Math heavy topics are often relevant in all sorts of scientific fields, but the theoretical nature of them often makes them hard to approach. I think what would make it much easier for researchers and students if math education would consider more hands-on or even gamified teaching methods. I would even argue that this could lead to deeper understanding and better intuition for math heavy methodologies. As an example for such a teaching method I build a shiny app where the user can try and fit a polynomial regression onto simulated data. I hope this achieves a hands-on and fun experience learning about least squares and polynomial regression.

x values are uniformly randomized. Then for each polynomial term (up to the 3rd degree) we randomize if it is included and if it is, a coefficient for it. After all terms we add a bit of random normal noise.

x    <- runif(40,min = -10,max = 10)
b0 <- ifelse(runif(1,0,1) > 0.5,0,round(runif(1,-10,10)))
b1 <- ifelse(runif(1,0,1) > 0.5,0,round(runif(1,-10,10)))
b2 <- ifelse(runif(1,0,1) > 0.5,0,round(runif(1,-10,10)))
b3 <- ifelse(runif(1,0,1) > 0.5,0,round(runif(1,-10,10)))
y_noNoise <- b3*x^3 + b2*x^2 + b1*x + b0
sd_noise <- ifelse(max(y_noNoise)>abs(min(y_noNoise)),
                   max(y_noNoise)/5 + .1,
                   abs(min(y_noNoise))/5+.1)
y <- y_noNoise + rnorm(length(y_noNoise), sd = sd_noise)
df <- data.frame(x, y)

Then the user can define their polynomial. The app will output a plot of the simulated data with a regression line of the polynomial and visualized residuals. In addition it will show the sum of squared residuals so the user can try and get the best fit.

for visiting and I hope you enjoy the app :)