A tweet straight up solved a problem I encountered while teaching. The problem: How can I explain why the confidence interval area for a regression line is curved when the regression line is straight.
This comes up when I use my favorite regression example. It explains regression AND the power that government funding has over academic research. TL:DR- Relative to the number of Americans who die by gun violence, there is a disproportionately low amount of a) federal funding and b) research publications as to better understand gun violence death when compared to funding and publishing about other common causes of death in America. Why? Dickey Amendment to a 1996 federal spending bill.
See graph below:
The gray area here is the confidence interval region for the regression line. And I had a hard time explaining to my students why the regression line, which is straight, doesn't have a perfectly rectangular confidence interval region.
Claus Wilke created this illustration via GIF to explain why the confidence interval for a regression line looks the way it does by inserting potential regression lines that could fit, given random sampling. He shared it via Tweet but it is also available in GitHub.
Sometimes, it is just easier to show a thing than come up with words for a thing, I believe, like when explaining what it is when we mean the best fitting line for a data set, confidence interval size and the likelihood of containing mu, the relationship between z-scores and the normal curve, and why you should always graph out your correlation data.
This comes up when I use my favorite regression example. It explains regression AND the power that government funding has over academic research. TL:DR- Relative to the number of Americans who die by gun violence, there is a disproportionately low amount of a) federal funding and b) research publications as to better understand gun violence death when compared to funding and publishing about other common causes of death in America. Why? Dickey Amendment to a 1996 federal spending bill.
See graph below:
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| https://jamanetwork.com/journals/jama/article-abstract/2595514 |
The gray area here is the confidence interval region for the regression line. And I had a hard time explaining to my students why the regression line, which is straight, doesn't have a perfectly rectangular confidence interval region.
Claus Wilke created this illustration via GIF to explain why the confidence interval for a regression line looks the way it does by inserting potential regression lines that could fit, given random sampling. He shared it via Tweet but it is also available in GitHub.
