(i) Let {x i : i 5 l, 2, ..., n} be a set of n data...

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(i) Let {x_i: i 5 l, 2, ..., n} be a set of n data points, and let x̅ be the average. Suppose that the units i are divided into two groups of sizes n_l and n₂, with n_l + n₂ = n. Without loss of generality, order the observations as

O that the data points for the first group appear first. Let

be the averages for the two groups. Show that

so that x̅ can be expressed as a weighted average of the averages from the two subgroups.

(ii) Do the weights w₁ and w₂ in part (i) make intuitive sense? Explain.

(iii) How does the finding in part (i) extend the case of g groups, where the group sizes are

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Introductory Econometrics A Modern Approach

ISBN: 9781337558860

7th Edition

Authors: Jeffrey Wooldridge

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Question Posted: Jul 08, 2020 02:32 AM

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(i) Let {x i : i 5 l, 2, ..., n} be a set of n data...

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nl'nl+l' "nl+2'

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i Let x1 be the average of the first group of n1 units and x2 be the average of the second gr...View the full answer

Introductory Econometrics A Modern Approach

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