Measures of Association

Measures of Association provides information about the relatedness between variables. Moreover, it helps to estimate the existence of a relationship between variables and their strength. They are as,

Measures of Association parts – 1.Covariance

• This shows how the variable y reacts to a variation of the variable x.
• And, its formula is for a population Cov( X, Y ) = ∑( xi − µx) (yi − µy) / N

2.The correlation coefficient (r)

• It is a number that ranges between −1 and +1. Moreover, the sign of r will be the same as the sign of the covariance. And, when r equals−1, then it is a perfect negative relationship between the variations of the x and y. Thus, the increase in x will lead to a proportional decrease in y.
• Similarly, when r equals +1, then it is a positive relationship or the changes in x and the changes in y are in the same direction and in the same proportion.
• Lastly, if r is zero then, there is no relation between the variations of both. And, any other value of r determines the relationship as per how r is close to −1, 0, or +1.
• The formula for the correlation coefficient for the population is ρ = Cov( X, Y ) /σx σy

3. Coefficient of determination (r2)

• It measures the proportion of changes in the dependent variable y and is explained by the independent variable x.
• Moreover, it is the square of the correlation coefficient r thus, is always positive with values between zero and one.
• And, if it is zero, the variations of y are not explained by the variations of x. But if it is one, the changes in y are explained fully by the changes in x. However, the other values of r are explained according to closeness to zero or one.

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