, cex = 1.3, col = "blue", main = "Quadratic" )

curve(equation, from=0, to=3500, n=10000, add=TRUE, col="firebrick1")