Question for entry level position

[Tiverton171]

I am going to interview for an entry level actuary position and on the writing sample questionare, I was asked the following question, but I need a little assistance with an answer. It has been about 10 years since taking college calculus.
• How would you determine the relationship between the amount of ice cream consumed in a year and the incidents of drowning that occur?
Any help would be appreciated.

[Trojan_Horse]

Ah, nice question.

I would say that you could perform a regression study with ice cream as the independent variable and drownings as the dependent variable. You'd probably find a pretty good model. You'd likely see a high correlation between ice cream consumption and drownings. You could then proceed to claim that if we would only eat less ice cream, fewer children would drown each year. You could develop public service announcements with major celebrities and push your cause until Congress bans ice cream completely.

You could do all of this and the statistics would back you completely. But you'd be wrong of course. Statistics are only useful when paired with reasoning. Before going through all of the trouble above, you could reason that the high correlation is simply due to the fact that people eat more ice cream when its hot, and they swim more when its hot. The more people swim, the more drownings there will be. There may be a high correlation, but no causal relationship.

This is a test to see if all of the stat courses you've taken in college have erased your ability to reason.

[Tiverton171]

I appreciate your help. Thanks again and have a great day.

[wat]

Ah, nice question.

I would say that you could perform a regression study with ice cream as the independent variable and drownings as the dependent variable. You'd probably find a pretty good model. You'd likely see a high correlation between ice cream consumption and drownings. You could then proceed to claim that if we would only eat less ice cream, fewer children would drown each year. You could develop public service announcements with major celebrities and push your cause until Congress bans ice cream completely.

You could do all of this and the statistics would back you completely. But you'd be wrong of course. Statistics are only useful when paired with reasoning. Before going through all of the trouble above, you could reason that the high correlation is simply due to the fact that people eat more ice cream when its hot, and they swim more when its hot. The more people swim, the more drownings there will be. There may be a high correlation, but no causal relationship.

This is a test to see if all of the stat courses you've taken in college have erased your ability to reason.

Well said, Trojan_Horse.

And if you like to use clichés or like one sentence summaries, "Correlation does not imply causation."

[Ken]

You might add that you should use ice cream consumption as a proxy for temperature if temperature data is not readily available. I would think that temperature's easier to measure than ice cream consumption.

[cadgret]

I am going to interview for an entry level actuary position and on the writing sample questionare, I was asked the following question, but I need a little assistance with an answer. It has been about 10 years since taking college calculus.
• How would you determine the relationship between the amount of ice cream consumed in a year and the incidents of drowning that occur?
Any help would be appreciated.

HI

did you get interview from nationwide?

[DLarsW]

I'd say, take a panel data approach that looks at annual draownings at the state or local level and the annual consumption of ice-cream. Gather data for multiple years and see if there's significant changes in the price of ice-cream over time(which cd be instrumented for ice-cream consumption) and control for regional and annual effects.

it'd be a lot of work, but one cd avoid the spurious correlations....

dlw