Question

For each of the following data sets, choose the most appropriate response from the choices below the table.
	Data Set #1				Data Set #2
	x	y			x	y
	10	18			-22	92
	13	12			-19	85
	18	8			-16	71
	24	2			-13	75
	27	0			-10	68
	32	4			-7	69
	21	7			-5	66
	41	13			0	62
	45	17			2	59
a.	A strong positive linear relation exists			a.	A strong positive linear relation exists
b.	A strong negative linear relation exists			b.	A strong negative linear relation exists
c.	No linear relation exists			c.	No linear relation exists
Determine the linear correlation coefficient for each dataset in problem #10.
		Linear Correlation for Data Set #1:
		Linear Correlation for Data Set #2:

Answer 1

Data Set 1

c. No linear relation exists

X Values
∑ = 231
Mean = 25.667
∑(X - M_x)² = SS_x = 1140

Y Values
∑ = 81
Mean = 9
∑(Y - M_y)² = SS_y = 330

X and Y Combined
N = 9
∑(X - M_x)(Y - M_y) = 22

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

r = 22 / √((1140)(330)) = 0.0359

Data set 2

b. A strong negative linear relation exists

X Values
∑ = -90
Mean = -10
∑(X - M_x)² = SS_x = 548

Y Values
∑ = 647
Mean = 71.889
∑(Y - M_y)² = SS_y = 908.889

X and Y Combined
N = 9
∑(X - M_x)(Y - M_y) = -655

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

r = -655 / √((548)(908.889)) = -0.9281