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Finding the prediction interval for a linear regression is a little
more complicated than just finding the St Dev of the various points.
It may be convenient to define the uncertainty of p as the standard
deviation of such fluctuations, but it is not the standard practice.
You should perhaps check a stats book for more info on the topic.
A quick run of the data through Minitab suggests that the +/-1 stdev
prediction interval (68.3% confidence level) for r = 0.62 is p =
30.25 +/- 6.5. This is half again as large as the interval you list.
The size of the prediction interval also changes across the range of
the graph.
A couple minor points.
1) The resistivity of Cu is about 10^-8, not 10^+8.
2) I get 4.004, not 4.04 for stdev, but that could be round off error
in the calculations or the original data.