Question

Five observations taken for two variables follow.

xi	4	6	12	4	15
yi	50	50	40	50	20

compute the sample correlation coefficient (to 3 decimals).


What can you conclude, based on your computation of the sample correlation coefficient?
There is a strong positive linear relationship

There is a moderate positive linear relationship

There is neither a positive nor a negative linear relationship

There is a strong negative linear relationship

There is a moderate negative linear relationship

Answer 1

Solution :

X	Y	XY	X^2	Y^2
4	50	200	16	2500
6	50	300	36	2500
12	40	480	144	1600
4	50	200	16	2500
15	20	300	225	400

n	5
sum(XY)	1480.00
sum(X)	41.00
sum(Y)	210.00
sum(X^2)	437.00
sum(Y^2)	9500.00
Numerator	-1210.00
Denominator	1309.05
r	-0.9243
r square	0.8544
Xbar(mean)	8.2000
Ybar(mean)	42.0000
SD(X)	4.4900
SD(Y)	11.6619
b	-2.4008
a	61.6865

The sample correlation coefficient = r = -0.924

There is a strong negative linear relationship .