We saw in Chapter 7 how bootstrapping could be used to get 95% intervals for the gradient of Galton’s regression of daughters’ on mothers’ heights. It is far easier to obtain exact intervals that are based on probability theory and provided in standard software, and Table 9.1 shows they give very similar results. The ‘exact’ intervals based on probability theory require more assumptions than the bootstrap approach, and strictly speaking would only be precisely correct if the underlying population distribution were normal. But the Central Limit Theorem means that with such a large sample size
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