library('MASS')
library('manipulate')

?mcycle

y <- mcycle$accel
x <- mcycle$times

plot(x, y, 
     xlab="Time (ms)",
     ylab="Acceleration (g)")


## smooth splines
fit_ss <- smooth.spline(x, y, lambda=1)
x_plot <- seq(min(x),max(x),length.out=1000)
y_hat_plot <- predict(fit_ss, x_plot)$y
plot(x, y, 
     xlab="Time (ms)", 
     ylab="Acceleration (g)",
     main="Smoothing Spline Fit")
lines(x_plot, y_hat_plot, col="#882255", lwd=2)
legend('topleft',paste0("lambda = ", fit_ss$lambda), bty='n')


## use manipulate to quickly see how 'lambda' affects fit
manipulate({
    fit_ss <- smooth.spline(x, y, lambda=lambda.slider)
    x_plot <- seq(min(x),max(x),length.out=1000)
    y_hat_plot <- predict(fit_ss, x_plot)$y
    plot(x, y, 
         xlab="Time (ms)", 
         ylab="Acceleration (g)",
         main="Smoothing Spline Fit")
    lines(x_plot, y_hat_plot, col="#882255", lwd=2)
    legend('topleft',paste0("lambda = ", fit_ss$lambda), bty='n')
  },
  lambda.slider = slider(0,0.01,1e-3,label='lambda'))