Developing Data Products - Project Assignment

When starting to learn statistics and data science methods it is often quite helpful to start developing a basic understanding of data and to get a feel for relations in data as well as correlations between variables.

This shiny webapp provides a simple game in which the user can try to guess the slope and the intercept of the linear regression line. The data is created randomly and constructed sucht that x and y are correlated with some noice added to the realtion based on the selected difficulty.

The data is created by using the relation y = b0 + b1 * x + eps, where the vector x is initialzed with random values following a normal distribution. The two values b0 and b1 are randomly created yielding the intercept and the slope respectively. The vector eps is then created using a normal distribution with mean = 0 and the standard deviation depending on the mean of the x vector and the selected difficulty (in this example fctr <- 6):

x   <- rnorm(n = 100, mean = 10, sd = 2)
b01 <- runif(n = 2, min = 0, max = 10)
eps <- rnorm(n = 100, sd = mean(x) * b01[2] / fctr)
y   <- b01[1] + b01[2] * x + eps

Suppose after a first glance at the data the user guesses 5 and 3 for the intercept and the slope respectively. The guess is drawn in the dashed blue line while the fit from the linear regression is indicated by the red line.

ggplot(mapping = aes(x, y.residual)) + 
    geom_line(mapping = aes(group = x), linetype = "dashed", alpha = 0.15) +
    geom_point(mapping = aes(color = gr)) + geom_hline(yintercept = 0)