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)
     
  8                                                     2
      5                                                     4
      9                                                     8
      8                                                     6

What is the numeric value of the slope (b)?

Answer 1

	X (Stress Score)	Y (Risk of Heart Attack)	X * Y	X2	Y2
	8	2	16	64	4
	5	4	20	25	16
	9	8	72	81	64
	8	6	48	64	36
Total	30	20	156	234	120

Equation of regression line is Ŷ = a + bX

b = ( 4 * 156 - 30 * 20 ) / ( 4 * 234 - ( 30 )²)
b = 0.667
a =( Σ Y - ( b * Σ X) ) / n
a =( 20 - ( 0.6667 * 30 ) ) / 4
a = 0
Equation of regression line becomes Ŷ = 0 + 0.6667 X

Slope = b = 0.667