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 37 48 42 52 56 61 62 46 45 47 55 70 24 72 31 102
Brain Activity -0.12 0.389 0.018 0.363 0.012 0.406 0.106 0.52 0.15 0.744 0.246 0.568 0.216 0.721 0.369 0.79

Given that the equation for the regression line is ŷ = 0.00753x - 0.06759, what is the residual for subject 15?

Answer 1

the residual is 0.2032

Explanation:

The regression line has been given as:

Y^ = 0.00753X-0.06759

The paired observation for X is (31, 0.369)

The value of X is the empathy score under subject 15 = 31

The value of the brain activity under subject 15 is 0.369

So we have y^ = 0.00753(31) - 0.06759

= 0.1658

Then the residual = y - y^

= 0.369 - 0.1658

= 0.2032

Therefore the residual is 0.2032

Please check the attachment for the table, it will aid you in understanding the solution