What is the volume of this rectangular prism?
2 answers:
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Answer:
See proof below.
Step-by-step explanation:
If we assume the following linear model:
And if we have n sets of paired observations the model can be written like this:
And using the least squares procedure gives to us the following least squares estimates for
and
for
:
Where:
Then is a random variable and the estimated value is
. We can express this estimator like this:
Where and if we see careful we notice that
and
So then when we find the expected value we got:
And as we can see is an unbiased estimator for
In order to find the variance for the estimator we have this:
And we can assume that since the observations are assumed independent, then we have this:
And if we simplify we got:
And with this we complete the proof required.