Hints for problem set 5
1. This is an easier problem than it looks. Work with the following formula:
b=cov(x; y)=var(x)
Now we want to estimate again under two cases:
1. x=x=100
2. y=y=12
Recall the formula: C ov(a1x+b1; a2y+b2) = a1a2C ov(x; y )
and var(ax) = a2var (x)
Now substitute the transformed variables into the equation for band solve
for the new estimate in each case, seperately.
2. For R2;recall that s2(e) = var(e) = 1
n1(e2
i):Using this and the
information given on se, we can solve for the sum of squared residuals (SSE)
and R2= 1 (SSE=SST)
For problems 4,5: The underlying distribution is binomial (the response is
yes or no in repeated trials). Use the formula for the variance of a binomial
= np(1-p) for each sample, and then assume that the underlying variance in
both samples is the same (make a pooled sample variance). Then form the
t-statistic/con…dence interval.
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