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: 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 rectangula...