Question

Empathy means being able to understand what others feel. To see how the brain expresses empathy, researchers recruited 16 couples in their midtwenties who were married or had been dating for at least two years. They zapped the man's hand with an electrode while the woman watched, and measured the activity in several parts of the woman's brain that would respond to her own pain. Brain activity was recorded as a fraction of the activity observed when the woman herself was zapped with the electrode. The women also completed a psychological test that measures empathy.

Subject	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
Empathy Score	42	49	37	51	62	58	58	47	48	50	65	63	27	72	34	119
Brain Activity	-0.109	0.394	0.01	0.374	0.032	0.418	0.099	0.506	0.156	0.744	0.248	0.563	0.22	0.721	0.359	0.781

Given that the equation for the regression line is y^=0.00692x−0.03658, what is the residual for subject 15?
ANSWER:   

120 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 15 subject - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Answer 1

We have given regression equation ,

y^=0.00692x−0.03658

For subject paired data value is (x= 34 , y = 0.359)

Substitute x=34 in regression equation

=> y^=0.00692(34)−0.03658

=0.1987

Residual  

= y - y = 0.359 -0.1987

=0.1603

Residual = 0.1603