More on Two Variable Relationships
|Main Concepts | Demonstration | Activity | Teaching Tips | Data Collection & Analysis | Practice Questions | Milestone | Fathom Tutorial|
• There is a tradeoff between interpretability and a perfect
fit. When in doubt, it's often best to prefer an interpretable model
over a perfect fit.
• Students will want to know which variable to transform or transform first. The "ladder of transformations" can help with this. (See YMS p. 201 or POD p. 250). Technology can also help. Fathom lets you easily try on different transforms to see which makes the scatterplot most linear.
• Students may ask why they just can't use the pre-programmed options on the TI calculator (for example "log", "exponent"). The pedagogical answer is that we see value in having students see how the relationship changes as different transforms are tried. The statistical reason is that we don't want to encourage students to simply try to find the transformation with the highest r-squared (or r) value. The correlation coefficient is only part of the story, and statisticians prefer a model with a lower r-squared value if the residual plot looks better.
• The "ladder of transformations" (YMS p. 201 or POD p. 250)
might be too much information from some students. This is okay, but
make sure they understand how to use a log, square-root, or inverse
• Be careful inventing exponential examples on the fly because
sometimes the transformation also requires a shift. In other words, y =
a + exp(bx) needs to be shifted by a-units before you can take a log