Question

calculate r and r2 for each data set. Interpret their values. Complete parts a through d.

a.

x   y
-2   -4
-1   -1
0   0
1   3
2   6

b.

x   y
-2   6
-1   3
0   1
1   0
2   -2

c.

x   y
2   3
3   2
3   4
4   2
4   3
4   4
5   3

d.

x   y
-3   0
-2   1
0   2
2   1
3   0

Answer 1

( a ) Correlation ( r )

r = 0.9897

r² = 0.9795

There is strong positive correlation between x and y

that 97.95 % of the variation in the dependent variable ( y ) can be explained by the variation in the independent variable.( x )

( b )

r = -0.9851

r² = 0.9704

There is strong negative correlation between x and y

that 97.04 % of the variation in the dependent variable ( y ) can be explained by the variation in the independent variable.( x )

( c )

r = 0

r² = 0

There is no correlation between x and y

that 0 % of the variation in the dependent variable ( y ) can be explained by the variation in the independent variable.( x )

( d )

r = 0

r² = 0

There is no correlation between x and y

that 0 % of the variation in the dependent variable ( y ) can be explained by the variation in the independent variable.( x )