1.2.2.0 OBJECTIVE
The main objective of this unit is to provide abroad understanding of the topics
Covariance and Variance which is preparatory to the more widely used simple and multiple regression analyses.
1.2.3.0 MAIN CONTENTS
1.2.3.1 Covariance and Variance
Sample covariance is a measure of association between two variables. The sample covariance, Cov(X, Y), is a statistic that enables you to summarize this association with a single number. In general, given n observations on two variables X and Y, the sample covariance between X and Y is given by
∑
(
̅
)(
̅)
…[2.19]
Where the bar over the variable signifies the sample mean. Therefore, a positive association would be summarized by a positive sample covariance while a negative sample covariance would summarise a negative association.
1.2.3.2 Some Basic Covariance rules
i. Co-variance Rule 1: If Y = V + W, Cov(X, Y) = Cov(X, V) + Cov(X, W)
ii.
Co-variance Rule 2: If Y = bZ, where b is a constant and Z is a variable, Cov(X, Y)
= bCov(X, Z)
iii. Co-Variance Rule 3: If Y = b, where b is a constant, Cov(X, Y) = 0 For example, Tables a) and (b) show years of schoolingS, and hourly earningsY, fora subset of 20 households in theUnitedStates. We are required to calculate the covariance.
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