# Football-shaped scatterplot

##### Posted on March 23, 2016

Using R to plot a football-shaped scatter diagram.

## Introduction

In all my *Introduction to Statistics* courses I need to discuss topics such
as association between two quantitative variables, correlation coefficient,
and of course scatter diagrams.

A particular type of scatter diagrams involves what some of my colleagues
at UC Berkeley call a **football-shaped** scatterplot. This is the generic
term we used to indicate that two (quantitative) variables X and Y,
supposedly distributed in fairly normal way, have a linear association.
Moreover, the diagram shows homoscedasticity (same amount of vertical spread).

How can you graph such a scatterplot in R? One approach that you can use is
to generate variables X and Y that follow a bivarate normal distribution. This
can be done with the function `mvrnorm()`

, from the R package `"MASS"`

.

The following code allows you to generate a bivariate normal distribution
based on summary statistics for variables X and Y. You need to specify the
univariate means, standard deviations (and variances), as well as the
desired correlation coefficient. Taking into account the provided inputs,
a vectors of means, and a variance-covariance matrix are obtained with
`mvrnorm()`

. And finally a scatterplot is produced with `plot()`

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