## Tuesday, July 10, 2012

### Embarrassing Fact of the Day

Felix Salmon has an article on how economists get tripped up by statistics.  See if you can solve the problem.

Apparently 72% of professional economists at leading universities not only got the question wrong, but got it extremely wrong when the information was presented in a regression output table.

I don't know what to say.  This makes me sad.

Update:  I decided to post my solution in the comments section for anyone interested.

#### 1 comment:

1. For those interested, here is my solution using just the information in the table:

We are told that the model is

y= c+xb+e

What we want to know is the value of x such that
F(y=0|x)=.05

where F(y|x) is the CDF of y conditional on x

We are told that E(e|x)=0 which is a typical assumption in regression analysis. Also, that Var(e|x) is a constant.

Also, if we assume that y|x is normally distributed, which is common, then the solution is straight forward.

Let G() be the cdf of the standard normal distribution.

We want the pieces for G([y-E(y|x)]/sd(y|x)).

E(y|x) is c+xb, which is .32+1.001x
sd(y|x)=sd(e|x) is given above as 29, but we could also get it using the R squared and the variance of y, which is given.

So we solve:
G([0-(.32+1.001x]/29)=.05

We then need to look up our value for the standard normal distribution that gives .05 probability to the left of that value. It's -1.645.

Then we have:
(-.32-1.001x)/29=-1.645

It's easy to solve from here:
x is approximately 47.