Unformatted text preview: probability of survival for a female who paid a $400 fare is
d. The probability that a female who paid a $400 fare survived is 142% 2 page 3
e. No, this does not make sense because we cannot have probabilities greater than 1. A
probit model would restrict the predicted probability to somethin g between 0 and 1 for
any values of the right hand side variables.
which implies: ̂
b. There are a couple of ways to do this. The easy one is to use the theorem
c. We know that the formula for the reported variance is
and that ̂
therefore, the denominator is unchanged. What about ? For Data set 1
the residuals are
, and for the Data set 2 they are
, so the value of for ̂
a. is equal to 16 . Thus the reported standard error for ̂ is √ . d. The t-stat is just the ratio of the coefficient and the standard error so the t -stat for
the same as the t stat for .
a. ( ̂ ) ̂
Therefore, ̂ is consistent.
b. This is just the standard OLS estimator, but our “Y” variable is now “X” and our RHS
variable is “Z”:
is also a valid equation to estimate (this is often called the
reduced form equation). Write down the OLS estimator ̂ .
As above, the OLS estimator for is:
̂ ̂ d. Show that the ratio ̂ is equal to ̂ . 3 is page 4 ̂
[ [ [ c. ( ̂ ) ( ) [ ̂] d. ( ̂) [( ̂ [ ̂ ]) ] [( ̂ *Note that all of the terms with so… )] [( )] are 0 after taking the expectation and that
( ( ) )
( 4 )...
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