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 5 7 5 7 12 4 3 6 3 11

Y 5 7 7 7 6 7 4 4 10 3

(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

(a)

Formula for Pearson correlation coefficient

	X	Y	XY	X2	Y2
	5	5	25	25	25
	7	7	49	49	49
	5	7	35	25	49
	7	7	49	49	49
	12	6	72	144	36
	4	7	28	16	49
	3	4	12	9	16
	6	4	24	36	16
	3	10	30	9	100
	11	3	33	121	9
Total	= 63	=60	=357	=483	=398

Pearson correlation coefficient : r = -0.367

(b)

Coefficient of determination : R² = (Pearson correlation coefficient)² = r² = (-0.367)² = 0.135

Coefficient of determination : R² = 0.135