# James Howard

## One Step Closer to Ending Open Enrollment

D.C. has extended the special enrollment period for the District’s health exchange. If this progresses, we are getting closer and closer to ending open seasons for benefits signups. This can only be a good thing.

## A Theorem on the Consumer Surplus

Theorem. Let $$m$$ be a scaling factor and $$y = \beta_0 + \beta_1 x_1 + \cdots$$ be a generalized linear model such that $$y$$ is the amount of a good or service purchased and $$x$$ is the price per unit of the good or service. If $$y^\prime = \beta_0^\prime + \beta_1^\prime x_1^\prime + \cdots$$ such that $$y^\prime = my$$ and $$x_1^\prime = x_1 / m$$, then,
$$-\frac{\hat{y}^{\prime\,2}}{2\hat{\beta_1^\prime}} = -\frac{\hat{y}^2}{2\hat{\beta_1}} \label{eqn:thm} \text{.}$$

If $$y^\prime = \beta_0^\ast + \beta_1^\ast x_1 + \cdots$$, then $$\beta_1^\ast = m\beta_1$$. 1 Similarly, if $$y = \beta_0^\ast + \beta_1^\ast x_1^\prime + \cdots$$, then $$\beta_1^\ast = m\beta_1$$. Therefore, if $$y^\prime = \beta_0^\prime + \beta_1^\prime x_1^\prime + \cdots$$, then $$\beta_1^\prime = m^2\beta_1$$. Accordingly,
$$-\frac{\hat{y}^{\prime\,2}}{2\hat{\beta_1^\prime}} = -\frac{(m\hat{y})^2}{2m^2\hat{\beta_1}} = -\frac{m^2\hat{y}^2}{2m^2\hat{\beta_1}} = -\frac{\hat{y}^2}{2\hat{\beta_1}} \text{.}$$

1. Jeffrey Wooldridge, Introductory econometrics: A modern approach, Cengage Learning, 2012, p. 40.

## Unsinkable in Space

Wikipedia is a wealth of random trivia. On the second Mercury mission, Gus Grissom’s capsule blew its hatch prematurely and the astronaut nearly drowned, as shown in The Right Stuff. There are a number of theories about what happened, but they are not important here. When Grissom was later selected as command pilot on Gemini 3, he and pilot John Young named the spacecraft Molly Brown, after a popular musical. Wikipedia sums up what happened next:

NASA publicity officials were unhappy with this name. When Grissom and his pilot John Young were ordered to come up with a new one, they offered Titanic. Aghast, NASA executives gave in and allowed the name Molly Brown, but did not use it in any official references. Subsequently and much to the agency’s chagrin, on launch CAPCOM Gordon Cooper gave Gemini 3 its sendoff by telling Grissom and Young, “You’re on your way, Molly Brown!” and ground controllers used this name throughout the flight.

Grissom later died in the Apollo 1 accident.  The Molly Brown mission patch is shown above.

## JMM Slides

Check out my slides from my talk at the 2014 Joint Mathematics Meeting.

## My letter in Significance Magazine…

Our Boo-boo

In an unsigned article on xkcd, the authors pity readers who do not recognize “What’s up, Doc?” Like the authors, Yogi Bear may be “smarter than the av-er-age bear” (which, I suppose is preferable to a mean bear) when stealing “pic-a-nic baskets.” But when expressing extreme delight, “Yabba dabba doo!” was Fred Flintstone’s catchphrase.