Bivariate Explorer

My course project for Developing Data Products, a course in the Coursera Data Science Specialization

Beginning statistics students have a difficult time developing an intuition for the bivariat normal distribution. To help students to improve their understanding of this important distribution, I created a shiny application, the Bivariate Normal Explorer, wherein a user may use sliders to modify the three parameters of such a distribution, the standard deviations of normal random variables x and y and the correlation of those variables. The number of datapoints in the sample is also specified. Note that the means of both variables are set to 0, since non-zero means will simply translate the plot. In the next three slides we'll look at the apps main panel for different parameter settings.

Slider parameter settings: \( \sigma_x = 2 \), \( \sigma_y = 3 \), \( \rho = 0 \), \( N = 1000 \)

The embedded R code is too lengthy to show.

Slider parameter settings: \( \sigma_x = 2 \), \( \sigma_y = 3 \), \( \rho = .5 \), \( N = 1000 \)

Slider parameter settings: \( \sigma_x = 2 \), \( \sigma_y = 3 \), \( \rho = .9 \), \( N = 1000 \)

As the previous series of slides illustrated, by modifying the parameters of this distribution one can develope an intuition of how the distribution's parameters effect the appearance of a sample from the distribution, and particularly how the regression line fits the distribution. It is ordinarily difficult to obtain this sort of intuition, but by experimenting (i.e., playing) with this Bivariate Normal Explorer, a student can quickly obtain an intuition concerning multivariate distribution in general. To explore this distribution yourself, go to http://rafaelespericueta.shinyapps.io/bivariate_normal_explorer and have some fun! :) To see the source code, go to: https://github.com/rafaelespericueta/bivariate_normal_explorer