Question

To test whether extracurricular activity is a good predictor of college success, a college administrator records whether students participated in extracurricular activities during high school and their subsequent college freshman GPA.

Extracurricular Activity	College Freshman GPA
Yes	3.55
Yes	3.28
Yes	3.93
Yes	3.75
No	2.96
No	3.83
No	3.44
No	2.79
No	3.89
No	2.75

(a) Code the dichotomous variable and then compute a point-biserial correlation coefficient. (Round your answer to three decimal places.)

____________

Answer 1

Solution,

First converting yes to 1 and no to 0 we get,

S.No	X	Y	(x-X bar)2	(y-Y bar)2	(x-X bar)(y-Y bar)
1	1	3.55	0.3600	0.017689	0.0063
2	1	3.28	0.3600	0.018769	0.0067
3	1	3.93	0.3600	0.263169	0.0947
4	1	3.75	0.3600	0.110889	0.0399
5	0	2.96	0.1600	0.208849	0.0751
6	0	3.83	0.1600	0.170569	0.0614
7	0	3.44	0.1600	0.000529	0.0001
8	0	2.79	0.1600	0.393129	0.1415
9	0	3.89	0.1600	0.223729	0.0805
10	0	2.75	0.1600	0.444889	0.1601
Total	4	34.17	2.4000	1.85221	0.6666
Mean	0.400	3.417	SSX	SSY	SXY

a)

Correlation coefficient r = S_xy / ()

= 0.316