Question

A nurse is interested in whether there is a relationship between daily levels of stress and likelihood of a heart attack. The stress scores (predictor variable) and risk of heart attack values (criterion variable) from a small sample of participants are depicted below (Values below are valid for this question only!)

Stress Score                                Risk of Heart Attack
(Higher values = more stress)     (Higher values = greater risk)
     
  1                                                     4
      8                                                     8
      7                                                     1
      4                                                     5

What is the covariance?

Answer 1

x	y			(x-x̅)(y-ȳ)
1	4			2.00
8	8			10.50
7	1			-7.00
4	5			-0.50

	ΣX	ΣY			Σ(x-x̅)(y-ȳ)
total sum	20	18			5.00

sample size ,   n =   4      
here, x̅ = Σx / n=   5.00   ,     ȳ = Σy/n =   4.50
              

covariance = Σ(x-x̅)(y-ȳ) / (n-1) = 5/3  =1.67