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Science Forum Index » Statistics - Math Forum » Uncertainty in extrapolated values
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| Stuart |
 Posted: Mon Mar 12, 2007 10:36 am |
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Guest
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Hello all,
I have a group of data (over time) through which I have fitted a line
of best fit using simple linear regression (y=mx+c). If I now
extrapolate future values from the best fit line, how do I calculate
the uncertainty in these values?
Thanks in advance,
Stuart |
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| Jack Tomsky |
| Posted: Mon Mar 12, 2007 10:36 am |
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Guest
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Quote: Hello all,
I have a group of data (over time) through which I
have fitted a line
of best fit using simple linear regression (y=mx+c).
If I now
extrapolate future values from the best fit line, how
do I calculate
the uncertainty in these values?
Thanks in advance,
Stuart
Let t be the time for which you want to extrapolate. Then the estimated regression mean at t is mhat*t + chat.
The variance of this estimated mean is
Var(mhat*t + chat) = sigma^2*Sum(xi-t)^2/[N*Sum(xi-xbar)^2], where xi are the xi in your sample.
Jack |
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