# Multivariate Quantitative Relationships

• ### Song: Correlation Does Not Imply Causation

A song for use in helping students to recognize and construct examples to illustrate how correlation does not imply causation.  Music & Lyrics © 2016 by Monty Harper.  This song is part of an NSF-funded library of interactive songs that involved students creating responses to prompts that are then included in the lyrics (see www.causeweb.org/smiles for the interactive version of the song, a short reading covering the topic, and an assessment item).

• ### CODAP: Common Online Data Analysis Platform

CODAP provides an easy-to-use web-based data analysis platform, geared toward middle and high school students, and aimed at teachers and curriculum developers. CODAP can be incorporated across the curriculum to help students summarize, visualize and interpret data, advancing their skills to use data as evidence to support a claim.

• ### Joke: Viral Cat Picture

A joke to be used in discussing the issue of regression to the mean.  Note that the word "meme" is pronunced like "meem." The joke was written in 2017 by Larry Lesser (The University of Texas at El Paso) and Dennis Pearl (Penn State University).

• ### Song: The r Song

A song to be used in discussing the notation for correlation with an accompanying video that includes information about interpreting the correlation. The lyrics were written by Mary McLellan from Aledo High School in Aledo, Texas as one of several dozen songs created for her AP statistics course. The accompanying video may be found at
https://www.youtube.com/watch?v=I1DenVRr3Ds The song may be sung to the tune of “Play that Funky Music,” the 1976 hit written by Rob Parissi and performed by the band Wild Cherry.

• ### Song: Standard Deviation of Residuals

A song for use in discussing the interpretation of the root mean squared error – or the standard deviation of the residuals. The lyrics were written by Mary McLellan from Aledo High School in Aledo, Texas as one of several dozen songs created for her AP statistics course. The song may to be sung to the tune of Michael Jackson’s 1982 hit song “Billy Jean.” Also, an accompanying video may be found at https://www.youtube.com/watch?v=RW-Rfn86CSQ

• ### Song: Standard Deviation of the Slope

A song to aid in discussing the idea that the regression line is itself random and understanding the idea of the standard deviation of the estimated slope. The lyrics were written by Mary McLellan from Aledo High School in Aledo, Texas as one of several dozen songs created for her AP statistics course. The song may be sung to the tune of the 2015 hit song “Hello,” by English singer Adele. Also, an accompanying video may be found at

• ### Song: R Doesn’t Change

A song to be used in discussing how the correlation coefficient is invariant to linear transformations (or just reverses sign when values are multiplied by a negative number). The lyrics were written by Mary McLellan from Aledo High School in Aledo, Texas as one of several dozen songs created for her AP statistics course. The song may be sung to the tune of the 1980 song “Hit Me With Your Best Shot,” written by Eddie Schwartz and popularized by Pat Benatar. Also, an accompanying video may be found at https://www.youtube.com/watch?v=t-LtFLuA5VY

• ### Song: Mean Mean on the Line

A song to be used in discussing the idea that the point of averages (x-bar, y-bar) always lies on the regression line. The lyrics were written by Mary McLellan from Aledo High School in Aledo, Texas as one of several dozen songs created for her AP statistics course. The song may be sung to the tune of the 2014 hit “Shake it Off,” by Taylor Swift. Also, an accompanying video may be found at https://www.youtube.com/watch?v=XeVR2024dY0

• ### Song: Interpret the Y-Intercept

A song that may be used in discussing the interpretation of the Y-intercept in a simple linear regression and the idea that the estimated Y-intercept may not make sense in the context of the problem (for example, taking impossible values or when X can never be zero) . The lyrics were written by Mary McLellan from Aledo High School in Aledo, Texas as one of several dozen songs created for her AP statistics course. The song may be sung to the tune of the 2013 song “Wrecking Ball,” by Miley Cyrus. Also, an accompanying video may be found at