ECO 306
NOUN
28 and in general statistical analyses, this unit discusses covariance and variance. The unit explains that, variance and covariance are two measures used in statistics. While variance is an intuitive concept that measures the scatter of the data, covariance on the other hand, is not that intuitive at first but gives a mathematical indication of the degree of change of two random variables together.
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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