By Richard D Smallwood
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Extra resources for A decision structure for teaching machines.
E. we assume that E(εi) = 0. Using an example that is explained more fully in Chapter 2, our working hypothesis is that changes in poverty vary as growth rates vary. e. our expected value of Yi conditional upon a given Xi À EðYi jXi Þ, using parameter estimates and observations on Y and X as follows: ^ i ^ þ βX Y^i ¼ α (1:3) where Y^i is an estimate of Y given X. The estimate of Y may also be referred to as the predicted value or fitted value of Y. e. relatively large) then it may suggest that countries with higher growth rates have reduced poverty more rapidly than countries with lower growth rates.
So provided your sample is large enough, then lack of BLUEness does not necessarily create insurmountable problems. This is because, for very large samples of data, we can invoke the law of large numbers: when large numbers of variables are averaged, errors will cancel out and estimates are more likely to be unbiased. More specifically, given the Central Limit Theorem (CLT), random variables will approximate the standard normal distribution in large samples. g. two important asymptotic properties are asymptotic unbiasedness and asymptotic efficiency.
The extent to which one variable covaries with another gives a useful clue about correlation because if variables are correlated then the covariance between them will be relatively large in comparison with the variances. The correlation coefficient is calculated from the covariances and variances as follows: P i À YÞ ðXi À XÞðY covðX; YÞ rXY ¼ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ¼ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ (1:11) P P varðXÞ Â varðYÞ 2 ðYi À YÞ 2 ðXi À XÞ where rXY is the correlation coefficient between X and Y.