Question

1. What is the percentage of shared variance between the midterm and final grades in the table below?

   Midterm	Final
   55	100
   60	80
   78	92
   79	95
   80	90
   55	90
   64	40
   89	75
   90	70
   92	82
   94	70
   100	100

   		13%
   		17%
   		25%
   		Less than 1%

Answer 1

the percentage of shared variance between the midterm and final grades is the % age square of the correlation coefficient.

X Values
∑ = 936
Mean = 78
∑(X - M_x)² = SS_x = 2784

Y Values
∑ = 984
Mean = 82
∑(Y - M_y)² = SS_y = 3150

X and Y Combined
N = 12
∑(X - M_x)(Y - M_y) = 38

where

X: X Values
Y: Y Values
M_x: Mean of X Values
M_y: Mean of Y Values
X - M_x & Y - M_y: Deviation scores
(X - M_x)² & (Y - M_y)²: Deviation Squared
(X - M_x)(Y - M_y): Product of Deviation Scores

and

r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = 38 / √((2784)(3150)) = 0.0128

The value of R², the coefficient of determination, is 0.0002.

hence the percentage of shared variance is less than 1 %.