Question

A researcher measures the relationship between Internet use (hours per week) and social interaction (hours per week) in a sample of 10 students. The following table lists the hypothetical results of this study.

Internet Use	Social Interaction
X	Y
6	5
7	5
4	7
8	7
13	5
4	8
4	3
6	4
1	10
11	2

(a) Compute the Pearson correlation coefficient. (Round your answer to three decimal places.)
  
(b) Compute the coefficient of determination. (Round your answer to three decimal places.)

Answer 1

Solution :

X	Y	XY	X^2	Y^2
6	5	30	36	25
7	5	35	49	25
4	7	28	16	49
8	7	56	64	49
13	5	65	169	25
4	8	32	16	64
4	3	12	16	9
6	4	24	36	16
1	10	10	1	100
11	2	22	121	4

n	10
sum(XY)	314.00
sum(X)	64.00
sum(Y)	56.00
sum(X^2)	524.00
sum(Y^2)	366.00
Numerator	-444.00
Denominator	774.25
r	-0.5735
r square	0.3289
Xbar(mean)	6.4000
Ybar(mean)	5.6000
SD(X)	3.0551
SD(Y)	1.2134
b	-0.3881
a	8.0839

(a)

Pearson correlation coefficient = -0.574

(b)

coefficient of determination = 0.329