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Multivariate Quantitative Relationships

  • 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.

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  • 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.

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  • 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.

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  • 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.

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  • A joke to use in discussing the meaning of the slope in a linear trend.  The joke was written in May 2019 by Larry Lesser, The University of Texas at El Paso, and Dennis Pearl, Penn State University.

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  • This paper comes from researchers at the NASA Langley Research Center and College of William & Mary.  

    "The experience of retinex image processing has prompted us to reconsider fundamental aspects of imaging and image processing. Foremost is the idea that a good visual representation requires a non-linear transformation of the recorded (approximately linear) image data. Further, this transformation appears to converge on a specific distribution. Here we investigate the connection between numerical and visual phenomena. Specifically the questions explored are: (1) Is there a well-defined consistent statistical character associated with good visual representations? (2) Does there exist an ideal visual image? And (3) what are its statistical properties?"

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  • This resource was prepared to give the practicing engineer a clear understanding of probability and statistics with special consideration to problems frequently encountered in aerospace engineering. It is conceived to be both a desktop reference and a refresher for aerospace engineers in government and industry. It could also be used as a supplement to standard texts for in-house training courses on the subject. 

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  • The Student Dust Counter is an instrument aboard the NASA New Horizons mission to Pluto, launched in 2006. As it travels to Pluto and beyond, SDC will provide information on the dust that strikes the spacecraft during its 14-year journey across the solar system. These observations will advance our understanding of the origin and evolution of our own solar system, as well as help scientists study planet formation in dust disks around other stars.

    In this lesson, students explore the SDC data interface to establish any trends in the dust distribution in the solar system. Students record the number of dust particles, "hits," recorded by the instrument and the average mass of the particles in a given region.

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  • The Student Dust Counter is an instrument aboard the NASA New Horizons mission to Pluto, launched in 2006. As it travels to Pluto and beyond, SDC will provide information on the dust that strikes the spacecraft during its 14-year journey across the solar system. These observations will advance human understanding of the origin and evolution of our own solar system, as well as help scientists study planet formation in dust disks around other stars. 

    In this lesson, students learn the concepts of averages, standard deviation from the mean, and error analysis. Students explore the concept of standard deviation from the mean before using the Student Dust Counter data to determine the issues associated with taking data, including error and noise. Questions are deliberately open-ended to encourage exploration.

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  • The Neutral Buoyancy Laboratory allows astronauts an atmosphere resembling zero gravity (weightlessness) in order to train for missions involving spacewalks. In this activity, students will evaluate pressures experienced by astronauts and scuba divers who assist them while training in the NBL.  This lesson addresses correlation, regression, residuals, inerpreting graphs, and making predictions.

    NASA's Math and Science @ Work project provides challenging supplemental problems for students in advanced science, technology, engineering and mathematics, or STEM classes including Physics, Calculus, Biology, Chemistry and Statistics, along with problems for advanced courses in U.S. History and Human Geography.

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