# Multivariate Quantitative Relationships

• ### Poem: Spurious Correlation Sestina

An interesting sestina poem to discuss measurement scales and can also be used while discussing spurious correlations if the teacher provides a guiding question such as “What part of the poem describes the relationship between quantitative variables, rather than just descriptions of quantitative variables? Are those relationships examples of 'Spurious Correlations' (per the title of the poem)? Explain briefly."   If the students need further help, the instructor might suggest that they focus on the second to last stanza.  The was written by Jules Nyquist, the founder of Jules' Poetry Playhouse, a place for poetry and play and published in the Journal of Humanistic Mathematics (2022) v. 12 #2 p.554.

• ### Song: My Data Lies Over the Average

A song about regression to the mean written by Dennis K Pearl from Penn State University in February 2022.  May be sung to the tune of the Scottish folk song "My Bonnie Lies Over the Ocean.  The audio recording was produced by Nicolas Acedo with vocals by Alejandra Nunez Vargas, both students in the Commercial Music Program at The University of Texas at El Paso.

• ### Cartoon: Ice-cream sales and shark sightings

A cartoon to aid in discussing confounding and correlative versus causal relationships, for example by asking students to suggest an alternate reason for the relationship besides the one jokingly illustrated in the cartoon.  The cartoon was created by English cartoonist John Landers in December, 2021 based on an idea by Dennis Pearl (Penn State University) and Larry Lesser (The University of Texas at El Paso).

• ### Dancing Correlation

A video using dance to teach about concepts involved with correlation.  This 2013 video is from the “Dancing Statistics” series developed by Lucy Irving from Middlesex University (UK) funded by a BPS Public Engagement grant and additional funding from IdeasTap.  Full credits are within the video.   The Dancing Statistics project is described at https://www.frontiersin.org/articles/10.3389/fpsyg.2015.00050/full

The video also comes with teaching notes for viewing by instructors who are logged into CAUSEweb.org.

• ### Cartoon: Non-Constant Variance

A 2020 cartoon illustrating the idea of heteroscedasticity (non-constant variance) that might be used to start a discussion on the important of the constant variance of errors in making inferences from regression models.  The cartoon was used in a 2021 Teaching Statistics paper "Statistical edutainment that lines up and fits," by Dennis Pearl from Penn State University and Larry Lesser from The University of Texas at El Paso.

• ### Hand Squeeze Activity

A quick "hands on" activity for an in-class experience of data collection as a simple linear regression example where students  predict the time needed for a human chain of hand squeezes to make a full circuit as a function of number of people in the chain.  The lesson plan  secondary school lesson plan adapted from Cynthia Lanius’ hand squeeze activity by Bo Brawner at Tarleton State University.

• ### Cartoon: Lookout Groups

A cartoon designed to support a discussion of using dummy variables to code for categories of a categorical variable in a regression model (e.g. 5 are needed when there are 6 categories). The cartoon was used in the February 2020 CAUSE cartoon caption contest and the winning caption was written by Dominic Matriccino, a student at the University of Virginia. The cartoon was drawn by British cartoonist John Landers (www.landers.co.uk) based on an idea by Dennis Pearl from Penn State University. A second winner in the February 2020 contest was "The grass really is greener on the homogeneity side," written by Jennifer Ann Morrow, an instructor from University of Tennessee. Jennifer's cartoon caption can be used in discussing the importance of within-group variability in judging differences between groups and the difficulty when the groups being compared have different levels of variability.

• ### Cartoon: Constellations

A cartoon that can be used for discussing the traditional theme of "Correlation does not imply Causation" as well as what observational evidence does provide the most convincing evidence of a causal relationship. The cartoon was used in the June 2019 CAUSE cartoon caption contest. The cartoon was drawn by British cartoonist John Landers (www.landers.co.uk) based on an idea by Dennis Pearl from Penn State University.

• ### Cartoon: The Mars Orbiter

A cartoon to initiate discussions about how the correlation is a unitless number that does not change with changes in the units of the variables involved.  The cartoon was created in February 2020 by British caetoonist John Landers based on an idea by Dennis Pearl (Penn State) and Larry Lesser (Univ of Texas at El Paso). An outline of a lesson plan for the use of the cartoon is given in a 2020 Teaching Statistics article by Dennis Pearl and Larry Lesser.

• ### Poem: This Function Dysfunction

A poem written in 2019 by Larry Lesser from The University of Texas at El Paso to discuss the simplest case of line of fit where the slope and correlation coefficients each have a value of 0.  The poem is part of a collection of 8 poems published with commentary in the January 2020 issue of Journal of Humanistic Mathematics.